Electron Cyclotron Resonance Ion Sources and ECR Plasmas 9781351453233, 1351453238, 0-7503-0107-4

Table of contents :
Content: Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Acknowledgments
1: SPECIFIC ELEMENTS OF PLASMA PHYSICS APPLIED TO ELECTRON CYCLOTRON RESONANCE ION SOURCES (ECRIS)
1.1 The breakthrough of the ECRIS and its plasma background
1.2 Preliminary aspects of plasma at the electron cyclotron resonance
1.3 Collective plasma phenomena
1.4 Atomic physics background in ECRIS plasma
1.5 Motions of charged particles in ECRIS plasma
1.6 Confinement in magnetic mirror fields
1.7 The difficult modelling of diffusion processes in magnetoplasmas
2: WAVE-PLASMA INTERACTIONS 2.1 Basic aspects of small amplitude EM waves incident on a cold magnetoplasma2.2 Specific aspects of waves in warm plasma
2.3 Electron heating in the ECR plasma
2.4 Wave launchers and coupling structures
3: THE ECRIS PLASMA STATES-BREAKDOWN, STEADY STATE AND AFTERGLOW
3.1 ECRIS breakdown at low pressure in a vacuum cavity
3.2 ECRIS steady state discharges, a tentative physical analysis
3.3 Simple magnetic bottle ECRIS
experimental steady state characteristics
3.4 Min-B ECRIS: steady state electron characteristics
3.5 ECRIS afterglow regimes (or post-discharge) 4.9 Ion extraction from the ECRIS plasma4.10 Emittance of a source (generalities)
4.11 ECRIS beam emittances
5: SIMPLE MIRROR AND BUCKET ECRIS FOR LESS HIGHLY CHARGED IONS
5.1 The history of the first ECR ion sources (1965-1973)
5.2 Modern simple mirror ECRIS
5.3 Overdense ECRIS at 2.45 GHz for ion beam processing
5.4 Industrial ECR plasma and ion sources research at Michigan State University
5.5 ECR plasma cathode (also called microwave plasma cathode)
5.6 ECRIS for specific weakly charged ions
6: MIN-B ECRIS FOR HIGHLY CHARGED IONS 6.1 A brief history of the development of ECRIS for multiply charged ions6.2 The status of understanding of min-B ECRIS
6.3 The magnetic structure in modern min-B ECRIS
6.4 Highly charged metal ions production in min-B ECRIS
6.5 Specific applications of the min-B ECRIS
6.6 Scaling rule attempts and practical results
6.7 Comparative min-B ECRIS
6 .8 Conclusions and prospects of min-B ECRIS
References
Index

Citation preview

Electron Cyclotron Resonance Ion Sources and ECR Plasmas

Electron Cyclotron Resonance Ion Sources and ECR Plasmas

R Geller Institut des Sciences Nucleaires, Grenoble (formerly Senior Physicist at Commissariat a VEnergie Atomique)

Institute of Physics Publishing Bristol and Philadelphia

© IOP Publishing Ltd 1996 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher. Multiple copying is permitted in accordance with the terms of licences issued by the Copyright Licensing Agency under the terms of its agreement with the Committee of Vice-Chancellors and Principals. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. ISBN 0 7503 0107 4 Library o f Congress Cataloging-in-Publication Data Geller, R. (Richard) Electron cyclotron resonance ion sources and ECR plasmas / R. Geller. p. cm. Includes bibliographical references and index. ISBN 0-7503-0107-4 (ppc : alk. paper) 1. Electron cyclotron resonance sources. 2. Plasma (Ionized gases) 3. Heavy ions. I. Title. QC702.7.M84G35 1996 539.7'33- -dc20 96-31451 CIP

Published by Institute of Physics Publishing, wholly owned by The Institute of Physics, London Institute of Physics Publishing, Techno House, Redcliffe Way, Bristol BS1 6 NX, UK US Editorial Office: Institute of Physics Publishing, The Public Ledger Building, Suite 1035, 150 South Independence Mall West, Philadelphia, PA 19106, USA Printed in the UK by J W Arrowsmith Ltd, Bristol

Contents

Preface

vii

Acknowledgments 1

SPECIFIC ELEMENTS OF PLASMA PHYSICS APPLIED TO ELECTRON CYCLOTRON RESONANCE ION SOURCES (ECRIS) 1.1 The breakthrough of the ECRIS and its plasma background 1.2 Preliminary aspects of plasma at the electron cyclotron resonance 1.3 Collective plasma phenomena 1.4 Atomic physics background in ECRIS plasma 1.5 Motions of charged particles in ECRIS plasma 1.6 Confinement in magnetic mirror fields 1.7 The difficult modelling of diffusion processes in magnetoplasmas

2

WAVE-PLASMA INTERACTIONS 2.1

1 1 14 25 60 93 115 131 147

Basic aspects of small amplitude EM waves incident on a cold magnetoplasma Specific aspects of waves in warm plasma Electron heating in the ECR plasma Wave launchers and coupling structures

147 158 168 200

THE ECRIS PLASMA STATES— BREAKDOWN, STEADY STATE AND AFTERGLOW

216

2.2 2.3 2.4 3

xi

3.1 3.2 3.3 3.4 3.5

ECRIS breakdown at low pressure in a vacuum cavity ECRIS steady state discharges, a tentative physical analysis Simple magnetic bottle ECRIS; experimental steady state characteristics Min-2? ECRIS: steady state electron characteristics ECRIS afterglow regimes (or post-discharge)

216 222 236 249 256 v

vi

4

CONTENTS

ION CHARACTERISTICS AND ION PROCESSES IN ECRIS PLASMA 4.1 4.2

Ion heating Improvement of multicharged ion confinement in ES potential traps 4.3 Theoretical ion confinement times with electrostatic potentials at steady state 4.4 Criteria for multiply charged ion production 4.5 The power flux criterion and the importance of the lifetime of energy r en in ion sources 4.6 The necessity of electron confinement, and low power dissipation 4.7 The neutral gas density criterion for MI production in steady state 4.8 Semi-theoretical analysis of highly charged ion production 4.9 Ion extraction from the ECRIS plasma 4.10 Emittance of a source (generalities) 4.11 ECRIS beam emittances

5

SIMPLE MIRROR AND BUCKET ECRIS FOR LESS HIGHLY CHARGED IONS 5.1 5.2 5.3 5.4 5.5 5.6

6

The history of the first ECR ion sources (1965-1973) Modern simple mirror ECRIS Overdense ECRIS at 2.45 GHz for ion beam processing Industrial ECR plasma and ion sources research at Michigan State University ECR plasma cathode (also called microwave plasma cathode) ECRIS for specific weakly charged ions

MIN-JB ECRIS FOR HIGHLY CHARGED IONS 6.1 6.2 6.3 6.4 6.5 6 .6

6.7 6 .8

A brief history of the development of ECRIS for multiply charged ions The status of understanding of min-B ECRIS The magnetic structure in modern min-B ECRIS Highly charged metal ions production in min-Z? ECRIS Specific applications of the min-Z? ECRIS Scaling rule attempts and practical results Comparative min-B ECRIS Conclusions and prospects of min-Z? ECRIS

266 266 267 268 271 273 275 276 278 289 303 307

311 311 325 331 346 351 357 362 362 365 376 380 391 394 398 409

References

413

Index

430

Preface

Let me begin with a few words about the strange genesis of this book. I was hired by the CEA (French Atomic Energy Commission) in 1948 and worked with them until 1993. From 1963, in the group I directed, I always had at least one ECR (electron cyclotron resonance) plasma experiment running and since 1965 at least one ECR ion source. However, when I retired, after so many years of interesting but hectic life I almost felt ready to quit completely my work, my good friends, my dear enemies and my capricious but beloved electrons— Then, Herve Nifenecker, the well known nuclear physicist, one of my cronies from long ago, asked me to ponder one of his brand new projects: ‘Try to transform a 20 keV singly charged ion beam, containing short-lived (r < 1 s) radioactive metallic ions, into a highly charged beam in less than one second. This point is one of the bottlenecks of the PIAFE project where we want to utilize neutron-rich (1+) ions formed inside the old Grenoble high neutron flux reactor—then transport these ions 300 metres further, multi-ionize them, and inject them into the old Grenoble cyclotron com plex... Having always preferred inexpensive original accelerator concepts rather than orthodox high cost routines, I promised to join the venture (where, by the way, I found again J L Belmont and a few other colleagues). So, in spring 1993, I moved into my new office at the Institut des Sciences Nucleaires (ISN) located just a few hundred metres away from my former headquarters. However, such a small distance was enough to radically change my life; my hectic activities, administrative tasks, compulsory immediate achievements were finished... I was free to breathe, to think, to dream. I was just politely encouraged to find a solution. Nobody disturbed the reverie of the old ECRIS veteran. Many thanks to all the ISN people for their kind savoir-faire. Thus, for the first time in my life, I could contemplate from the windows of my office the mysterious actions of time. The pink buds became green, the swallows came, filled the torrid sky with their twittering and departed; I saw the yellow leaves drop from the birch trees and whirl in the humid wind of autumn. Then gradually nature became more torpid, frosty and white. Had the time eventually come for me too to hibernate? One day during a snow storm I observed how the flakes arrived gently and silently on the window pane of my office. This image encouraged me vii

viii

PREFACE

to ponder how a metallic ion beam could be slowed down before hitting a solid surface (where the metal particles would stick for a long while). For that the beam has to collide with some invisible targets. But what kind of collisions should I consider? Elastic or inelastic collisions with atoms? Binary Rutherford collisions? Obviously, their cross sections are too small, so I came to the unusual idea promoted 50 years ago by Chandrasekhar of considering the collective collisions with the plasma of an ion source. The ions should be completely slowed down by collective ion-plasma collisions, then be simply trapped inside the very plasma of a min-Z? ECRIS, multi-ionized by the hot electron and extracted... all of which is possible in a fraction of a second. So ended the PIAFE reverie, because this purely theoretical idea, of course, had to be checked in an unquestionable experimental set up, the preparation of which needed time (in effect the verification was ascertained more than a year later). But what should I do in the mean time? That was the question. I then recalled that, from several sides, I had been asked to write about the secrets of ECR ion sources. But I was not at all decided whether to accept such a difficult task. I also recalled the joke muttered in the eighties by accelerator people: ‘EBIS engineers at least understand why their source performs poorly, whereas the poor ECRIS people don’t even understand why the ECRIS performs so well’. At that time I should have taken up the challenge, but I was too busy and harassed. In addition anyhow, some accelerator people began to utilize the source which revolutionized the heavy physics done with cyclotrons. Why should I write a book today? Most of the above-quoted accelerator people are now out of the business... or keep silent where ECR plasmas are invoked. A book is time devouring, and exhausting work. Would it not be better for me to allay the torments of my winter days with the poetry of the psalms or some modern painting (which is my usual solace)? I also asked myself a few pertinent questions as probably every potential author does. For instance: (a) Who needs such a book? (b) What are the fields the book would cover? Then there are more subjective questions: (c) Am I not too ambitious, is it not pure vanity? (d) Will I have the talent, the energy and the time to finish such a book? (e) How will I treat the nonlinear phenomena with linear models? After a while as the worm was already in the apple, more narcissism invaded my thoughts, (f) Is it not a shame that the new generation of ion sourcerers re-investigate subjects that have already been treated? (g) Why do they forget or omit to quote what has already been done? An African proverb says: ‘when a sorcerer dies in the bush... a whole library burns’. Then a mysterious voice whispered in my ear: Write it even if it is only vanity. Write it before the library burns. No matter if the physics is linear or not, write what you can. Anyhow, it will be the first treatise about ECR ion sources. The book will trigger some feedback with a natural desire for criticism.

PREFACE

ix

Maybe a better book will then be written by somebody else. C ’est la vie. But in fact, another disquieting feeling made me decide to begin the book. I noticed that I had forgotten the names of some of my colleagues and even of my adversaries. In other words, I partly decided to write this book because it was a unique occasion to go back to my younger years, to revisit once more in my mind my colleagues, to recall not only their names but also their smiles or grimaces, their voices and their arguments. Without the pros and even more without the cons of my colleagues, I would have done very little in the field of ECR ion sources. They pushed me inside the ECRIS adventure, and they are the catalysts for this treatise. Before describing briefly the contents of the book, let me first specify to whom this book is not addressed. It is not addressed to those who believe that elegant mathematical developments are the basic instrument of progress in ion sourcery and ECR plasma physics. In my opinion, the theoretical models of ECR plasma are often too vague for good derivations and computerizing. We probably need better physical visions rather than equations. Consequently, this book cannot be an academic treatise and it is not basically addressed to students. It is intended to guide researchers and users of ECRIS and ECR plasmas, since the field of development of ECR applications has grown dramatically over the last 15 years. The book should serve as a review, and a reference for the field. The background assumed of the reader is physics graduate level. Readers will find in chapter 1 a gentle heuristic introduction to complex nonlinear plasma physics applied to ECR. They will find a few tentative explanations which have never been invoked in other books on plasmas. They will understand that plasma theory is a long term adventure though it already shows many positive returns. But those who confuse particle dynamics added to atomic physics with plasma physics are wrong, because in ECR plasmas the collective effects are determinant and that is what I try to show in this book. In fact, chapter 1 is a recapitulation of some useful atomic physics and classical plasma concepts with emphasis on ECR phenomena. But it also contains a few allusions to subjects not usually covered in books on plasmas. I have also dared to add a few, personal non-orthodox concepts on collective plasma ‘effervescence’. Finally, if this chapter seems so long (nearly one third of the book) one should find the explanation in my stubborn and firm belief that all further ECRIS progress depends on a better knowledge of ECR plasma physics. Chapter 2 treats linear and nonlinear ECR effects. Famous plasma theoreticians have already tackled this issue with more or less success. Only the Utopian case of very small amplitude EM waves in a cold plasma (Te = 0) has a solid basis. Therefore, I have tried modestly to show the complexity of the

x

PREFACE

issue .with a minimum of equations and a maximum of experimental examples and heuristic proposals. I have quoted as much as possible those pioneers who dared to propose some solutions and those who just like me, remain somewhat perplexed when faced with the realm of nonlinearities. However, I underline forcefully the difference in behaviour between underdense and overdense ECR plasmas (the latter plays, to my mind, a major role in the nonlinearities). In the following chapters I describe ECR plasma states (breakdown, steady state and afterglow) with their different properties. Chapter 3 deals mainly with experimental electron characteristics, which are particularly dependent on the wave interactions and on the magnetic mirror effects, whereas the ion properties seen in chapter 4 depend much more on the neutral gas background and the ion plasma density. I then recall the criteria for multiply charged ion production and the ion extraction from the plasma. I consider the formation and the beam emittances. However, these last chapters are voluntarily condensed since they are treated in all the well known books on ion sources and beam dynamics. Chapter 5 concentrates on ECR plasma sources for low charged ions whose importance is now recognized in many fields. They are more and more utilized in all kinds of ion surface processes and especially in microelectronics. Their great advantage is the absence of filaments and electrodes and their ability to be expanded to large size plasma discharges. However, in order to recall the truth (and satisfy my ego) I could not refrain from writing a chapter on the invention of the ECRIS in 1965 and to comment on the exceptional results of this first generation of sources. Then follows the description of various types of modern ECRIS with an effort of categorization. Note that the so-called microwave sources (where an ECR effect is not clearly established) are not included. Chapter 6 is entirely devoted to the highly charged ion production in min-B ECRIS. The term min-Z? ECRIS (though not very nice) is utilized to designate an ECR source where the particle confinement is obtained in a magnetic structure where the field modulus has a minimum value in the centre. Again I recall their historical development, their plasma characteristics, their scientific criteria and their basic technology. I underline the importance of the fundamental parameters but I also insist on the empirical improvements which play a considerable role in the progress of the modern prototypes. In the last chapter of this treatise I describe briefly contemporary ECRIS prototypes and their performances. Finally, let me express the hope that this book will encourage further thinking and research, and that the young generation of talented ion sourcerers will be interested in what has been thought and done up to now. I would then be happy and rewarded. I would also appreciate any comments that could improve this book. R Geller

Acknowledgments

Very many sources were utilized in compiling the material in this book and many people quoted in the references should be cited here by name. I hope that they will forgive me these omissions. In fact, I have even to admit that many of my English expressions are not mine since I learned a great deal of my English in the scientific literature about plasma physics. However, firstly I wish to express my gratitude to my colleagues of my former CEA plasma team, who contributed so much, and over so many years, to the success of the ECRIS. Many thanks also to all those, from different horizons, who encouraged or criticized ECR plasmas. In addition, I wish to express my appreciation to Drs B Vignon and J Chauvin, Directors of the Institut des Sciences Nucleaires, for their hospitality over the last three years during which this book was written. My gratitude is also due to Mr Favro, who prepared many diagrams, Mme Langellier, who deciphered some of my manuscripts, and Mme Laidet, who typed all the text. On a more personal note, let me express my thanks to Tom Green, the well known Culham ion sourcerer, who filtered not only my numerous flaws in English but also some faults in thinking; and finally to my wife Annie, who accepted patiently my scriptural whim and became in the meantime an expert...in botany! Grenoble, 1 April 1996

xi

1

SPECIFIC ELEMENTS OF PLASMA PHYSICS APPLIED TO ELECTRON CYCLOTRON RESONANCE ION SOURCES (ECRIS)

1.1

1.1.1

THE BREAKTHROUGH OF THE ECRIS AND ITS PLASMA BACKGROUND

Ion sources—generalities

1.1.1.1 Applications, categories and desirable properties o f ion sources. Ion sources have acquired a wide variety of applications. They are used in a variety of different types of accelerator for nuclear research; have application in the field of fusion research; and are used for ion milling and implantation, in isotope separators, as a means of rocket propulsion, in mass spectrometers, etc. The positive-ion sources may be subdivided into sources specifically designed to generate singly charged ions and those designed to produce very highly charged ions. In both cases, desirable qualities of an ion source are large ion yield, little gas flow (i.e. high ionization efficiency), low ion energy spread, high brightness and low emittance. Practical considerations such as reliability, long source life and ease of changing ion species are sometimes even more important. Under these conditions, a first conclusion can already be drawn. Though utilized for a century, the short-lived filaments and hot cathodes should, if possible, be eliminated and long-lived electron emitters should supplant them. The breakthrough of the ECRIS is surely the result of the elimination of the cathodes, but as we will see there are also other reasons. Ion source concepts and development of ion sources have been described in thousands of different studies. Many of them are reviewed in books. Six important modern books deal with sources and beams. One can find in these volumes a large collection of ion sources and references [ l] - [ 6 ]. Our purpose is to present ECR plasma concepts and ion sources which were not thoroughly analysed in the above books. 1

2

SPECIFIC ELEMENTS OF PLASMA PHYSICS

1.1.1.2 Methods o f ion formation in the plasma reservoir o f ion sources. Ions are extracted from plasmas which are the usual ion reservoirs. The principal method of positive-ion formation inside the ion reservoir is electron impact. Surface ionization, spark discharge, laser ionization, field ionization etc are other possibilities. Electron impact. A common method of ionizing a gas or vapour is to pass high-velocity electrons through it, with the ions being formed as a result of electron-atom collisions. Electron energies are typically about 100 eV, but in some special sources they have to be as high as 100 keV. An externally applied magnetic field is frequently used to cause the electrons to travel along a helical path and thereby increase the ionization efficiency. Examples of ion sources utilizing this concept are the duoplasmatron and the Penning ion source, but also the electron cyclotron resonance ion sources, often called ECRIS. The principle is based on the presence of neutral atoms Ao in the source which are ionized by electrons e having energies larger than the ionization potentials of Ao. One then obtains ion A+ according to the reaction: e + Ao -> A+ + e-b e. When numerous ionizations occur in the medium all the charged particles (ions and electrons) interact and generate the so-called source plasma from which the A+ ion beams are extracted with the help of a negative extraction potential, which separates ions from the electrons. Thermal ionization. Atoms possessing low ionization potentials can be ionized by allowing them to strike a heated surface having a high work function. Provided that the ionization potential of the atom is less than or about equal to the work function of the surface, there is a high probability that the atom will be thermally desorbed as a positive ion. The method is particularly well suited to producing ions of the alkali metals. Spark discharge. There are several variations of this technique, but basically a spark is induced between two electrodes, one of which, at least, contains the element to be ionized. Generally speaking, the spark consists of a high-density, high-temperature plasma from which ions can be extracted. The spark can be produced by applying a high alternating potential between two fixed electrodes or by mechanically breaking contacting electrodes. Laser ionization. A focused beam from a high-power pulsed laser can be used to produce a small ball of dense plasma from essentially any solid, and positive ions can be extracted from this plasma. The high temperature of the plasma results in the formation of many multiply charged ions; however these ions are energetic, and the beam emittance is not always convenient [9]. In principle, lasers or other strong sources of electromagnetic radiation can be used to produce ions by photoionization. A photon can directly ionize an atom if its energy exceeds the ionization potential of the atom, but the probability of photoionization is low. Field ionization. If an atom passes close to or is absorbed on a very sharp point where the electric field exceeds a few times 1 0 1 0 V m -1 , there is a probability that it will be ionized; the phenomenon is known as field ionization. Such large

THE BREAKTHROUGH OF THE ECRIS

3

electric fields can be achieved in the vicinity of a specially sharpened tungsten needle placed close to an annular electrode, and gas or vapour passing close to the tip of the needle can be ionized. 1.1.1.3 The particular importance o f specific ion source plasmas. Ion source engineers are faced with the task of understanding and dealing with the issues of generation, extraction and transport of the ion beam. The transport and extraction problems are similar for most types of ion source. Their basic equations are unquestionable and their experimental aspects seem rather well understood. They are treated in great detail in books on ion sources [1], [2], [6 ]. In fact, they belong to the field of particle dynamics with rigorous mathematical bases. Ion generation is another field, much less understood or developed, located somewhere in plasma physics famed for its complexity and empirical technology. Most studies concentrate on (i) (ii) (iii) (iv)

engineering issues, atomic physics for ion production, surface phenomena occurring on the electrodes and walls and properties of electrical arcs and discharges.

However, it is important to recall that, in fact, plasma phenomena dominate other considerations and that adequate emphasis has not been given to plasma physics. Relationships between ion source performance and plasma performance are rarely underlined, though the ions are extracted from plasmas, which are the usual ion reservoir. The ion beam current is first of all determined by the plasma density, the magnetic field configuration, the electron plasma temperature, the plasma size, the plasma homogeneity etc. The beam extraction and the beam optics may optimize or worsen the beam quality but never change the intrinsic properties of the source. Thus (i)

the beam composition is determined by the ion composition inside the ion reservoir, (ii) the ion charge state is determined by the electron plasma temperature, the ion lifetime and the plasma density of the ion reservoir, (iii) the beam emittance is fixed by the ion temperature, the plasma turbulence and the magnetic field in which the reservoir is located and (iv) the beam properties depend on the percentage ionization of the plasma, whose constituents are electrons, ions and neutrals (non-ionized particles). If the ionization is less than 10% the role of the neutrals is considerable, but in the opposite case (called highly ionized plasma) the physics of the ion reservoir is dominated by collective plasma effects and this is the case of high-performance ion sources. So we come to the following very simple conclusions: specific, highperformance ion beams are extracted from specific high-performance plasmas.

4

SPECIFIC ELEMENTS OF PLASMA PHYSICS

Even though some plasma concepts remain unsettled, modern engineers in the field of ion sources just cannot ignore basic plasma physics. Let us recall that for instance the ECR plasma concepts which determine the exceptional potential of ECRIS are the result of pure plasma R & D (1963-1979) later applied to ion source design. The aim of this book is to build a bridge between ECRIS engineering and ECR plasma physics.

1.1.2

Positive ion source concepts [20]—[27]

1.1.2.1 Arc sources and confinement sources. The classical concepts utilize arc plasmas but for different reasons these plasmas are difficult to confine. In addition, due to the erosion of the electrodes, they are not very reliable. Therefore, nowaday plasma confinement sources without electrodes are preferred and promoted. Note that both concepts allow light (protons and alpha particles) and heavy-ion production. A heavy ion can be singly ionized (one electron removed), can be fully stripped, as in argon-18+ , or can have any intermediate charge state. Singly charged heavy ions are most frequently used in industrial applications in isotope separators, mass spectrographs, ion implantation etc. These are much easier to generate than multiply charged ions, and frequently the experimenter has several source concepts to choose from, depending upon the application and the physical characteristics of the element to be ionized. Among these sources, the overdense ECRIS is now very fashionable and we study this in detail in chapter 5 of this book. On the other hand, multiply charged heavy ions are almost exclusively used in fundamental research in accelerators, particularly cyclotrons, linear accelerators and synchrotrons. A very considerable amount of research has been devoted to developing such sources. Until 1982, the bulk of this was directed to perfecting the Penning ion source (often referred to as PIGIS), and to the laser ion sources, but electron beam ion sources (EBIS) and min-Z? ECRIS, which are plasma confinement sources, gave better results. Finally, the ECRIS are now dominating since they yield ion flows which are orders of magnitude larger than those of EBIS (whose particular qualities are appreciated in some specific applications) (figure 1 . 1 . 1 ). 1.1.2.2 Two typical examples o f arc sources [7], [8]. Duoplasmatrons. The development of the duoplasmatron ion source in 1956 marked the beginning of the high-current era for proton sources. The duoplasmatron makes use of an arc discharge which is constricted as it passes into a very strong magnetic field shaped by iron or mild steel inserts in an intermediate electrode and anode. The beam is extracted at the point where the arc has reached a very small diameter and a very high brilliance. Sources of this

THE BREAKTHROUGH OF THE ECRIS

5

Figure 1.1.1 Comparative optimum yields of charged particles per second of EBIS {a), ECRIS (b ), PIGIS (c ) for neon, argon and oxygen (1990).

type have been developed for accelerators and are described and commented on in all the books on ion sources [7]. Penning ion sources. These sources are based on a high-current gaseous discharge in a magnetic field with gas at a relatively low pressure (10 - 3 Torr). The source (figure 1.1.2(a)) consists of a hollow anode chamber, cathodes at each end, a means for introducing the desired element (usually a gas) and electrodes for extracting the ions. The cathode may be heated to emit electrons, which then help to initiate the arc discharge current, creating the plasma in which the atoms are ionized. The discharge column between the cathodes (the plasma) consists of approximately equal numbers of low-energy electrons and positive ions. The electron density is much larger than can be accounted for by the primary electrons from the cathodes. The average energy of plasma electrons may range from a few volts to a few tens of volts. Electrons travel parallel to the magnetic field, are reflected from the opposite cathode and make many traverses of the length of the hollow chamber. The electrons confined by the magnetic field and the cathode potential thereby have a high probability of making ionizing collisions with any gas present in the chamber [8 ].

6

SPECIFIC ELEMENTS OF PLASMA PHYSICS

C a th o de Beam compression

Zones of

G un

Gas A rc plasm a

ECR

D rift rubes S C solenoid—

Hexapole K.Cal-hode

L He cooled panel —

-A n od e A

Solenoids—

Electron beam co lle cfo r-

ECR Plasma ▼ Ions i|r Ions

(EBIS) (a)

(ECRIS) (b )

(PIG IS) (c)

Figure 1.1.2 Main elements of the three IS capable of delivering highly charged ion beams (EBIS, [10], [11], [97], PIGIS, [6], [8] and ECRIS).

The net result of all the processes in the arc plasma is that some partially stripped atoms diffuse perpendicular to the magnetic field out of the arc towards the extraction system. High yields of charge state l +- 8 + (and for heavier elements, perhaps up to 1 2 +) have been obtained for many elements of the periodic table. In figure 1.1.3, we see PIGIS multiply charged ion performance compared to that of ECRIS. Five drawbacks have pratically eliminated the PIGIS from the race towards high-performance sources for multiply charged ions. The yield of multiply charged heavy ions from Penning sources cannot be significantly improved, largely as a result of (i) the short ion-containment time, (ii) the relatively high source pressure (which increases ion recombination), (iii) too short a lifetime of the hot cathode ( 2 0 h), (iv) too low an electron energy inside the arc and (v) the poor reliability since the performance changes when the electrodes erode during its operation. In short: though still very popular for less highly charged ions, PIG ion sources are not reliable for highly charged ion production. A large collection of different arc sources may be found in specific books [ 1]—[6 ] and in the proceedings of conferences on ion sources [21]—[25]. 1.1.2.3 Examples o f confinement sources (figure 1.1.2(a) and (b)) [10]-[12], U 4 1 [15]. The minimum-B ECRIS. Promising sources designed to overcome the limitations of the PIGIS are the ECRIS, based on magnetic confinement, and the EBIS, invented by Donets [10], whose principle is based on electrostatic confinement. However, contemporary EBIS are expensive high-performance sources which are not suited for many routine operations, whereas the min- B ECRIS are much more robust, versatile, practical and rapidly operative. Such a source is simply made of an empty metallic box filled with very low-pressure vapours, microwaves and specific magnetic B fields for plasma confinement (note that none of these three elements is degradable). The plasma confinement is

THE BREAKTHROUGH OF THE ECRIS

7

Figure 1.1.3 Typical values of the ion charge q produced by PIGIS and min-B ECRIS suited to accelerator applications for the elements up to atomic number Z = 92.

generally obtained by superimposing solenoidal and multipolar fields such that the modulus of the magnetic field is minimum in the centre of the box and maximum near the walls. In between there exists an ECR surface which is a closed magnetic surface where the Larmor frequency of the electrons is equal to the frequency of the injected microwaves. Electrons crossing this surface are then energized by the electron cyclotron resonance. When they pass many times through the resonance, according to their random phase, they acquire a global ECR heating, yielding energies of tens of kiloelectron volts and thus exceeding the ionization potentials of many highly charged ions, but as the ion charges are obtained step by step through successive electron-ion collisions (see section 1.4.9), the ions need long exposure times to many electron impacts (i.e. long plasma confinement). The source has generally two stages in series: the first one creates, at ECR, a cold plasma at relatively high gas pressure (> 10- 4 Torr) which replaces the cathodes. The plasma electrons diffuse towards a very low-pressure second stage where ECR 2 energizes the electrons inside the confined plasma. Due to the absence of cathodes and any kind of electrode, the longevity of the source is unlimited. The magnetic fields are obtained with ordinary or superconducting coils, permanent magnets or with a mixture of these. The sources can operate continuously or be pulsed. Continuous beams of several microamperes of C6+, N7+, O 8 and Ne10+ have been routinely extracted

8

SPECIFIC ELEMENTS OF PLASMA PHYSICS

Figure 1.1.4 Beam current accelerated by RFQ as a function of beam current extracted from both a duoPIGatron and single-mirror ECRIS [13].

from these sources and large currents of highly charged heavy ions are available. The ECRIS eliminates all the drawbacks of the PIGIS: ions are confined, hot electron emitters are eliminated (no filaments or cathodes), gas pressure is very low and the energy of the electron can be adjusted by tuning of the ECR parameters. The operation is very reliable and the source can operate for weeks or months without dismantling. Nevertheless throughout this book we will study the limitations of the ECR plasma in order to improve the performance even more. ECRIS development is still a challenge [29]—[39]. The simple mirror ECRIS (see chapter 5). In these sources only solenoidal B fields are provided. Thus the confinement becomes poorer and comparable to the confinement of PIG sources. Subsequently, the purpose of these sources is to produce less highly charged or even singly charged ions. However, even for accelerators, these ECRIS also promise to supplant arc discharges as highcurrent injectors, since they seem to allow better beam transport. For instance figure 1.1.4 shows the proton current accelerated by an RFQ (radio frequency quadrupole) system as a function of the beam currents extracted from both the ECRIS and the duoPIGatron (which is the name of a very high performance PIGIS). The ECRIS produces a slightly higher accelerated beam current with less than half of the extracted beam current of the duoPIGatron. Furthermore, the hydrogen mass flow rate is reduced by a factor of five [13].

1.1.3

The leading role played by ECRIS in fundamental research on heavy ions [16]

1.1.3.1 Applications with accelerators. The so-called PIGIS were used until quite recently in heavy ion accelerators so multiply charged ions could only be obtained by incorporating, if possible, some additional strippers to remove

THE BREAKTHROUGH OF THE ECRIS

9

electrons (see chapter 6 ). However, strippers introduce many difficulties and reduce the overall reliability. ECRIS now dominate as they produce directly highly charged ions. Figure 1.1.5 shows that an immediate increase in performance is obtained by replacing a PIGIS with an ECRIS. This can be illustrated by considering the situations for cyclotrons and synchrotrons. The particle energy (in megaelectron volts per nucleon) delivered by a cyclotron is given by W = K ( q /M ) 2 where q and M denote the charge and the mass of the accelerated ion respectively, and K is an efficiency factor that depends on the size of the machine and its magnetic field strength. K generally lies between 10 for smaller cyclotrons and 800 for the most powerful. By increasing the ion charges by a factor of two to four one can increase the particle energy by fourfold to 16-fold without altering anything else. This represents a bargain because the cost of such a change (i.e. replacing a PIGIS by an ECRIS) is orders of magnitude less that the cost of increasing K by the same amount. (For instance, in order to increase the value of K by 16, the size of the accelerator must be considerably enlarged and the mass of iron and copper of the new cyclotron should be roughly increased by 1000.) Note, however, that ECRIS are external ion sources and cannot be placed between the ‘dees’ of a cyclotron like small PIGIS. Therefore, specific injection lines have been realized [17] and are now utilized in most cases (Belmont’s Inflector). The situation is somewhat different for existing synchrotrons. Synchrotrons, like cyclotrons, can be adjusted to cope with all values of e = q /m but their injector systems (including linear accelerators) do not have the same flexibility. However, if the entire synchrotron complex is capable of accelerating alpha particles (q /M = 0.5), as most of them are, then they can immediately accept a variety of completely stripped ions such as 1 2 C6+, 1 4 N7+, 1 6 Os+, ^ N e 10"1", 3 2 S16+ and 4 0 Ca20+. For instance, CERN’s super proton synchrotron (SPS) providing up to 200 GeV per nucleon has therefore been able to achieve beam energies of 3.2 TeV with 1 6 0 84' ions and, more recently, 6.4 TeV with 3 2 S16+ particles, thus permitting an investigation of quark-gluon matter to start without building a special heavy-ion tevatron. In CERN’s SPS ring, an ECR ion source is coupled through a radio frequency quadrupole to an existing linear accelerator capable of accelerating 1 6 0 6+ and 3 2 S12+ (£ ^ 0.37) to 12 MeV per nucleon. After passing through a foil that strips away electrons (see below), these particles are transformed into 1 6 0 8+ and 3 2 S16+ and then accelerated without further modification by the whole CERN complex comprising a booster ring, the proton synchrotron (PS) with 12 GeV per nucleon and the SPS (figure 1.1.6) [28]. In autumn 1994 with a new heavy-ion injector at CERN a lead beam of 2.9 x 107 ions per pulse was accelerated in the SPS up to an energy of 157 GeV/u. The ion source was in operation almost continuously over a period of about 1 year and proved to be very reliable. It produces a current of more than 100/zA of Pb27+ (after the first spectrometer) during the afterglow of the pulsed discharge.

10

SPECIFIC ELEMENTS OF PLASMA PHYSICS

ii

10 20 2b 40 50 60 70 80 90

z

Figure 1.1.5 The impact of ECRIS on heay-ion physics carried out using some well known accelerators. The doubly hatched areas are the regimes covered by the original accelerators; the singly hatched areas are those available to some well known accelerators equipped with ECRIS.

The impact of ECRIS and their capacity to open up additional fields of research in heavy-ion physics is illustrated in figure 1.1.5 for existing accelerators. The doubly cross-hatched regions define the energies and atomic numbers that could be handled by these accelerators until 1983. The large, singly hatched regions outline the regimes that are accessible to these accelerators equipped with ECRIS systems in 1995. Finally, somewhat over-simplifying the situation, we can say that, to obtain higher particle energy, accelerator people have the choice either to utilize ECRIS on existing high-cost systems or to construct new giant-budget accelerators. Let us also emphasize that presently more than a thousand specialists in highenergy physics utilize accelerators equipped with ECRIS, but that ECRIS are also mounted on heavy-ion synchrotrons for medical research [18].

THE BREAKTHROUGH OF THE ECRIS

11

Figure 1.1.6 The CERN accelerator complex. Simply by replacing a classical arc source with a min-2? ECRIS (• in the above figure) one could increase the beam energy from ~ 200 GeV (protons) to 3.2 TeV for O ions, 6.4 TeV for S ions and later to 34 TeV for Pb ions (with an improved linac) [28]. Without the ECRIS, the cost of these improvements would have been many orders of magnitude higher than the cost of the ECRIS.

1.1.3.2 Applications in atomic physics research. Atomic physics research can be performed with accelerators at high and medium energy. As the types of available ions, with different charge states, are now extremely diversified a huge field of research is ready for investigations. On the other hand, low-energy physics with highly charged ions was given impetus by the pioneering studies initially proposed by Bliman in 1968. In fact, the fusion research revealed that highly charged ion impurities were present in all machines and studies were necessary to understand their behaviour in the plasma. The time had come to start considering what was the most needed collision programme for fusion. Clearly, the choice was in favour of low-energy ions but electron ionization of ions was initiated using crossed beam techniques (although unsuccessfully). It appears that the fact that ultra-high vacuum is a prerequisite to perform this type of measurement has been totally ignored. Meanwhile, Bliman observed that ion stripping in ion-atom collision had cross-sections as important as those one was trying to measure. This caused the reorientation to charge-changing ion-atom collisions, which appeared to be the most obvious thing to do. Cross-sections were measured, rate coefficients calculated and it was suggested to the fusion physicists that these data should be accounted for in modelling impurities. Further the spectroscopic observation of these collisions would give some insight into the collision dynamics but also make possible identifications of unknown lines, which constitutes the basis of a diagnostic

12

SPECIFIC ELEMENTS OF PLASMA PHYSICS

-------------- ►

R.I.B.E. (Reactive Ion Beam Etching) (Chemical Assisted Ion Beam Etching)

ECRIS

(Implantation)

ECRIS

ION BEAM

---

^

ION BEAM ----------

I.B.S.D. (Ion Beam Sputtering Deposition)

I.A.D. (Ion Assisted Deposition)

Ion Beam Sputtering Deposition with Ion Assistance

Figure 1.1.7

Some applications of ECRIS in industrial ion processing.

technique in fusion machines (temperatures and impurity distributions). At the same time, the study of the interaction of slow highly charged ions with surfaces was started. This was a first step to the observation of Coulomb explosion at the surface and of multiply excited ions and atoms (hence, the concept of the ‘hollow atom’ by J Briand) [45]. This boosted other basic studies [46]. Many of these early experiments were performed at the AGRIPA laboratory in Grenoble which was the first facility equipped with an ECRIS (1980). It used gaseous elements up to fully stripped ones. All these ions had a large Coulomb potential which induced various interactions on atoms and surfaces with small ion kinetic energy. As this field of research is vast, many other facilities were equipped with ECRIS after 1983 [40], [44], [448]. Thus, ECRIS have opened up new areas of research in the low-energy

THE BREAKTHROUGH OF THE ECRIS

13

range, i.e. without an accelerator, by offering many kinds of highly charged ion collisions. The provision of facilities for several hundred researchers in the fields of atomic and surface science has allowed a renaissance of this discipline all over the world. It is out of the scope of this book to cite the thousand original papers dealing with this topic, but let us cite the proceedings of the conference on highly ionized atom physics [40]—[43] and to salute on this occasion a few physicists who boosted this research with ECRIS: S Bliman, F W Meyer, F de Heer, H P Winter, E Salzborn etc. 1.1.4

Applications of ECRIS in industrial ion processing (figure 1.1.7)

Even ECRIS for less highly charged ions are now on the verge of having a significant impact on a number of other fields. The principal attractions are enhanced reliability compared to arc discharge ion sources with short-lived cathodes, and, in many instances, higher currents of the desired ion (such as reactive ions). Thus different manufacturers of high-current ion implanters already depend on ECRIS (see chapter 5). Most of the ECRIS applications in the microelectronics processing arena have been driven by a large effort from Japanese plasma system manufacturers, especially when it was believed that ECR systems could provide high-resolution etching of silicon to better than 0.5 fim dimensions (high anisotropy of etching and high selectivity are also expected). The role of the ECRIS parameters, the efficiency of the source and the potential uses are only now beginning to be investigated. In 1989, Asmussen reviewed the issues associated with ECR plasmas with particular reference to their use as plasma processing sources [47]. Another review was presented in [19]. Nearly 20% of the papers of the last international conference on ion sources dealt with these topics (often called microwave plasma sources). Many of the investigations are performed in Japan. In one of the review papers the merits and demerits of these sources with respect to classical ion sources are compared [48]. 1.1.5

Conclusions of section 1.1.

During the last decade, electron cyclotron resonance ion sources (ECRIS) have transformed heavy ion physics. Because ECRIS can generate substantial currents of very high-charge-state ions, the size and the cost of new heavy-ion accelerators have been reduced considerably and the energy of old machines has been increased dramatically. The unsurpassed reliability of ECRIS is also attractive in an industrial environment. ECR ion sources operate comfortably for hundreds of hours on feed gases that ruin arc discharge ion sources. In some ion sources the hot cathode is now replaced by a small ECR plasma which works as a nondestructive electron donor. Thus ECR plasma supplants little by little the arc plasma in many fields. The development of ECRIS is still continuing. Alternative methods of introducing microwaves, and gas mixtures, are still being investigated; different

14

SPECIFIC ELEMENTS OF PLASMA PHYSICS

magnetic field configurations are being evaluated. Other extraction geometries are being considered. Together, these promise higher beam current and ion charged states, lower emittance, increased microwave power efficiency, improved feed gas utilization, simplified tuning etc. However, these are mainly technological aspects. None of the above-cited modifications should be undertaken without a better understanding of the behaviour of the ion reservoir. In other words, the central issue remains the study of the important parameters of the ECR plasma in its magnetic configuration. All the exceptional properties of ECRIS depend on ECR plasma concepts which are not easy to approach and still leave many questions open. These concepts are lacking in all books on ion sources probably because the studies are complicated and still continuing. Only some scattered knowledge of the ECR plasma has been published in compilations of journal articles dealing with plasma or fusion reseach. Other material exists in proceedings of ECRIS workshops and ion source conferences. Our purpose is to gather these dispersed elements in a comprehensive manner and add some pieces to the puzzle which is far from being completed. To illustrate the ECRIS breakthrough, let me recall that the first ECRIS and the first ECR cathode worked in 1965 [53]. At the first international conference on ion sources in 1969 [20], only one single paper dealt with ECRIS. At the second conference in 1972, there were two contributions and at the sixth conference in 1995 [25] 70 papers out of some 220 contributions dealt with ECR.

1.2

1.2.1

PRELIMINARY ASPECTS OF PLASMA AT THE ELECTRON CYCLOTRON RESONANCE

Ignition of laboratory plasma [49]

Four states of matter exist on earth: solid, liquid, gas and plasma. A substance may exist in one or more of these states, depending upon certain values of quantities such as temperature and pressure. In the laboratory, if we start to tackle a solid substance, we may change it to a liquid by adding energy to it. The substance melts when the ‘heat of fusion’ of the substance has been added at the melting temperature. If the temperature is raised enough, the liquid evaporates when the ‘heat of vaporization’ has been added and a gas is formed. A solid substance directly becomes gaseous when the heat of sublimation has been added. If more energy is added to the gas, a point is reached when the gas ionizes. This occurs according to Saha’s equation when the heat of ionization is added. However we have already seen in section 1 . 1 . 1 . 2 that electron impact is a more general means of ion formation than thermal ionization and ECRIS are based on electron impact with electrons

PRELIMINARY ASPECTS OF PLASMA

15

accelerated by high-frequency EM fields. We have now created a collection of ions and electrons, which we call a plasma. The ionizing process has divided the molecules and atoms of the gas into separate electrons and ions. A simple definition of a plasma might be a large collection of approximately equal numbers of ions and electrons, meaning that a plasma tends to be electrically neutral, but in section 1.3 we will define the plasma state better through the concept of Debye length. Note that to effect ionization of a neutral atom or molecule enough energy must be added to it to allow one or more of the bound electrons to escape from the atom. The energy is then shared by means of collisional and collective processes between plasma particles. As already mentioned, since the ions and electrons making up the plasma are electrically charged they may be accelerated by means of applied combinations of dc or ac electric, magnetic and/or electromagnetic fields. This acceleration can be sufficient to increase the energy of the plasma particles until they cause more ionization of neutral atoms by collision. Note also that there are always a few charged particles present even in ‘un-ionized’ gas, so that this process may be used to ‘ignite’ a plasma (breakdown) (see section 3.1).

1.2.2

Self-destruction of laboratory plasma

On earth solid, liquid and gaseous matter is long lived under normal conditions; in contrast plasma matter is very short lived and it disappears immediately if one does not try to conserve the electrical particles. The best particle lifetimes obtained in the laboratory are of the order of 1 0 ~ 2 s; generally they are less than 10- 6 s. All the difficulties of laboratory plasmas stem from their tendency to self-destruction due to the process opposite to ionization called recombination. In this effect, electrons and ions come back together to form neutral atoms. This situation, if it were to exist by itself, would eventually result in the complete disappearance of the plasma state. However, if ionization is also occurring at the same time, the plasma can continue to exist. In the plasma bulk the main recombination process is charge exchange but the most efficient global destruction process is recombination on the walls which occurs when ions and electrons move towards the walls of the plasma container where they just disappear after recombination. Thus the laboratory plasma must be kept isolated from the walls and in a concentrated form. In short there are two vital plasma issues. (i)

The first problem is the choice of a suitable means of production of the plasma, through electron impact ionizations achieved by accelerating the electrons at low gas pressures. (ii) The second problem is the storage of the plasma isolated from the walls (also called plasma confinement). This is the more difficult issue.

16

1.2.3

SPECIFIC ELEMENTS OF PLASMA PHYSICS

The need for plasma confinement-magnetoplasma

1.23.1 The confinement principle. To achieve confinement one utilizes the electrical properties of plasma particles. Once ionized, the plasma particles are affected by electric and magnetic fields. If a scheme could be made which confined a man-made plasma so that it did not interact with the walls and kept it concentrated for a long time, the biggest problem would have been solved. Until now however systems have mainly used externally applied electric and magnetic fields to attempt to produce, if not adequate, at least reasonable, confinement. When the plasma is contained in a magnetic field we deal with magnetoplasma, which is a medium where involved electron and ion motion is expected. The particles then exhibit different kinds of helical trajectory due to their gyromotion inside the magnetic field (see section 1.5). These complicated particle trajectories hinder the leakage of particles directly to the walls and thus contribute to the confinement by considerably increasing the path length to the walls and also the time needed to traverse this path. The particle transport process is called diffusion. In the absence of a magnetic confinement field the equations of particle motion are well known with a well defined diffusion coefficient. In a magnetoplasma the diffusion coefficient D becomes a tensor, indicating in short the existence of coefficients D\\ and D±. D\\ describes the diffusion of the plasma particles along the B field lines and D i the diffusion across the B field lines, which should be considerably reduced (see section 1.7). 1.23.2 The failure o f a general confinement theory o f the magnetoplasma (figure 1.2.1). According to classical theories, diffusion across the B lines should decrease drastically with increasing magnetic field (D L oc B ~2). In fact it does not and anomalous diffusion occurs, which is proportional to B ~ l . The problem of anomalous diffusion in magnetoplasmas has been a continuing subject of investigation over the last 50 years. In section 1.7 we try to tackle the issue but our efforts will mainly emphasize the difficulties of an adequate description of the collisions which are the driving processes of diffusion. We will then consider collective collisions and turbulence and we will be obliged to recognize that our theoretical approach to turbulent plasma is still insufficient and our short review of diffusion phenomena in magnetoplasmas will just show that no satisfactory theory of diffusion exists to date (see section 1.7). 1.2.3.3 The struggle fo r the right orders o f magnitude in the magnetoplasma. Finally, we recognize that particles are more or less confined in a magnetoplasma but not as well as expected. The confinement is capricious and unpredictable and so is the matter of magnetoplasma. As the global confinement times are orders of magnitude shorter than foreseen, it follows that other transport coefficients such as electrical conductivity or thermal conductivity are in the same situation.

PRELIMINARY ASPECTS OF PLASMA

17

Anom alous Plasma Diffusion

Figure 1.2.1 Plasma trapped in a simple magnetic mirror exhibiting anomalous diffusion losses across the field lines.

Under these conditions modelling of a magnetoplasma becomes untrustworthy. Thus the equations of balance of particle creation and loss become unreliable due to the badly determined losses. It is pretentious and vain, according to some theoretical concepts, to predict accurate values of plasma density, particle temperature, electrical or thermal conductivity. Only theories supported by limited scaling laws based on experiments are trustworthy to a certain extent. Generally when, in a modelled magnetoplasma, the predicted parameters are of the same order of magnitude as the experimental ones, one considers that the agreement is good and that the theoretical approach is acceptable. Only the exponent is significant; one number before the exponent is plenty, two numbers are no better (section 1.7.5). However, even though the particle motions are not predictable and are questionable, the electrons, between two ill defined collisions, are frozen on the B field lines and gyrate around them. Therefore let us briefly introduce three principal characteristics of the particle gyromotion in magnetoplasma, which are unquestionable. 1.2.4

Particle gyromotion in magnetoplasma

The equation of motion for a charged particle in an electric and magnetic field is given by the Lorentz force m r — F = e (E + r x B ).

18

SPECIFIC ELEMENTS OF PLASMA PHYSICS

Much useful insight into the confinement properties of magnetoplasmas can be obtained from a study of the motion of individual non-interacting particles in electric and magnetic fields. The basic equation predicts helical trajectories with a gyroffequency and gyroradius (see section 1.5) during rather chaotic motion. 1.2.4.1 Gyroradius (also called cyclotron radius or Larmor radius). In a simple case where the electric field E = 0 a particle with charge e in motion with velocity v± , perpendicular to a magnetic field of strength B, experiences a force on it that is perpendicular to both the particle velocity and the magnetic field. This force is given by F = ev±B = e ( B x v). Because the force is transverse both to the velocity and to the field, the particle moves in a circular orbit, as if ‘tied’ to a magnetic field line. The radius of this gyro-orbit is given by m v_l P = ~e¥' This is called the cyclotron radius, gyroradius or Larmor radius. The mean gyroradius of the magnetoplasma electrons of average energy We (eV) is nm c p — — pe — n0.0035

B

cm

where the magnetic field B is given in kilogauss. Similarly, the mean ion radius for ions of charge state z, mass number A and average energy W* (eV) can be written as p + — pi = 0. 16—

cm

(B in kilogauss). For the same energy and field strength, the electron cyclotron radius is smaller than the ion cyclotron radius by the square root of the mass ratio. In usual ECR plasmas for energies from a few electron volts to some 10 keV and magnetic fields of a few kilogauss pe has values between 0 . 1 mm and 1 cm. 1.2.4.2 Helical trajectories and sense o f the gyromotion. In the previous expressions, the particle energies are referred to the energy components in the direction perpendicular to the magnetic field. The particle velocity parallel to the magnetic field is unaffected, and the resultant particle motion is a helix centred about the field line to which the particle is tied. Because the electrons and ions carry opposite electric charges, the sense of their gyromotion is opposite; electrons rotate in a right-handed sense with respect to the direction of the magnetic field, and ions are left handed. Thus for efficient wave-electron interaction, the electric wave field should rotate in the same sense as the

PRELIMINARY ASPECTS OF PLASMA

19

Figure 1.2.2 Geometry of right- and left-handed circularly polarized waves propagating along Bq with electron and ion Larmor radii and corresponding senses of gyromotion.

electrons. Therefore mainly right-hand polarized waves (R waves) are useful at ECR (figure 1.2.2). L2.4.3 Gyrofrequency (or cyclotron frequency). The particle cyclotron motion occurs at a very well defined angular frequency, called the ion or electron cyclotron frequency, which is given by (Oq —

eB . _ — - f q. m

This can be expressed conveniently as f ci = 1.52 z B /A

(MHz).

and f ce = 2.8 B

(GHz)

where B is again in kilogauss. For magnetic fields of a few kilogauss the electron cyclotron frequency is a few to a few tens of gigahertz and the ion cyclotron frequency is typically a few hundred kilohertz to a few megahertz. 1.2.5

Global characteristics of plasmas at the electron cyclotron resonance

7.2.5.7 A selective energy transfer from the waves to the electrons. As ECRIS are based on ECR plasmas let us very briefly describe the properties of the latter before studying them in more detail throughout this book.

20

SPECIFIC ELEMENTS OF PLASMA PHYSICS

In contrast to other magnetoplasmas, where the electrons are energized by externally applied continuous electric fields, in ECR plasmas, the electrons are energized by the combined effects of EM wave fields and static B fields, which is generally conducive to a high ionization efficiency. This useful property, resulting from reduced charged particle losses to the wall, is only one of the many advantages of microwave-generated magnetoplasmas, others being, for example, an efficient microwave power transfer from the feed line to the discharge, even at very low gas pressures, and the absence of electrodes in contact with the plasma. When the frequency of the EM wave is equal to the gyrofrequency of the electrons the waves can transfer their energy to the electrons in a selective manner called electron cyclotron resonance (ECR) and one obtains a particularly efficient coupling of microwaves to the magnetoplasma. 7.2.5.2 Wave coupling to collisionless ECR plasma. To sustain efficiently an ECR plasma with electromagnetic energy one has first to determine the mechanisms of wave absorption. Even though electron-atom collisions seem essential to the process sustaining the plasma, at low gas pressures they contribute only weakly to the electromagnetic energy absorption. In such a case, one must operate under conditions where collisionless absorption is possible (see section 2 .2 ). Collisionless ECR absorption results from a resonant wave-particle interaction which causes damping of the wave. Such a mechanism occurs when electrons rotating at an angular frequency coce around B q field lines are travelling with a velocity Vz along the field lines. When the wave has a right-hand circularly polarized electric field component in the plane perpendicular to Bo, these electrons see this component at a Doppler-shifted frequency co' = co ± p V z where f$ is the component of the wave vector along B. For co = coce, the electrons are submitted to a constant electric field and gain energy from the wave (see section 2.2). The corresponding absorption process is called cyclotron absorption. It is accompanied by an increase of the electron velocity component in the direction perpendicular to B q. This energy increase is subsequently shared within the whole plasma volume through some rare genuine collisions and through nonlinear processes. These mechanisms constitute the basic ingredients of ECR plasmas. Basic studies of wave-plasma interactions teach us that as already mentioned, for ECR absorption, we need a wave with an adequate polarization, namely a right-hand wave which is a pure transverse wave. In practice, however, the presence of boundaries does not allow the propagation of pure transverse electromagnetic waves, thus the wave electric field always possesses an axial component which does not directly contribute to ECR absorption. Fortunately, it happens that the E field of a wave in the plane perpendicular to B q can always be decomposed into right-hand and lefthand circularly polarized components. Only the right-hand wave component is absorbed through ECR absorption and the remaining fraction (left-hand polarized

PRELIMINARY ASPECTS OF PLASMA

21

and axial component) of the wave power is either absorbed after some conversion processes or reflected without being absorbed. According to the wave-plasma theories we also know that (i) the amplitude of the electric wave field tends towards a maximum when a wave enters a resonant zone, thus the ECR zone is a privileged location for the energization of the electrons and (ii) that the (R) waves can in most cases propagate inside the magnetoplasma towards the ECR zone without great difficulty (see section 2.1). Based on theories and experiments, we now know many things about the ECR, but some aspects remain to be ascertained and the research is continuing. This is particularly true (i) for the extraordinary wave component (X wave) which feels a special resonance (upper hybrid resonance) whose effects are often included in the global aspects of the ECR and (ii) when nonlinear wave-electron interactions take place, which occurs when substantial RF power is introduced in the plasma. 1.2.53 Typical wave frequencies, wave power and magnetic fields fo r ECRIS. Until now, the utilized wave frequencies have been in the range 2.45-28 GHz. Klystrons and magnetrons, which are the usual wave generators, operate at fixed frequencies, typically, 2.45, 5, 6.3, 8 , 10, 14, 16, 18 and 28 GHz. They are commonly called RF (radio frequency), HF (high-frequency) or /xW (microwave) power generators: their powers generally are between 50 W and 5 kW (according to the need). The static magnetic fields required for ECR are given by B =

f e e /

2.8

where B is in kilogauss and f ce in gigahertz. Thus typical magnetic fields in the ECR zones normally lie between 0.875 kG and 10 kG. 1.2.5.4 Usefulness o f mirrors and uselessness o f toroidal configuration in ECRIS. The two basic functions of the magnetic field are to keep charged particles as far as possible from the walls and to allow an efficient transfer of the electromagnetic energy to the plasma. Because charged particle transport occurs mostly along magnetic field lines (in spite of anomalous cross-B motion) to some extent the geometry and extension of the region filled with plasma can be optimized by a convenient choice of the spatial configuration of Bo, the static magnetic field. Varying the magnetic field configuration intensity makes it possible to move the position of the resonance zone and thereby optimize the tuning. Thus, ECR plasmas can be generated under various static magnetic field configurations. Let us immediately discard toroidal configurations since they are closed plasma structures. In such a case the confinement is improved but it seems very difficult to extract ions from them in an efficient way. Thus they are useless for ion sources. There remain two basic confinement systems: (i) the magnetic

22

SPECIFIC ELEMENTS OF PLASMA PHYSICS

field is directed essentially parallel to the plasma axis and, at some point along the vessel, the field lines are forced to converge. A so-called magnetic mirror is then created. Such configurations are generally obtained simply by using a set of electromagnet coils around the plasma vessel. The required Bo configuration is controlled by the spacing between coils and/or by the current (direction and intensity) flowing through them. Unfortunately, these simple mirror systems yield only mediocre confinement: (ii) multipolar magnetic fields are used with min-B configurations which are the highest-performance systems but their production is more sophisticated. The confinement systems are treated in section 1.6 and will not be discussed further here. In both types of static B field configurations ECR zones are provided where the energy transfer from the waves to the electrons is supposed to be optimized and in both types the magnetic field lines conduct the plasma to an ‘open end’ from which ions are extractable. 1.2.6

Distribution function and quasi-electron temperatures in ECR plasmas

Although ECR plasmas like most magnetoplasmas never achieve a Maxwellian distribution of velocities, they may approach it and it is convenient to assume that the plasma is described by one or more Maxwellian velocity distributions. However we have already mentioned that the collisions are very rare and that they are not binary as in an ideal Boltzmann type gas. Due to the combined effects of EM fields and static magnetic fields some electron motions with respect to the magnetic field lines are enhanced and others impeded. Subsequently the velocity and energy distribution functions might be different when one considers directions parallel to the field lines or perpendicular. In addition due to the ECR effect two electron populations are often observed: the classical bulk population and a superthermal, energetic, beamlike population (see figure 1.2.3). Thus the plasma is obviously non-thermal and non-isotropic. Under these conditions a description of the ECR plasma should give the location and velocity of each plasma particle as a function of time but this is impossible to obtain. Therefore, in spite of its inaccuracy it is customary to use the distribution function / to describe an ECR plasma. From the Boltzmann theorem it is known that under the action of ‘binary’ collisions an ideal gas relaxes to a Maxwellian distribution of velocities /

m

\ 3/2

nf(v) = n ( 2 n K T )

exp(—mv / 2 K T )

where h = N / V , with N the number of particles of a certain type (e.g.ion or electrons) in the system and V the volume of the system. In the Maxwellian distribution, the parameter 7 , which definesthe distribution function, is the temperature of the plasma.

PRELIMINARY ASPECTS OF PLASMA

23

1,0

or

0,0

0

0,2

0 ,4

0,6

0 ,8

1,0

1,2

VELOCITY

1,4

1,6

1,8

2,0

2,2

2,4

2,6

v

Figure 1.2.3 (a) A Maxwell-Boltzmann distribution function for an isotropic plasma. (b) Distribution function of a plasma with a non-thermal feature (drifting ECR electrons in the tail of a Maxwell-Boltzmann distribution).

Having no better choice, though ECR plasmas are poorly described by a Maxwellian, one generally relates the experimental distribution function to the Maxwellian distribution, by describing the system as a plasma at temperature 7\ with T defined by the above formula. In fact, Te is a quasi-temperature proportional to a kind of average electron energy. 1.2.7

Self-generated waves in ECR plasmas

1.2.7.1 ES plasma waves [50], [51]. In addition to the externally launched EM waves (aimed for energy transfer to the electrons in the resonance), there are a large number of possible oscillations in a system of coupled oscillators with many degrees of freedom such as an ECR plasma. Most of them are self-generated or somehow excited wavelike disturbances which will propagate in the plasma. ECR plasma can propagate linear and nonlinear waves. Linear refers generally to very small-amplitude waves whereas nonlinear refers to largeamplitude waves. Among the latter one observes different electrostatic waves (also called plasma waves since they cannot propagate outside the plasma). They

24

SPECIFIC ELEMENTS OF PLASMA PHYSICS

propagate if there is a distribution of electron velocities or an average electron velocity in the plasma. The most famous are the Langmuir waves aroused by an initially displaced clump of electrons oscillating at frequency cop. We will see that these oscillations are possibly everywhere and always nascent in the plasma (see section 1.3) and cop increases with plasma density. They might cause ES shock waves (solitons), waves propagating transverse to the magnetic field lines (Bernstein waves), harmonic and subharmonic waves with beat frequencies etc. They are probably the agents of plasma turbulence and will be invoked again and again in the following chapters. 1.2.7.2 EM waves; plasma radiation [50]. When analysing the EM noise issuing from an ECR plasma, one observes in addition to the injected waves some wave frequencies linked to possible plasma instabilities, driven by discrete modes. One also measures frequencies linked to plasma radiation, emitted either from radiating atoms (recombinations and excitation free-bound transitions (see section 1.4) or from accelerated charges). This latter case occurs mainly when an electron encounters another charged particle and makes a sudden change in direction; it then radiates in the so-called free-free transition yielding Bremsstrahlung, but energetic electrons also hit the solid walls and create the usual x-ray radiation (see section 3.2). Finally, electrons moving in circular orbits radiate at the cyclotron frequency and its harmonics. In particular if the electrons are energetic (relativistic), which often occurs in ECR plasmas, there is more energy radiation from all the harmonics than from the fundamental. The main interest in ECR plasma radiation comes from the fact that the radiation properties can be used for plasma diagnostics helping to measure the electron temperature, electron distribution functions, densities etc. Note that the useful information has to be extracted from a very noisy spectrum where the presence of the externally launched EM waves is overwhelming (which makes the diagnostics difficult). The propagation properties of these large-amplitude incident EM waves in the ECR plasma are analysed in section 2.2. 1.2.7.3 Ion sound waves. An ECR plasma also propagates low-frequency ion waves, where the ions form zones of compression and rarefaction just as ordinary sound waves do. In this process, the charge separation electric field provides the coupling between electrons and ions. Even standing ion sound waves are observed in ECR plasma when the electron temperature Te is much higher than the ion temperature 7}; the electron pressure provides the restoring force and the heavy ions provide the inertial process. The speed of propagation is given by Tonks and Langmuir [52]

yeK T e + Y jK Tj

(

COLLECTIVE PLASMA PHENOMENA

25

where ye and y,* are the usual ratios of specific heat for electrons or ions respectively, Af/ the ion mass and K the Boltzmann constant. In ECR plasmas the ion sound waves are often generated together with Langmuir waves when cop comes close to c o r f (see section 1.3.9). They do not harm the ECR plasma but they are harbingers of critical conditions which can trigger strong plasma losses when some experimental parameters of the magnetoplasma are then changed. Note that the magnetic field does not hinder the ion oscillations, but other types of magnetosonic wave are possibly excited in the ECR plasma and many ill defined waves are certainly present. Their roles are not clearly analysed and they seem to be of secondary importance. 1.2.8

Preliminary conclusions

We have briefly emphasized the avantages of ECR plasmas without hiding the complexity of the issue. In the next chapters we will propose more involved parameters in order to obtain a better description. However most of our knowledge is based on linear approaches in ‘cold’ plasma. If many aspects still remain unexplained this is mainly due to nonlinear processes in ‘warm’ magnetoplasmas with anomalous diffusion losses. These effects are not yet ‘ascribable’ by simple theoretical models. In the meantime, semi-empirical approaches are often successful and challenging. Anyhow, studying ECR plasma requires more than simply considering particle losses. One must also take into account the complex properties of the wave sustaining the discharge, for example, its dispersion and field configuration, and determine how the wave energy is transferred to the discharge. Thus ECR plasma has become a quasi-separate field of experimental plasma research, with many favourable results. For ion source engineers the interest in electron cyclotron resonance plasmas essentially arises from their efficient wave coupling, robustness, versatility, flexibility and also the fact that, in spite of their low pressure, these plasmas can be used to generate substantial concentrations of charged particles by achieving high degrees of ionization with little input power. All these experimental advantages are now recognized and conterbalance the theoretical difficulties inherent to plasma physics and its instabilities. In any case, all other ion sources dealing with magnetoplasmas also encounter troublesome situations.

1.3

1.3.1

COLLECTIVE PLASMA PHENOMENA

Macroscopic electrical neutrality and microscopic deviations from neutrality

A basic property of a plasma, which is a consequence of collective interactions among the charged particles, is the tendency toward electrical neutrality. If, over

26

SPECIFIC ELEMENTS OF PLASMA PHYSICS

a given volume of the plasma, the density of electrons should differ appreciably from the positive ion density, large electrostatic forces will come into play. As a result, the charged particles will move rapidly in such a manner as to approach a condition of charge equality. The order of magnitude of the electrostatic fields that would result from a departure from electrical neutrality over an appreciable volume may be obtained by considering, for instance, a typical homogeneous ECR plasma in which the density of both ions and electrons is 1012 particles cm-3 . Suppose that in some manner all the electrons present in a sphere of plasma of radius r cm were suddenly removed; the strength of the resulting electrostatic field E , as derived from Gauss’s law, would be

Q 1 E = - - a----r l 4n£0

(MKSA)

where Q is the value of the charge removed. If ne is the electron number density of the plasma, then Q = - n r nee when e is the electric charge. Upon substituting this result into the above equation, it follows that rn ee E = ------. ne0 If the radius of the sphere is taken as 1 cm, then it follows that E = 6 x 105 V cm - 1 so the field strength has an enormous value. A departure of only 1 % from charge equality would give rise to a field of 6000 V cm - 1 near a sphere of radius 1 cm. Although on a macroscopic scale the distribution of positive and negative charges in a plasma must be the same, there are microscopic deviations from neutrality. As a result of the thermal motion of the charged particles there will sometimes be an excess of positive charges and sometimes an excess of negative charges. The reverse situation will, of course, exist in a volume near to an electron. The difference between the positive and negative charge densities will obviously be greater in the immediate vicinity of any given charged particle and it will fall off with increasing distance. This leads to the conclusion that every charged particle may be regarded as being surrounded by a cloud having a net charge of opposite sign. The uniform distribution of these microscopic ‘clouds’ throughout the plasma then leads to the macroscopic neutrality. As for the length of the microscopic non-neutral plasma, it is called the screening or shielding distance (or Debye length). For instance, it is a measure of the distance from an ion

COLLECTIVE PLASMA PHENOMENA

27

beyond which the cloud, with a net negative charge, screens off the Coulomb field of that ion from the field of another ion moving nearby. It is for this reason that the term ‘shielding distance’ is used. Due to their attractions and repulsions the electrons may be forced into oscillatory motions. This phenomenon, called electron plasma oscillation, is characterized by the electron plasma frequency. Since the number of charged particles in the shielding volume is quite large, a particle can interact with many others in traversing a distance equal to the shielding distance. For this reason, as will be shown below, the effect of so-called long-range interactions is more important than that of short-range encounters in producing large-angle scattering of any given charged particle as it passes through the plasma. The combined effect of all the particles within the shielding volume is called collective interactions.

1.3.2

The relative importance of the collective parameters

For describing classical collective effects in a plasma, there are three principal characteristics: the Debye length A d , the plasma frequency cop and the longrange 90° particle scatterings (also called Spitzer collisions) which are due to many small Coulomb deflections of the plasma particle and which are different from binary collisions. In a relatively quiescent plasma these collective phenomena are well understood, and quantitatively determined. We will develop these concepts and comment on their importance in ECR plasma. Unfortunately not all types of ECR plasma are quiescent, and many of them are turbulent plasmas where nonlinear processes are caused by the generation of non-controlled internal waves and different instabilities. The origins of the turbulence, which is characterized by internal fluctuating fields, are multiple and it is out of the scope of this book to study the state of plasma turbulence which will only be briefly described in section 1.3.8. However, it is important to inform our reader that, for instance, the thermalization of the plasma particles, i.e. the randomization of the particle drifts, can equally well be obtained through 90° Spitzer collisions (quiescent plasma) as through fluctuating random fields (turbulent plasma). In the latter case the Spitzer collisions are obscured by the turbulence and become negligible. Similar ambiguities exist for the often debated plasma diffusion through the magnetic field. The classical collisional diffusion cannot explain the anomalous plasma losses. Therefore it is not worthwhile to follow heavy mathematical developments in order to improve a formula by a factor of two or three when sometimes several orders of magnitude separate theory and experiment. However, even if sometimes the Spitzer collisions are obscured by turbulence (which is also a collective plasma effect but not yet quantitatively describable) the Debye length and the plasma frequency concepts remain unquestionable and their effects have to be considered in ECRIS plasma.

28

1.3.3

SPECIFIC ELEMENTS OF PLASMA PHYSICS

General properties and relations between the Debye length A # and the plasma frequency ujp

1.3.3.1 The Debye length A D [53]. A macroscopically neutral collection of charged particles has certain basic properties that are fundamental to its analysis as a plasma. Perhaps the most important of these are the electrostatic shielding of the Coulomb interaction force between charged particles and the spontaneously nascent plasma oscillation. We have seen that, although a plasma is macroscopically neutral, it is locally non-neutral on some sufficently small microscopic scale called the Debye length A D, and its volume is the Debye sphere. Inside the Debye sphere, i.e. over a distance of A e l e c t r i c fields (even very strong fields) are allowed to exist, but beyond A d the fields are completely screened as we will see in the next paragraph. Among the electric fields, inside a Debye sphere, electromagnetic wave fields with a wavelength X < A d are plausible. Moreover electrostatic oscillation fields due to the spontaneously nascent plasma oscillations at cop are present. The plasma frequency cop is such that we can write the following relation: 2n A d ~ vth — where vth is an average thermal velocity of the oscillating electrons inside the Debye sphere. The above relation stipulates that the maximum elongation of the electronic oscillations cannot become larger than a Debye length. 1.3.3.2 The electron plasma frequency a)p. A plasma behaves in some situations as a system of coupled oscillators. One basic oscillator frequency of the plasma state is the plasma frequency cop, defined as

(CSG) with f p ~ 1 0 4 v ^ H z , where n is the number of particles per cubic centimetre, and m is the electron mass. It is customary to call cop the plasma ‘frequency’, even though it has units of radians per second. In MKS units, one obtains

or

(Op = 56.4Vn rads

(M K S A )

COLLECTIVE PLASMA PHENOMENA

29

n(m-3) — ^

Figure 1.3.1

Plasma frequency against electron density.

E(X!)

Zi Figure 1.3.2

Xo Plasma slab at t = 0.

In figure 1.3.1 we plot cop versus the plasma density. This graph is very useful because the plasma frequency is often used as a means of specifying the electron density in a plasma. 1.3.4

Particular properties of the plasma frequency

Quasi-certitudes (QC) and subsequent assumptions (SA). For an unbiased critique of the properties let us consider as (QC) those assumptions which are no longer debated in well known books of plasma physics, and as (SA) those which are either still debated or ignored. 1.3.4.1 cop and the plasma (or Langmuir) oscillations (QC). If electrons in a two-component plasma are displaced slightly from their equilibrium position Xo, they will experience a force that seeks to return them to X0. When they arrive at the equilibrium position, they will have a kinetic energy equal to the potential

30

SPECIFIC ELEMENTS OF PLASMA PHYSICS

energy of their intitial displacement, and will continue past X 0 until they have reconverted their kinetic energy back to potential energy. The frequency of this simple period harmonic motion will be at cop, the plasma frequency. This phenomenon is known as an electron plasma oscillation or Langmuir oscillation. In all plasmas, quiescent or turbulent, there is a natural trend for Langmuir oscillations which are always nascent somewhere in the plasma bulk (figure 1.3.2). 1.3.4.2 o)p and EM wave propagation in plasmas (cut-offfrequency) (QC). If we should attempt to propagate a plane monochromatic wave through the plasma medium, the solutions to the wave equation will be of the form e^kz~m^ where k is the wave number In f co — = — = k. vp vp vp is the velocity of propagation in the plasma defined as 1

Vp~ T H ^ ' As long as £ = £o(l — co2/co2) is positive, vp will be real and plane electromagnetic waves can propagate. If £ is negative, then vp and k are imaginary and propagating solutions do not exist. Since co2p is proportional to plasma density, the result is that, as the plasma density increases, a point will be reached where co2/(o2 > 1 and then propagation is cut off. Experimentally, this point is often observed in ECRIS and the plasma may very sharply cut off the transmission of EM waves through it as its density builds up. However, due to the presence of magnetic field, some exceptional propagations are still allowed in a magnetoplasma (see section 2 . 1 ). 1.3.4.3 The importance o f cop in ECRIS plasma; overdense plasma. The cut­ off property of the plasma oscillation is of paramount importance in ECRIS because the injected waves have to reach the ECR zone inside the plasma. If (op > corf the RF waves can be reflected (i.e. cut off) but they can also be absorbed by the plasma through nonlinear processes (SA). In this case we will see in section 2.2 that a turbulent plasma is possibly generated (SA). If one wants to avoid unknown processes and allow the microwaves to penetrate into the ECR plasma, one has to limit the plasma density somehow. In such a case the RF power, the magnetic field and the gas pressure are voluntarily matched to obtain adequate wave penetration. Only then is it possible to transfer the wave energy efficiently to the electron in the ECR (QC). Otherwise ill defined transfer mechanisms occur (QC). When cop > corf one generally stipulates that the plasma is overdense.

COLLECTIVE PLASMA PHENOMENA

31

1.3.4.4 The basic mechanism o f the always nascent plasma oscillations (QC). To introduce the concept of plasma frequency, consider a uniform plasma slab. Assume that at t = 0 all the electrons in the interval x\ < x < xq are displaced to the left of x \ . Further assume that ions are fixed. The excess charge to the left x\ is hoe(xo — x\). From Gauss’s law, this produces a field at x\ in the —x direction of magnitude E (x 0 = — (x0 - x i ) eo (figure 1.3.2). This field exerts a force on the electrons at x \, the equation of motion for which is m ex\ = eE (x\) = ^ - ^ - ( xq — x\). £o In terms of the relative displacement, £ == x0 - x\ This equation may be written

£ | + ( ^ ) f =0. a t1

\ m e£o/

This is the harmonic oscillator equation, with solution %(t) = A exp(icopet) + # e x p (—icopet) where

is the electron plasma frequency frequency is

A similar definition for the ion plasma / z72.2M 2e2n0\xl/2

(Dpi =

\ m tso

)

where z is the ion charge state. Thus we see that the plasma frequency is a natural frequency of oscillation* for each species in the plasma. As is well known from the theory of harmonic oscillators, the oscillations can be excited in response to an external stimulus with frequency less than or equal to the natural frequency. Thus each plasma species can respond to a perturbation with frequency co < cop. Because ^ pi

32

SPECIFIC ELEMENTS OF PLASMA PHYSICS

electrons are able to respond to much higher-frequency perturbations (i.e. microwaves) than are ions. Therefore in ECRIS plasmas only cope oscillations are basically important. 1.3.4.5 Amplitudes o f the oscillating electric field at plasma frequency (SA). We know that A D ~ vth/2ncop and, according to the definition of A #, over a distance equal to A D strong oscillating fields are allowed. Beyond, due to the screening effect, these fields are completely damped and only a global temperature 7\ associated with a potential Uth = K T je , remains observable on a macroscopic scale. Hence we can write that the local oscillating field at cop integrated over a distance A D yields this macroscopic potential [54].

o Replacing A d by its value we find the handy formula

£ (Vcm -‘ ) ^ 2 x 1CT3\ / K T (eV,n(cm^K The formula shows that the amplitude of the oscillating field increases with .Jn (i.e. with (op) and %/T. In figure 1.3.3 we represent some values of Ep for interesting ECRIS electron densities and temperatures and emphasize that fields of the order of kilovolts per centimetre are present inside the ECR plasma but only over microscopic distances of the order of the Debye length. However, for an electron the Debye sphere is an infinite universe and inside this volume the oscillating Ep fields can be in competition with the other driving forces of the electron, namely the local electric fields, the magnetic fields and the ECR forces [55]. 1.3.4.6 (op oscillations, Langmuir waves (QC) and Bernstein waves (QC). We have seen that the amplitude of the (op oscillations can reach high values. It is quite understandable that such oscillations generate some propagating waves. Electrons moving into the oscillation zone with their thermal velocity will carry information about the oscillating fields. The existence of plasma oscillations has been known since the studies of Langmuir in the 1920s; however, it was not until 30 years later that a detailed theory was published by Bohm and Gross [56] explaining how waves linked to cop would propagate and how they could be excited. The waves are sometimes called Bohm-Gross waves, but in general they are termed Langmuir waves (LM waves). It is the thermal motion of the plasma electrons which causes their propagation. The frequency of the wave Colm is given by

COLLECTIVE PLASMA PHENOMENA

33

t * oE £ Q

g cc H O Lii LU

n PLASMA DENSITY (cm’3) Figure 1.3.3 Eip oscillating electric field amplitude as a function of plasma density at some values of the electron temperature. Typical conditions for various sources : 1, singly charged positive ion ECRIS; 2, multiply charged ion ECRIS [54].

vth is the thermal electron velocity: vfh = 3K Te/ m e and k is the propagation vector of these waves (see section 2.2). Langmuir waves are not EM waves, but ES waves. They cannot propagate outside the plasma. The k vector is oriented parallel to the electric wave field and its value acts upon the wave frequency. Thus the frequency is linked to the local plasma density and temperature. We can replace vth by other plasma characteristics, for instance cop and A d \ one would then find another relation coL M = a > j[l+ 3k2A 2D]. As the (Op oscillations are always and everywhere spontaneously nascent in the plasma, LM waves are also everywhere spontaneously nascent (SA); they play therefore a leading role. However, in a magnetoplasma the electrons are orbiting on their Larmor radii p i and gyrating at coc while moving into the oscillation zone. The waves thus generated according to Bernstein take into account this information [57] with m = 1, 2, 3, —

00bn = m2(°c D + (M p /vc)2 + F m (k 2p l )] where F m (k2p 2) depends on a Bessel function and K is the wave number of the mth Bernstein mode. 1.3.4.7 Wave potential trapping; breakdown o f linear models in large-amplitude waves (QC) [58]. When we consider an electron in a large amplitude wave field we can no longer write that F = m x = eEo sin cot

(1.3.1)

34

SPECIFIC ELEMENTS OF PLASMA PHYSICS

since even when the wavelength is much less than L (where L is a characteristic length of the plasma) Eo can no longer be quasi-uniform (i.e. E0 presents necessarily some gradients in space). In the simplest, unidimensional case, grad E is a linear function of X ~ dE V E oc — X. dX At point X the electron is submitted to the new force ,d E 0 F = m'x = e E0 + X sin cot dX

(1.3.2)

and we determine X [ T d£~| eE 0 X — / \E 0 + X — sincuf = -(sincur) J I dX J mco2 which we put into (1.3.2) and find F = \eE0 sin cot \ +

e2 _ dEo . 2

;E q—— sin cot mco2 dX

(1.3.3)

An average force due to grad E appears when one integrates over one period T j T

(F)

- /o

T

eE 0cotdt H

e dE sin 2 cot dt. E0 — j eEosi mco1 dX o

(1.3.4)

Since / sin 2 cur = 1/2 and the first term of (1.3.4) is zero the average force o becomes 1 e2 d(E 0)2 (1.3.5) (^> = — mco1 4 mco2 dX A force F always derives from a potential \/r and subsequently (F) = egradVf where grad^ =

4mcu2 V (£ 02)

with

eE\ * = 4

or

E2 ^ = 0 .4 x lO11- ^ co*

(MKSA)

(1.3.6)

COLLECTIVE PLASMA PHENOMENA

35

Electron moving slower than

Electron moving faster than wave first goes to the right and then to the left, etc...

~^ Crest move at phase velocity v = CO/k

Figure 1.3.4 A potential wave showing trapping of charged particles. The particle motion described is relative to the wave phase velocity co/k ( Ee < eE2/4mco2). The trapping is conducive to nonlinear electron-wave interactions [49].

Thus in large-amplitude spatially non-uniform wave fields, we find pseudopotentials \fr (also called ‘Gaponov and Miller’ potentials) which might trap electrons if their energy is smaller than \j/. Then the electron-wave interaction becomes necessarily nonlinear since the electron not only follows the oscillating field but also rebounces in a moving potential trap. The breakdown of linear theory occurs clearly when the bounce frequency cot, becomes larger than co. Hence the interactions of electrons with all large-amplitude waves become nonlinear (figure 1.3.4). This can occur in the resonance zones where largeamplitude EM waves are converted into large-amplitude ES waves (Langmuir and Bernstein waves— see section 2.2.4). 1.3.4.8 The ponderomotive forces and the cop oscillations (QC). case, for a single electron one can write (1.3.5) as follows

In a general

(1.3.7) If one introduces the electron density (i.e. cop) one finds

(MKSA)

(1.3.8)

which is also called the ponderomotive force (just another word for nonlinear behaviour). Note that this force holds not only for Langmuir waves but also for EM waves [59], that it is proportional to the gradient of (E 2) and since the drift for each electron is supposed to be the same [59] the force is proportional to co2p /co2 i.e. to the plasma density (SA). The higher the amplitude of the waves and the ratio of co2/co2 1 the stronger the nonlinearities (SA). For co2/co2 1

36

SPECIFIC ELEMENTS OF PLASMA PHYSICS

linear behaviour is plausible; for (*)^/(o2 » 1 nonlinear behaviour is probable (SA). Hence the time scaling of cop, o)c and o) will play a determining role in the collective plasma behaviour (SA). When the plasma waves become nonlinear the ponderomotive forces push the plasma, causing local density depressions called cavitons (see section 1.3.8 .2 ) where ES waves are trapped (not to be confused with electron trapping). These waves form an isolated entity called also envelope solitons whose solutions are possibly describable by the nonlinear Schrodinger equation or by the Kortewegde Vries equation [59]. Note that the cavities are dug by the ponderomotive force, in three dimensions, and the cavities now trap the energy of the waves which according to (1.3.8) increases the ponderomotive effect even more and enforces the density depressions etc, leading to a caviton collapse which liberates the energy and then contributes to the electron heating (see section 2.2) (SA). 1.3.5

Ap,

Debye length or screening distance (QC)

1.3.5.1 Debye length, Debye spheres and the existence o f a true plasma. By definition A D is the distance it takes for a plasma to shield itself from an applied continuous electric field. In other words it represents a length within the plasma over which these electric fields are excluded: thus A D is also a minimum dimension of a neutral plasma and subsequently one admits that a uniform homogeneous neutral plasma is quasi-unipotential. Only when an inhomogeneous plasma contains parts with different densities, particle velocities or temperatures linked together by gradients is it possible to imagine differences of potentials. Electric fields are therefore mainly located between the plasma and walls, in ‘sheaths’, which are not homogeneous plasmas. We can also say that A d provides a measure of the distance over which the influence of the electric field of an individual charged particle is felt by the other charged particles inside the plasma. The moving particles arrange themselves in such a way as to effectively shield any electrostatic fields within a distance of the order of the Debye length and this shielding of electrostatic fields is a consequence of the collective effects of the plasma particles. Let us compare the potentials of a charged particle in a vacuum and inside a plasma. The electrostatic potential of an isolated ion of charge q is

In a plasma, electrons are attracted to the vicinity of the ion and shield its electrostatic field from the rest of the plasma. Similarly, an electron at rest repels other electrons and attracts ions. This effect alters the potential in the vicinity of a charged particle. The potential of a charge at rest in a plasma is given by

COLLECTIVE PLASMA PHENOMENA

37

Figure 1.3.5 Debye length against n and Te. where A D is the Debye length. It can be shown that

A f, =

( ^ r ) '

(MKSA)

A o =740 {( T- \) ' » where n is the density of electrons (or ions) (cm-3), T is the temperature in (eV), A d is in centimetres. The Debye length, which is a measure of the sphere of influence of a given charge in a plasma, is directly proportional to the square root of the temperature T and inversely proportional to the square root of the electron number density, ne. In figure 1.3.5 we plot the Debye length versus plasma density and electron temperature for possible ECRIS application. The relation 0 = (q /r ) exp(—r / A D) describes a Coulomb potential at small r (r « A/)) but decreases much more rapidly than a Coulomb potential for r ^ A d ■ Thus the electrostatic potential arising from a microscopic nonuniformity in density— for example, the location of a charged particle— is shielded by a cloud of other charged particles within a distance A d • However, in order for this argument to be valid, the number of particles inside a sphere of radius A D must be substantial. We may compute the number of particles inside a sphere of radius A D to be

4

.

4

»«„ = 5 4 A „ » „ = 5Jr

(e tK T \ yl ^ j »o.

It is required that this number be not too small, or the shielding effects predicted by the theory will not take place. A simplified condition for good shielding is

38

SPECIFIC ELEMENTS OF PLASMA PHYSICS

that the average interparticle spacing be considerably less than the Debye length. This condition may be expressed as

The conditions for the existence of a ‘true’ plasma can be summarized as the following inequality:

where L is some characteristic dimension of the plasma. Thus we note again that the Debye length obviously prescribes a lower limit on the macroscopic dimensions (L) of a plasma, by definition. For L < A D the medium would behave as a collection of free charges dominated by mutual two-body interactions, which is in contradiction with the concept of a plasma. 1.3.5.2 Debye length, individual particle motions and collisional scattering. When the condition of the existence of a true plasma is satisfied, the motion of a charged particle is determined by collective, long-range interactions with many particles, rather than by the sum of many individual two-body interactions. These collective interactions can be represented by fields which can be calculated with electromagnetic theory using the charge and current distributions. The dominance of these long-range collective interactions over local, twobody interactions is fundamental to the analytical characterization study of a plasma. It allows us to deal with the problem of calculating individual particle motion in electric and magnetic fields, rather than the infinitely more complex problem of simultaneously calculating all the mutual interactions among the ~ 1015 particles that constitute the ECRIS plasma. Only when interactions take place in which the particles approach each other closer than A D can these events be treated separately as collisions. Again let us note that plasma oscillations also introduce collision-like scattering when ES fields, randomly generated by the Langmuir oscillation over distances of the order of A d , reach very high values as shown in section 1.3.7. Thus the random fluctuations of plasma turbulence can also play the role of scattering collisions. 1.3.5.3 The Debye length, the sheaths and biased electrodes in ECRIS. When a boundary surface is introduced in a plasma the perturbation produced extends only up to a distance of the order of A D from the surface. In the neighbourhood of any surface inside the plasma there is a layer of width of the order of A £>, known as the plasma sheath, inside which the condition of macroscopic electrical neutrality need not be satisfied. Beyond the plasma sheath region there is the plasma region where macroscopic neutrality is maintained. The sheaths are automatically created by the ambipolar diffusion (see section 1.7) when a

COLLECTIVE PLASMA PHENOMENA

39

plasma is in contact with a solid surface. Since the electrons move faster than the ions, there will normally be a tendency for electrons to leave any given region of the plasma more rapidly than do the ions. At the floating potential of a solid surface in contact with a plasma, there is no net current flow to or from the surface, and so the rates at which positive and negative charges reach the surface must be equal. This can be achieved only if there is a sheath of plasma near the solid surface where the number of electrons exceeds that of the ions. Within this sheath, which is somewhat analogous to the oppositely charged cloud surrounding a charged particle, electrical neutrality is not preserved [145]. The concept of the Debye length may also be useful in considering the effects of various probes or other solid elements that are immersed in a plasma. Potentials may develop or may be applied to these devices. The conditions under which they perturb the plasmas can be obtained by considering that sheaths of the order of a Debye length will develop if the probe is floating, but may not develop if its bias potential is of the order of the local potentials present in the plasma. Bias potentials (dSheath ~ A D(V / K Te) xt21) greater than the local potentials often result in thickening of the sheaths and a consequent increase in the perturbing effects inside the unipotential plasma. In ECRIS, electrodes are not necessary. However they are occasionally employed outside the hot plasma zone, on the magnetic axis. If the electrode floats, it becomes negative with respect to the hot plasma and creates an electric field E\\B. Thus it reflects electrons leaking along the axis and attracts ions arriving on the plasma edge and forms a Bohm-type sheath [60] with possible oscillations and a special potential profile [145]. When the source works at very low gas pressure and few ionizations occur, a negatively biased electrode saves leaking plasma electrons and its effect is beneficial for plasma maintenance since the impinging ions generate secondary electrons on the electrode which are reinjected in addition into the plasma. This effect is then improved when the electrode is negatively biased. Under these conditions it can replace the first stage of the ECRIS (see section 6 ). However biased electrodes near the cylindrical wall of the ECRIS may have damaging effects since they favour the ignition of arcs across the magnetic field lines. 1.3.6

Long-range coulomb scattering (QC)

1.3.6.1 The relative importance o f Spitzer collisions [61]-[64]. The longrange encounters (or distant collisions) represent the multiple interactions of a single particle with many other particles such that the net effect is to give a large-angle scattering, i.e. about 90°. In principle, these long-range encounters can extend over the whole distance over which the Coulomb forces are effective, i.e. the whole of the plasma. However, in order to make possible the calculation of the cross-section (or equivalent mean free path), it is necessary to choose a distance, given by the Debye shielding length, within which interaction of a

40

SPECIFIC ELEMENTS OF PLASMA PHYSICS

(M)Z-|e

\l/ Figure 1.3.6

Z2e

Coulomb scattering.

charged particle with other charged particles may be supposed to occur. Beyond this distance, the plasma may be regarded as being electrically neutral, so that the particle under consideration is not affected by Coulomb forces. Spitzer has promoted Chandrasekhar’s [61] idea that in strongly ionized plasma (ECRIS plasmas are in this category) the cumulative deflections due to small-angle scattering are actually larger than those due to single large-angle scatterings [62], [63]. These cumulative small-angle scatterings resulting finally in a 90° deflection are then supposed to be the most active scattering mechanism inside the plasma. It must be recognized that this is only true in relatively quiescent plasmas. For instance, when the ECR plasma is inside a stabilizing min-B structure (see section 1.6), Spitzer collisions are probably important, whereas in a plasma with strong fluctuating fields the effects of the turbulence yield more scatterings than the cumulative deflections and the Spitzer collisions become negligible. 1.3.6.2 Expressions fo r Spitzer collisions in the laboratory system [63]. Consider a particle of charge n e and mass M whichpasses a scattering centre of charge zie at an impact distance b. The particle feels a deflecting force of magnitude z \ Z i e 2 /b 2 for a time of the order of 2b/v. Hence, it suffers a momentum deflection of i ( * „ ) = £ !« £ ? “

bl

v

= W

bv

(COS)

(1.3.9)

where v is the particle velocity (figure 1.3.6). The corresponding angular deflection is A (M v)

2Z \ Z i e 2

This deflection angle is in the plane defined by the incident and scattered directions. If the particle passes through a plasma of density n , these deflections are in random directions and hence A0 = 0. However, (A # ) 2 is not zero and there is a random walk, in angle, away from the original entry direction. The total square deflection in a distance X is directly proportional to the number of scatterings and is given by the expression [63]

COLLECTIVE PLASMA PHENOMENA

41

bmax=KD bmm (1.3.11)

The upper limit on b recognizes the fact that electrostatic shielding screens out the effect of charged particles beyond the Debye radius and has the value KT ^

= t

o

= A /)*

(L 3-12)

The lower limit is taken to be the classical distance of closest approach defined by e2 M v2 bmin

2

or bmin

2e2

(1.3.13)

~ M v2 '

It follows that the mean free path for a random walk scattering through an angle of magnitude jr/2, i.e. (A# ) ~ 1, is given by

X9°

%Ttn(z\Zie2/ M v 2)2 \n ( h D/b min)'

(1-3.14)

Now an ‘effective cross-section’ for a 90° deflection by means of multiple collisions can be defined in the usual manner *90° = — . 71(790°

(1.3.15)

Hence

= i81 (

W

1' " ( t )

< C G S )'

( 1 ' 3 1 6 )

For most ECRIS plasmas \n(A o /b min) has a value between 10 and 20 and is quasi-insensitive to plasma parameters. It is also called the Coulomb logarithm and is often expressed by In A [62], [64]. However the reader should be cautioned that this is not a cross-section in the usual sense since there is not a linear relation between deflection angle and number of scattering centres but rather a square-root dependence. The quantity

42

SPECIFIC ELEMENTS OF PLASMA PHYSICS

A9 o° is a measure of the depth of penetration required for a multiple scattering through an angle of magnitude 7t / 2 . If a particle passes through a thickness which is 1 0 0 times greater, it does not suffer 1 0 0 deflections through 90° but only about ten of these. Nevertheless, a 9 o° is a useful quantity in comparing the effects of Coulomb scattering and other collisions. The cross-section for single Coulomb scattering is obtained from the usual Rutherford formula. It is

' ~ * ( ^

) 2

< ccs)

Hence, the multiple scattering exceeds single scattering by the factor In(bmax/b min) and the deflection through large angles via multiple small-angle collisions is about two orders of magnitude more probable than deflection via a single-angle collision. 8

1.3.6.3 Spitzer collision times and frequencies in the centre o f mass (CM) system. The characteristic time required for a 90° deflection in the CM system by multiple small-angle collisions depends on the relative velocity between particles Uf = v\ — v2 and the reduced mass M ' = m \m 2/m \ + m 2 . Then, instead of (1.3.16) one obtains

e' - = ( ^ ) 2i inA

,mksa)

a 3 -i7)

and we can write

y 90° =

r 90° =

A 9o° / £ / '

with

V90o = nCfgQo U'

where v9 o° is the collision frequency. Note that until now we assumed that the scattered particle has an arbitrary mass M and we ignored the electron mass m\ and ion mass m2. Only the charges z\ and Z2 were specified. This is not important for ee and ei collisions because the deflection in the laboratory system is comparable to the deflection in the CM system when m\ < m2. Thus for electron-electron scattering (ee) and for the scattering of electrons on ions (ei) the above expressions are also good estimates of the characteristic time for 90° deflection in the lab system and one finds that v ^ 0 ~ v9 q0 and ~ r ^ Q. Calling these characteristics Spitzer frequencies and times xsp, good handy formulas then give for ee, ei and ii collisions [51]:

COLLECTIVE PLASMA PHENOMENA

10

n(crrt'3)

43

1CT

Figure 1.3.7 Self-collision time as a function of electron energy and density. The dark zone is for high-charged ion ECRIS.

v£jo = T -> = 5 x 10~6 n (c
ln [A o /fc ]/r/

< =

(eV)

(1.3.18)

~ z4(me/ m i ) l/2(Te/ T j ) 3/2v,90o.

In figure 1.3.7 we plot the Spitzer ee collision frequencies for typical ECRIS plasma parameters.

1.3.6.4 Spitzer collisions fo r ion-electron scatterings. We have, for ions on electrons, A0ie ~ (me/m i)A 0 . Thus the test particle must travel approximatively m i/m e times the distance (^ 9 0 °) required for a 90° deflection in the CM system before a 90° deflection occurs in the laboratory system. Consequently the characteristic time for a 90° deflection in the lab is about m i/m e times the characteristic time for a 90° deflection in the CM system. Thus

44

SPECIFIC ELEMENTS OF PLASMA PHYSICS

1.3.6.5 Momentum transfer in the Spitzer collisions [65]. The energy transferred from particle 1 to particle 2 in a collision can be found from the collision kinematics (conservation of energy and momentum). For an initial energy of E$, for particle 1, the energy transferred, A £ , is AE Am \m i 9 { 9C\ — sirr I — I . E0 ( m i + m 2)2 \ 2/ Multiple small-angle collisions that produced a 90° deflection in the CM system would cause a change in energy that can be estimated from the above equation with 0C = 90° AE ^ 2m\m2 E0

( m i + m 2)2 ’

Thus like-particle collisions result in the transfer of about half of the initial energy in a 90° deflection time. For electrons scattering on ions or ions scattering on electrons, the fractional energy transfer in a 90° deflection is only about m e/m i. Hence the characteristic time for energy transfer, rm, is related to the 90° deflection time by ee

m T [i m

^

ee

90

,^ r ei 90°

~ rt 90° il -

xei ~ xmie - , m

\ m eJ M i

T e>

me

The above formulas are valid for cold plasma (z = 1; Te ~ 7}). For ECRIS, one has to take into account the values of z and (Te/T i)3/2 in the Spitzer times for 90° deflection. 1.3.6.6 Consequences o f the Spitzer collisions in ECRIS: cold ions, hot electrons and collisionless plasma. We see that electron momentum transfer times equal the Spitzer times, thus electron heating (energy equipartition) through ee Spitzer collisions seems much easier and faster than ion heating through ei Spitzer collisions (r*1 > r ^ Q). A number of important conclusions follow immediately. The electrons in a ECRIS plasma exchange energy with each other and can reach an equilibrium distribution on a rather short time scale. Let us now consider the hierarchy of characteristic times in usual ECRIS plasma: we note that vee and vei are much smaller than (oce and a)RF (which are generally between 2.5 and 20 GHz). Hence they do not impede the electron gyromotion. Therefore ECR plasmas are termed collisionless plasma, and this remains true in most cases even when inelastic and elastic collisions are added to the Spitzer collisions (see section 1.4).

COLLECTIVE PLASMA PHENOMENA

45

The electrons transfer energy to ions, or vice versa, on a time scale that is (m i/m e) times longer than the time required for the electrons to equilibrate with themselves. For example, in an ECRIS plasma with a density of 10n cm - 3 at Te = 10 eV, vee lies between 105 and 106 s_1. Thus electron thermal equilibrium is reached on a very short scale, a few microseconds (which is in general shorter than the electron lifetime) whereas ions would be heated by the same electrons on a time scale of about milliseconds. If their lifetime is shorter than these values they will never be heated at all by ei collisions and will remain cold. The contrast increases for more energetic electrons: when Te ~ 1 keV one finds vee between 102 and 103 s_1. Only if the electron lifetime could match these values would it be possible to obtain an electron thermalization through ee collisions. As for the ions, their lifetime is absolutely too short to be heated by the electrons. We now understand why in most ECRIS plasmas hot electrons are mixed with cold ions. The electrons which are energized in the ECR do not have the time to heat the ions. Thanks to this cold-ion property the ECRIS may provide ions beams with small emittances (see section 4.1). However, there is also another interesting property in plasmas with energetic electrons and cold ions: as the ee collisions between energetic electrons are rare, their collisional diffusion will be weak and their confinement will be possible, whereas the ii collision rate, which at a first glance looks much smaller than V9 Q0 , can become the main scattering agent because the ion temperature is very low (v^qo is proportional to 7] _ 3 / 2 and to z \ Z i ) and highly charged ions might increase the scattering [6 6 ]. Of course, all the above properties hold only if no other collision phenomena prevail in the plasma. Thus, when one ignores all the turbulent fluctuations, mainly the 90° collisions provide the randomizing effect on particle motion, and when one considers the case of electrons drifting under the influence of an external RF field these collisions tend to disorder the directed drift motion. In the field direction the equation of motion is

me

dve

du it

~ mevP = —eE —

r 90 ei °

where the last term describes the rate of dissipation of ordered momentum due to collisions. Hence the motion of the electrons will only be impeded in ECRIS plasma when vel ~ cdrF which might occur at very low RF frequency and/or when cold electrons populate the plasma (Te 100 eV, 7} ~ 3 eV), where only the long-range (90°) ion-ion collisional damping with V£cident of the order of 104 m s - 1 (i.e. some 10 eV of incident ion energy) can be efficient since the thermalized ion energy is of some electronvolts (see section 1.3.6 .6 ). The slowing down is then obtained over distances of some 10 cm. Under these conditions the super-thermal ions, after a few ion-ion plasma collisions, are thermalized (in some 1 0 “ 4 s) and trapped among the ions of the support gas; hence they become cold and Maxwellian and are confined like the other ions. This property is utilized for the trapping of radioactive ion beams inside an ECRIS plasma (see section 6.5.2.2) where the effects of ii collisions dominate the other ion scattering effects (since the slow ions do not respond to high-frequency electric fields). A mathematical expression for this slowing down is given by Delcroix and Bers [6 6 ]. 1.3.7

Collective electron scattering caused by plasma oscillations and corresponding collision frequency u Up

1.3.7.1 Introduction to the concept o f the collective collision frequency v(Dp (SA). Classical collisions based on atomic physics and plasma physics processes are insufficient to describe all the collision-like processes inside an ECR plasma and especially when such a plasma is turbulent (for instance they cannot explain the anomalous particle losses in simple magnetic bottles). For these reasons, we propose a new global type of electron collision frequency v^p related to the always nascent cop oscillations. Such a global collision frequency can explain the ill defined diffusion coefficient V ± when one considers that V ± is proportional to vWp (see section 1.7). In fact, we propose non-classical collisions in order to ‘cover’ the unknown collective effects due to various instabilities or fluctuations which influence the electron motion. As it is impossible to track separately all these fluctuations, we will try to globalize them. For this let us emphasize that all the observed

COLLECTIVE PLASMA PHENOMENA

Figure 1.3.8 Electron v ^ collisions in strongly effervescent plasma.

47

The circles

represent Debye spheres inside the ECRIS plasma.

instabilities depend in theory somehow on o)p (and on the confinement system, i.e. coce). Thus instead of detailing the build-up of collective instability effects, let us rather identify the parameters which act on the cop oscillations which seem to be the basic trigger of these effects and which behave like (collective) collisions. We know that the growing wave instabilities cannot describe ‘quantitatively’ the plasma equilibrium but if we could evaluate an order of magnitude of the global collective collision rate (without detailing the instabilities) we would be able to predict a global plasma behaviour by writing balance equations. 1.3.7.2 Oscillating fields in the Debye spheres (SA). Let us consider the possible transit time of an electron passing through a Debye sphere where cop oscillations are localized (figure 1.3.8). By definition A D ~ vth (Op ~ = vthJP where Tp is the period of the cop oscillation. We have seen that the amplitude of the oscillating field E p reaches large values (figure 1.3.3). Subsequently, Debye spheres with oscillating fields are plausible electron scatterers. As the transit time of electrons through A o is ~ A o / v th ~ Tp, the electrons of the velocity distribution with ve < vth, will ‘see’ the oscillations and produce Langmuir waves but a group of swift electrons whose velocity is greater than vth, will traverse the Debye sphere in less than one period of cop, thus they will not even *seeJ one entire oscillation, but only random fields oriented in all directions, and they will be subjected to random kicks. After having crossed several successive Debye spheres (with nascent E p fields) their motion become

48

SPECIFIC ELEMENTS OF PLASMA PHYSICS

stochastic and not oscillatory. In ECR plasma, the electrons are also submitted to drifts, whose drift velocity is added to the thermal velocity (vD a E /B ). Under these conditions the stochasticity is enhanced. In short, one can consider that swift electrons suffer collision type deflections inside the successive Debye spheres they traverse and we assume that v(Dp is the corresponding collision frequency. Hence the conjugate concepts of Debye spheres and cop oscillations allow the hypothesis of v ^ , a type of collision frequency never mentioned before. Following our assumption to evaluate vWp we have to ask what is the corresponding mean free path k (1)p (i.e. how far from one oscillating Debye sphere will an electron drift before crossing another Debye sphere with oscillations knowing that the oscillations are not nascent simultaneously everywhere). We can only presume that Xa)p is larger than A D and therefore the time interval A t is larger than Tp and consequently v(J)p will be smaller than cop; this can be written % ~ ^(x)p! I n

with

T
vw . Consequently T < vei27t/cop and knowing vei and cop, one deduces T < 1 0 -5 . Conversely in underdense simple tandem mirror ECRIS (without min-R) the loss cone seems totally disconnected from the ei Spitzer collisions, and other measurements show that the lifetime of the electrons is ~ 1 0 0 times smaller than in the previous example. Hence in this simple mirror configuration one would find T ~ 1 0 -3 , and we stipulate that v ^ is now the dominating collision frequency since we cannot propose other classical collisions (table 1.3.1). Finally in small overdense tandem mirror ECRIS, the measured electron lifetimes are once more 100 times shorter (leading to T = 10-1) (table 1.3.1). 1.3.7.4 Relations between the effervescence and the stimulation o f plasma oscillations. Now, how can we link this range of T to physical processes in ECRIS? For this, as already specified, it is well known from the theory

V(op > CDce V(op > CDfj0unce

idem 0 + nonlinear wave conversions micro + macro-instable (bad B curvature) © idem © + nonlinear wave conversions 0 idem 0 + gradients © idem © + strong gradients

min- B excessive PRF, overdense

simple mirror large, underdense

simple mirror large, overdense

simple mirror small, overdense

10-4

< 10~3

10~3

10‘ 2

KT1

very small, very overdense

idem © + gradients (drift instabilities) ©

min-B small, dense

1 upper limit

vm„ > veN > Vei

idem © + micro­ instabilities ©

min- B large, underdense

V(op > Vei > VeN Vcop > 0)ce V(j)p CDfj0unce

Z vcoii ~ vmp

(Dp > CUc„ = (DRF

Vei -> VeN

vwp < vei EVcoll ~ Vei

(Dce = OJrf

10"5

Vcoll

spontaneous (local) ©

min-R large quiescent

lower limit < 1(T5

time scaling

ECRIS plasma

assumed stimuli for (Dp

off resonance no mirroring v±/vl{ ~ 1

nonclassical v cold e~ only

loss cone cold + hot e~ ± mirroring

V(op

nonclassical v v1/ v l > 1

less performant than © © ©

cold + hot e~ mirroring

t)X/V|| > 1

vei -> loss cone

classically

ECR plasma properties

q+

single

q+

low

q+

high

charge

q+ ion

Empirical calibration of the effervescence T in different ECRIS configurations with some typical characteristics.

T

Table 1.3.1

COLLECTIVE PLASMA PHENOMENA

50

SPECIFIC ELEMENTS OF PLASMA PHYSICS

-J ! STABLE

field lines

UNSTABLE

Figure 1.3.9 Schematic diagrams of magnetically confined plasma in regions where the plasma is hydromagnetically (left) stable and (right) unstable.

of harmonic oscillators, that the oscillations at cop can be excited in response to a given stimulus with frequencies of (Opfln or less. Therefore let us envisage a few plausible stimuli which are capable of causing ‘forced’ electron displacements (in addition to the spontaneous electron-ion separation of section 1.3.4 which is valid for minimum effervescence). Among the stimuli we note for instance (i) E fields due to instabilities (see section 1.3.9), (ii) E fields due to internal electron waves, namely those generated by wave conversions near or above the upper hybrid resonance (see section 2.3), (iii) grad is processes due to gradients of density and temperature (see section 1.5), (iv) grad B with /xgrad B forces and (v) curvature drifts in ordinary mirror configuration. (iii) and (v) apply opposite forces on the electrons and ions and seem to be particularly strong stimuli; (i) and (ii) are high-frequency waves stimulating only electrons. As soon as oscillations at cop are excited, these oscillations may trigger instabilities whose growth rates, frequencies and thresholds depend on the values of cop. Among the instabilities ‘micro-instabilities’ are observed in all ECRIS. They are mainly due to perturbations of the electron velocity distribution, and occur when 0.1 < co2/co2RF < 20, i.e. in underdense and overdense ECRIS [223]. Bad curvature of the B lines yields MHD instabilities (due to magneto hydro­ dynamics). ‘Macro-instabilities’ are violent MHD loss processes occurring when n K T //jio B 2 > 0 . 0 1 (i.e. when co2/co2RF ^ 1 ) but they are triggered mainly in simple magnetic mirrors and not in min-B traps (figure 1.3.9) (see sections 1.6.3 and 3.2.7). On the other hand, magnetic and electric gradients privilege electron-ion

COLLECTIVE PLASMA PHENOMENA

51

separations. Thus the smaller the plasma size the larger the gradients and the larger the effervescence. Note also that for overdense plasma nonlinear wave conversions are always observed and in addition in overdense plasmas the amplitude of the cop oscillations grows, delivering stronger electron deflections and a better efficiency of the collisions. Thus we emphasize the leading role of overdense plasma. Probably, the cumulative effects of the invoked stimuli are conducive to variations of T over five orders of magnitude (see table 1.3.1). Moreover T decreases with increasing electron energy since relativistic electrons pass through a Debye sphere in less than 10~ 10 s and then the cop oscillations cannot act on them, whereas in overdense cold electron plasma (Te < 10 eV) T becomes maximum (especially in nonstabilized magnetic structures). Thus, like the Spitzer collisions, v^p increases globally with ne and decreases with Te. Although the above arguments are only speculative, they are linked to ECRIS experiments. They allow one to establish a hierarchy of the agents of effervescence in ECR plasma and yield realistic orders of magnitude for these non-classical collective collision frequencies (inside non-relativistic ECR plasma) expressed by v„, ~ J T 104n'/2

where T is given in the table and ne is in cm-3 . 1.3.8

Fluctuating potentials and turbulence (SA)

1.3.8.1 Generalities. We always assume that a true thermal plasma is quasi­ unipotential (section 1.3.4.5) in contrast to plasma sheaths where steady-state potential drops are localized. Let us now consider that fluctuating potentials are somehow generated in the quasi-unipotential plasma. What the linear approach specifies is that the fluctuating potentials should not exceed a given thermal potential Uth = K T /e obtained by stating that the kinetic electron energy W*,-* — K T e is balanced by the potential energy Wpot = eUthAs in ECR plasmas the electron ‘temperatures’ are rather high, one can imagine the existence of large fluctuating potentials. The questions now are: where are they located? What are their frequencies and what are their amplitudes? Following Golovanisvsky’s assumption the fluctuating potentials are necessarily related to some characteristic plasma lengths and times [5 4 ]. The typical lengths are then chosen to be A d and the times are those of co~l . Under these assumptions the fluctuating potentials must be strongly

52

SPECIFIC ELEMENTS OF PLASMA PHYSICS

related to the Langmuir oscillations. This assumption leads to the initial location of the fluctuating fields inside Debye spheres, with field magnitudes E p ( V c m ) ^ cf ~ l O - y ^ T (eV)n( cm-3) as shown in section 1.3.4.5, for the Langmuir oscillation. However, the transition from the harmonic Langmuir oscillations to the sporadic fluctuations is not yet mathematically derived. What we know is that it introduces necessarily nonlinear wave transformations i.e. nonlinear plasma physics. In section 1.3.7 we tried to circumvent this difficulty through the concept of a global frequency v(Dp based on cop oscillations and empirical calibrations. Let us just recall that theoretical studies of plasma turbulence involving very complex nonlinear physics emphasize the leading role played by the Langmuir oscillations in the triggering of plasma turbulence. It is assumed that during the so-called parametric decay (see section 2 .2 ) the fluctuations may occur at frequencies much lower than o)p. According to these assumptions the Langmuir waves are transformed into plasmons, phonons, cavitons etc before establishing a state of turbulence which is precisely characterized by strong fluctuating potentials with a broad frequency spectrum in a macroscopically quasi-unipotential plasma. Now we will briefly invoke some of these modern theoretical concepts. 1.3.8.2 Various tentative descriptions o f plasma turbulence (SA). turbulence is still the realm of many ill defined concepts. (i)

Plasma

A first school of thought assumes that turbulence is the final state of the evolution of plasma instabilities which are the initial cause: therefore no turbulence occurs when instabilities are absent from the plasma. (ii) Other physicists think that all waves inside the plasma, and not only unstable waves, contribute to the state of turbulence. The plasma being a system of numerous coupled oscillators, favours wave-wave interactions, which open the way to nonlinear transitions. Thus a given largeamplitude wave can decay by generating harmonics which interact with the fundamental wave and with the other harmonics they form other waves at beat frequencies which interact with all other waves etc until a broad frequency spectrum is reached. The transition is often called parametric decay. In this case turbulence is possible without instabilities. (iii) In section 1.3.4.8 , we noted that in ECRIS plasma large-amplitude waves are created or injected into the system and this might trigger nonlinear phenomena. In addition (see section 2.2) these waves convert into different internal plasma waves, which might interact with the already present self­ generated waves. In any case, the assumption of coupled oscillators leads to great complexity as shown for instance by Chen [6 8 ]. Moreover the difficulties are not only mathematical but also semantic since we have no clear definitions of the interactions and words replace numbers. (iv) For an experimentalist, plasma turbulence is simply the opposite of plasma quiescence. In the latter, no conspicuous noise is observed when diagnostics

COLLECTIVE PLASMA PHENOMENA

53

are probing the plasma, but below what level the plasma remains nonturbulent now depends on the sensitivity of the probe. (v) These objections become marginal when one invokes the modern semantics proposed by the Russian school of thought which involves new quasi­ particles, strongly related to the always nascent Langmuir waves (and other waves); hence all plasmas are supposed to be somehow turbulent^ One assumes that the kinetic energy of a clump of electrons inside the E field of an LM wave is W^n = I nm ( ^ 2) while the wave potential energy (Wpot) is proportional to E 2. Here n is the electron density, (V ) the oscillatory electron velocity and E the amplitude of the electric field of the LM wave. We can always state that (Wpot) = (Wkin) but now the plasma is not only a mixture of electrons and ions. It is supposed to be a mixture of electrons, ions and ‘plasmons’ which are the carriers of (Wpot) whereas the usual plasma particles are only the carriers of As for instabilities they are a temporary result of (Wpot) ^ (W ^n)• In a general case, Golovanivsky even proposed that the stochastic fluctuations are of pure thermal origin and thus are unavoidable. For this purpose he simply assumed that [69] {Wpot) s {Wkin) ee n K T . In most models, the LM waves seem somehow responsible for the stochastic plasma fluctuations, but other plasma waves carried by other quasi-particles may contribute to the turbulence. 1.3.8.3 Plasmons, phonons and cavitons (SA). Nonlinear LM waves were predicted theoretically in 1972 and since that time numerous theoretical works have dealt with this topic [70]—[74]. In the physics of nonlinear waves in plasmas the waves themselves are considered as a collection of quanta with energy hco and linear momentum h k of each quantum. In the case of LM waves the quanta are called ‘plasmons’ while in the case of the ion-acoustic waves they are called ‘phonons’. The intensity of a plasma wave then is characterized by the plasmon or phonon densities. A homogeneous plasma wave field appears then as a plasmon or phonon gas of homogeneous density. The main characteristic of such a plasmon gas is that it is unstable and undergoes a cascade of nonlinear transformation if some specific conditions are satisfied. The first transformation, equivalent to parametric decay, occurs when

(1.3.19) Each plasmon decays to another plasmon with a smaller frequency col2 and a smaller wave vector k i 2 and in addition to a phonon with frequency eos and

54

SPECIFIC ELEMENTS OF PLASMA PHYSICS

wave vector k s so that ojL\

= a)i2 -f cos

(1.3.20)

k Li = k L2 + k s

(1.3.21)

where a)i\ and k L\ are the frequency and the wave vector of the initial plasmon. The above condition being easily satisfied, the plasmons immediately generate phonons which continuously reduce the plasmon energies (frequencies). Since the frequency of an LM wave colm = yjco2 + \ k 2vfh decreases whereas the plasma parameters cop and vth remain constant, the wave vector diminishes considerably. Subsequently the plasmons begin to ‘condense’. Thus the plasma is filled by aplasmon condensate and a phonon gas. At thisstage we can consider that thefrequenciesof the plasmon gas andthephonon gas already exhibit a broad spectrum. The energy accumulated in the phonon gas is small compared with the energy of the plasmon condensate because hcoi hcos. Therefore the phonon gas does not affect the plasma stability and ion sound waves are easily observable even in quiescent plasma. On the contrary, the plasmon condensate is basically unstable and leads to a second cascade of nonlinear transformation [69] which has collective aspects (in contrast to the instability of each individual plasmon during the parametric decay stage). This instability, which is referred to as the ‘modulation instability’, is such that the initially homogeneous LM wave background violently fragments. Thus the energy of the electrostatic oscillations is no longer uniformly distributed over the plasma but is rather concentrated in a plurality of localized bubbles. The plasma density inside the bubbles decreases automatically in such a way that the sum of the trapped oscillating electrical field pressure and of the kinetic plasma pressure is equal to the ambient plasma pressure. The initially homogeneous plasma density is thus spatially modulated by the bubbles. As a result of this second nonlinear evolution inside the plasma the wave energy is trapped in density cavities, called ‘cavitons’ which move freely in the plasma. The E field of the cavitons may possibly scatter the plasma electrons in a sporadic way and thus account for the turbulent behaviour. Note that the ponderomotive force (section 1.3.4.8) leads to a similar description of cavitons. 1.3.8.4 Plausible caviton characteristics in turbulent ECRIS plasma (SA). Following Golovanivsky [69] to estimate the characteristic time of ‘cavitonization’ one can use the expression for the increment of the modulation instability: Imod = (op(me/3 M )1/2(w /n kT e) 1/2

(s~')

(1.3.22)

where w is the energy density of the wave. In the case of an argon plasma m e/3 M = 4.5 x 10“ 6 so that in this example Imo(i = 2 x 107 s _ 1 and the caviton birth time is about W = 11Imod = 50 ns (1.3.23)

COLLECTIVE PLASMA PHENOMENA

55

which is short with respect to most plasma times in ECRIS. Hence, as the Langmuir waves are nascent everywhere in the plasma, the cavitons are also present everywhere in the plasma. Assuming that the above-given model of cavitonization is really what happens in a turbulentECRIS plasma, in order to evaluate some other values for cavitons one can use theformulas given by Nezlin [69]. For a 10 GHz multiply charged ion ECRIS: n = 3 x 1011 cm -3, Te = 500eV, P Rf = 500 W, one then finds that the density drop in a caviton with respect of the ambient plasma is Sn /n = wnkTe ~ 0.1. (1.3.24) The caviton diameter is D = 5 .5 A D(nkTe/w ).

(1.3.25)

Vcav < (kTe/ M ) '/2.

(1.3.26)

The velocity of a caviton is

According to these formulas the cavitons in a 10 GHz ECRIS contain about 1 0 % less density than the ambient density, are several millimetres in diameter and move with velocity less than 4 x 106 cm s - 1 in the case of argon plasma. The electrical field amplitude E cav inside a caviton can be evaluated from the pressure equilibrium condition S0E 2cav = SnkTe.

(1.3.27)

The field amplitude reaches values comparable to the amplitude of the ES oscillation at cop inside the Debye sphere. At this stage we can say that large oscillating fields, at frequencies lower than the initial cop, but generated originally by the cop oscillations, are concentrated inside quasi-particles called cavitons, which move inside the plasma. The cavitons, which contain the initial energy of the LM waves, constitute large energy reservoirs. They are also capable of heating the electrons after imploding, and thus provide a heating model. Therefore we consider that the modern theory of plasma turbulence proposes new approaches for many ECRIS problems but the model needs absolutely experimental verification before being accepted (today it is still considered as an outsider though new nonlinear approaches are urgently required). Note that the other nonlinear models, involving solitons, lead also towards cavitons. They remain mathematical approaches without providing better quantitative evaluations. After all, in the world of particle physics, since 1960, many new particles with odd properties have been invented in order to describe the matter and today nobody discards the models involving quarks, gluons, bozons etc. As the classical particles do not describe plasma turbulence well, why not consider odd

56

SPECIFIC ELEMENTS OF PLASMA PHYSICS

plasma particles if they prove to be better models? However, this is not yet ascertained since the new quasiparticles seem not to depend on the magnetic fields whereas ECRIS turbulence seems linked experimentally to a)ce/a)pe. In this case, plasmons associated with Bernstein waves (instead of Langmuir waves) or damping of these waves through the Sagdeev-Shapiro mechanism have been considered by Golovanivsky [73].

1.3.8.5 Turbulence and instabilities in ECR plasma. Many plasma physicists still assume that instabilities and turbulence are interconnected. Hence a chapter on collective plasma phenomena should incorporate studies of instabilities. These studies however, constitute a vast field of plasma physics (predicting instabilities which are not always observed and ignoring instabilities which were not predicted). The study of instabilities is tedious— and constitutes a separate discipline which is out of the scope of this book. Nevertheless, we cannot just ignore instabilities and leave them entirely to specialists. In sections 3.2.7 and 3.5.5 we will try to summarize some general aspects and point out a few particular cases related to ECRIS plasma, where one observes macro-instabilities (often called MHD instabilities) and micro-instabilities. In addition RF and drift instabilities might be excited. In short, like turbulence, instabilities are often unavoidable in ECRIS and one has to live with them. C ’est la v ie ... However, we will see that, if one wants to minimize them, one should utilize min-R structures, avoid overdense plasma, keep the ratio of RF power/source volume as small as possible and maintain a convenient plasma size in order to weaken plasma gradients.

1.3.9

An early experiment demonstrating some collective plasma effects involving u>p, u?ce and A d [78]—[80]

1.3.9.1 Resonant RFplasmoids [76]. In 1959,1 performed a series of amazing experiments with RF plasmoids which illustrate some enigmatic aspects of this chapter and which I briefly describe in the following lines. An RF generator with a frequency range 8-40 MHz and an RF voltage amplitude variable from 0 to 2 0 0 0 V was coupled to a pumped glass vessel with an RF loop or two metallic electrodes inside the vacuum (figure 1.3.10(a)-(d)). Langmuir probes measured the electron densities ne and electron temperatures Te against RF power, gas pressure and RF frequencies (3 x 106 < ne < 3 x 107 cm-3 ; 5 x 104 < Te < 2 x 105 K). When the gas pressure was decreased from 10~ 3 to 10~ 5 Torr a plasmoid with strongly limited contours was built up in the vessel. Its size decreased with decreasing pressure (i.e. the distance from the plasmoid towards the wall increased). This was already known previously

COLLECTIVE PLASMA PHENOMENA

57

Figure 1.3.10 Different plasmoids obtained when coRF ~ o)p. G, RF generator; P, plasmoid; E, metallic electrodes; S, Langmuir probe; W, Wilson seal; V, vacuum pump; g, grid; A D, Debye length.

[75], [77]. The plasmoid was supposed to be generated by a multifactor effect [77]. Let me now summarize the new discoveries. (i)

(ii) (iii)

(iv) (v)

When the plasmoid was formed, it was possible to reduce VRF to practically 0 V whilst the plasmoid was maintained unaffected (as if a much stronger VRF was applied) (figure 1.3.10(a),(b),(c)). The plasmoid took more or less the shapes of the container walls (several plasmoids in several glass vessels with one RF generator (figure 1.3.10(d)). The probe measurements yielded ne and Te values such that the corresponding Debye length A d oc y/T Jn was always smaller than the distance from the plasmoid to the wall (i.e. smaller than the sheath (see section 1.3.5.3)). The plasmoid diameter decreased to a minimum roughly equal to A Dand then exploded (i.e. min plasma size ~ A d (see section 1.3.5.1)). The plasma density of the plasmoid was roughly equal to ncrdefined by (Dp = coRF (see section 1.3.3.2 and figure 1.3.11).

58

SPECIFIC ELEMENTS OF PLASMA PHYSICS

£ CD

10 ' CL

D I coce the plasmoid does not feel the presence of B\ the plasma resonance persists. (ix) When coce = corf = (ope (i.e. when B ~ (m/e)cope) the plasmoid disappears for weak values of E RF or diffuses in the container for high values of E r f . The plasma resonance is then dominated by the ECR effects. (x) Only when coce > copet does a plasma appear, which is trapped in the B mirror field (figure 1.3.13). Similar results are observed in cusped mirrors. This last experiment presumes that magnetic electron mirroring is only possible when p, = W ± /B is invariant and is not perturbed by plasma oscillations during its spiralling motion (see section 1.6.3). This point has to be emphasized because

60

SPECIFIC ELEMENTS OF PLASMA PHYSICS

it is never clearly stated in books on plasma physics: mirroring of electrons seems only possible when coce > cope. Thus, overdense ECR plasmas (cope > coce = coRp) are not well confined in a magnetic trap. This is particularly true for small, overdense plasmas in mirrors where ~ cope > coce (see section 1.3.7 and 1.3.8 .5). In this case Fp = eE p > Fmagn = ev x B, evidencing a lower B limit for confinement (see figure 1.6.10, later). A similar conclusion was drawn by Golovanivsky in 1994 [54] but it is based on a more theoretical rationale including stochastic collective oscillations inside a thermalized plasma.

1.4

1.4.1

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

Collision times and characteristic plasma times

1.4.1.1 Collision parameters. Collision processes are conveniently described by the concept of a cross-section which is the usual way to express the collision probability. However, cross-sections are not practical for immediate use in ECRIS. The most useful concepts related to the cross-section are the mean free path and the collision frequency. If the collision cross-section is a , the incoming particle travels a distance k = lmfp = —

no

(cm)

(1.4.1)

known as the mean free path, before it suffers a collision. If the incoming particle weretravellingwith speed u, relative to the target particle, it would travel onemean freepath in a time rc. The reciprocal of this timeinterval is the collision frequency r c_ 1 = vc = n o v . (1-4.2) In most cases the cross-section is a function of the velocity u, and the velocities of the target particles are thermally distributed. The effective collision rate per particle is the average value of the product of cross-section and velocity, i.e. vc = n ( o ( v ) v )

(s-1)

(1.4.3)

For many incident particles, the total rate of events per cubic centimetre per second is R = nin2(crv)it2-

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

Figure 1.4.1 The general behaviour of ionization cross-section ax (cm2) ionization rate coefficient 5, (cm3 s"1) recombination coefficient arec (cm3 s-1)

61

versus electron energy Et .

R contains (a v) also called the ionization rate coefficient when a = aion (figure 1.4.1). Si = {crionv) (cm 3 s-1). (1.4.4) The variations of 5, with the electron energy are much softer than those of oion and over a small range of electron energy. Si is often considered as a quasi­ constant value. Comparisons of 5/ with a rec which is the recombination ratio coefficient, gives an immediate idea of the dominant process (figure 1.4.1). 1.4.1.2 The hierarchy o f times in ECRIS [82]. The collision frequency v is the most convenient collision parameter in ECRIS because its value can be compared to typical plasma frequencies such as the cyclotron frequency coc, the Spitzer frequencies vei, vee and Va the plasma frequency cop, the bounce frequency cob in a mirror system and all kinds of wave frequency co introduced into or self-generated in the medium. In this chapter, among the collision frequencies, we will consider those due to the presence of neutral particles inside the plasma, namely the ionization, recombination and momentum transfer frequencies. To evaluate their respective importance let us sort out the most important frequency scalings— yielding a hierarchy of times in ECRIS. We have already seen in section 1.3 that when (D r f

^

o )p

the EM waves do not propagate normally in the plasma, which is then termed overdense. For particle collisions to have the time to occur, the lifetime of the particle in the plasma must exceed the time between two collisions \ T lif e \

—

^ lif e

^

^

c o llis io n •

62

SPECIFIC ELEMENTS OF PLASMA PHYSICS

When we consider other plasma times, for instance the passage of an electron through the ECR which has a duration of r ecr and we find that 1JEC r V 1 = Vec R < Vcollision then the resonance will be impeded by collisions. If the opposite occurs the ECR process is collisionless. If we consider the electron helical path in a magnetic mirror and we have collisions between two mirror reflections (bounce time) i.e. [*bounce\

—^bounce

Vcollision

then the mirror confinement— and the helical path— will be disturbed by collisions; if the opposite occurs the mirroring is quasi-collisionless. In general, whatever the type of collisions, when we have ^collision >

ce

the behaviour of an ECR plasma will be strongly modified and requires a detailed analysis. 1.4.2

Binary electron collision frequencies and free paths

In an experimental plasma study, the various binary collision processes among plasma constituents must always be taken into consideration so that their true effects on plasma behaviour can be determined. The binary collisions deal with encounters of one electron with one target particle (atom, ion). The large number of possible collision processes and their varying degrees of importance under different plasma conditions make it quite difficult to account comprehensively for all collisions. As many experimental and/or theoretical cross-sections are given with large error margins, we preferred to consider averaged values coming from different sources. Thus the main purpose is to assemble credible data for some of the more important electron collision processes in ECR experiments and to present these data in a form that facilitates studies. That is to say, the data are plotted as ‘collision frequency’ and ‘collision mean free path’ versus electron energy. This presentation permits the direct comparison of the collision frequency with other characteristic frequencies of the ECR plasma. On the other hand direct comparison of the mean free path with the other characteristic dimensions, Debye length, Larmor radius, plasma dimensions, wavelengths of applied signals and interaction region dimensions etc, is desirable. We present only collision data for electrons which may have an important influence on the basic behaviour of the plasma. Therefore, total, elastic, momentum transfer, ionization and excitation processes are considered for a wide range of electron energy, in commonly used support gases such as He, H 2 , N 2 and Ar. These examples yield typical orders of magnitude, which allow one

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

63

to consider more specific gases or vapours by comparing their specific crosssection with those of the common support gases. 1.4.3

Total electron collision frequency (figure 1.4.2) [82]—[85]

At the beginning, let us consider a low-power plasma with many neutral atoms and rather low percentage ionization. We start our presentation of electron collisions with the total collision frequency which is the total number of collisions per second per electron for all encounters involving either a strong change in direction or energy, or both, for the incident electrons. That is to say, if a beam of electrons with uniform velocity u f c m s " 1) covers a distance x (cm), the beam density n (cm-3) at the velocity v changes from the original density no to n = no e x p ( - N a x ) = n0 exp( - P cpox) = no exp(—vc) == no exp(—x/A) where each identity represents an alternative way of characterizing the collision probability, with N (cm-3) the density of target particle (3.54 x 1016 at 1 Torr and 273 K), a (cm2) the total collision cross-section, Pc (cm-1) the total probability of collision at 1 Torr and 273 K, v (s-1) the total collision frequency, A (cm) the total collision mean free path, t (s) = x /\v \ = x / v and po the pressure (Torr) 273/ T K. The relations between the parameters of the above equations are 2.83 x 10- 7 PC v Po

1.0 /P cpo. Figure 1.4.2 gives the total electron-neutral collision frequency versus electron energy for He, H 2 , N 2 and Ar. They are derived from well known cross-section data. Figures 1.4.3 and 1.4.4 show some specific total cross-sections for helium, hydrogen, alkali metal vapours and rare gases, allowing comparisons. It should be noted that, far from obeying the ‘billiard ball theory’, oei varies a great deal with incident energy except in the case of He and H 2 at very low energies. Nevertheless, atoms from the same column in the periodic table behave, on the whole, in the same manner. Thus the curves are very similar for the alkali metals on the one hand, and for the rare gases on the other. However, the effective cross-section of the alkali metals is a great deal higher than that of rare gases (because their electron clouds are more diffuse). Coming back to the usual support gases, some mean free paths are illustrated in figure 1.4.5. All the data are given for gas pressure equal to 1 Torr and can be immediately reconverted for lower pressures.

SPECIFIC ELEMENTS OF PLASMA PHYSICS

64

oc QC

e

g

CO

o< >§

O o 2 oQC o h- > O UJ _l

LU

—I

£ o

10*1

1.0

10

100

1000

ELECTRON ENERGY (eV)

Figure 1.4.2 The total electron-neutral collision frequency versus electron energy for H2, He, N2 and Ar at 1 Torr [82].

The general behaviour demonstrated in figure 1.4.2 is for collisions to increase with electron energy at lower energies and then to more or less saturate at electron energies above about 10 eV. However, Ar exhibits ‘resonance’ phenomena in the lower-energy range which are ascribable to the Ramsauer effect [85]. Globally we observe that for usual ECRIS gas pressures (10-810“2 Torr) the mean free path XT is not only very long with respect to all the other characteristic lengths of the plasma (Larmor radius, Debye length, wavelength, etc) but also even longer than the plasma dimensions. Thus one has to invoke the effects of the magnetic field resulting in spiralling electron motion with mirroring i.e. rebouncing electrons, which allows the electron to move over long distances before colliding with another particle.

1.4.4

Elastic electron-neutral collisions [82]-[84]

1.4.4.1 Angular scattering. We now single out elastic electron-neutral collisions from the total collisions. An elastic collision is defined as one which does not alter the internal energy state of the colliding particles (projectiles and target). In the case of an elastic electron-neutral collision, there is only a slight transfer of energy A E from the kinetic motion of the electron (mass m,

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

0 1

2

3

4

5

6

7

8

9

65

10

Figure 1.4.3 Total effective cross-sections versus the square root of the electron energy [87] for alkali metal vapours.

'/Ee /e V Figure 1.4.4 Total effective cross-sections versus the square root of the electron energy [87] for helium, hydrogen and rare gases.

66

SPECIFIC ELEMENTS OF PLASMA PHYSICS

1

10 ELECTRON ENERGY

100 >

Ee (eV)

Figure 1.4.5 Total electron-neutral mean free path versus electron energy for He, H2, N2 and Ar at p = 1 Torr [82]. velocity v) to that of the neutral particle (mass Af, velocity ~ 0) &E ^ — — (l/2 m v 2) M ao

(1.4.5)

where a 0 is the elastic electron-neutral cross-section and am is the momentum transfer cross-section for the electron-neutral collisions. Since inelastic electron-neutral collisions are only important for electron energies above several electronvolts (see section 1.4.5), elastic electron-neutral collision frequencies for He, H 2 , N 2 and Ar are identical to the total frequencies of figure 1.4.2 in the low-energy range. The equivalence is obscured for higher electron energies by the influence of the inelastic processes. It appears that elastic collisions are approximately equal to the total values for electron energies up to about 50 eV. At higher energies, the ionization collisions v* become dominant (see figure 1.4.8). The most important consequence of an elastic collision is the possible deflection of the electron. This effect is described in terms of a ‘differential’ cross-section I q(0) d£2 = /o sin# dO d

0 scattering angle

Figure 1.4.6 Forward scattering probability o{6) for electron-molecule collisions with different values for the kinetic energy of the electron [83].

i.e. it is a measure of the intensity of scattered electrons as a function of the scattering angle. The differential cross-section is related to ctq by

n In (1.4.6)

o o Angular scattering distributions were thoroughly discussed by Massey and Burhop [83] and these authors find that, aside from the diffraction maxima and minima, 7o is usually only slightly dependent on 0 for electron energies below a few electronvolts but they note that it becomes more and more peaked with increasing electron energy in the higher-energy range. In this latter case the elastic collisions do not strongly scatter the electrons (figure 1.4.6). Finally, for energies less than 1 eV, the de Broglie wavelength is much larger than the target. It is assumed that scattering is then isotropic and independent of the energy (a independent of (p). As for higher energies, the wavelength is small in comparison with the dimensions of the target, which tends to give a well defined shadow; only very small angles of diffraction occur.

1.4.4.2 Electron-neutral momentum transfer and electron-ion momentum transfer [82]. The frequency of pure e-N momentum transfer (at low electron energy) is shown in figure 1.4.7. When the incident electron suffers an angular deviation in an elastic collision with a neutral particle, it loses a fraction (1 — cos0) of its forward linear momentum; the momentum transfer can be described statistically in terms of a momentum transfer cross-section

68

SPECIFIC ELEMENTS OF PLASMA PHYSICS DC DC

O E > O zLLI D o

Figure 1.4.7 Electron-neutral momentum transfer frequency versus electron energy [82] (p = 1 Torr).

n 2n

-

i

f

(1 —co s0 )I00 sin# dO d0 = (1 —cos0)a0).

(1.4.7)

0 0

am represents the cross-section for a hypothetical collision in which the total forward momentum of the electron is lost, i.e. vm = N a mv is the number of mv units of forward momentum lost per second per electron and is denoted as the momentum transfer collision frequency. This characterization is useful in the study o f diffusion in plasmas with low percentage ionization where the e-N collisions are frequent. am can be calculated directly from (1.4.7), beam measurements of I q(0) being used. As discussed earlier, I q is essentially isotropic for lower electron energies, in which case equation (1.4.7) gives om & ao (diffraction maxima and minima have little effect on the average of (1.4.7). At higher electron energies, a m should fall further and further below a 0 with increasing energy due to the peaking of 7o about 0 = 0. In any case the electron-neutral momentum transfer collision at low electron energies plays a similar role in the weakly ionized plasma as the 90° electron-ion Spitzer collisions in the strongly ionized plasma. In low-electron-temperature plasma (Te < 10 eV), working at relatively high pressure (> 10-3 Torr), provided that fluctuating fields are negligible, the e-N collisions are responsible for randomization processes. In figure 1.4.8, we compare e-i Spitzer collisions and e-N momentum transfer collisions, at different hydrogen pressures for a relatively cold electron plasma, with density 108 < n < 1014. We see that above Te ~ 1 eV the Spitzer frequencies can become smaller than veN for gas pressures greater than 10“ 5 Torr emphasizing the important role played by e-N collisions in weakly ionized plasma. 1.4.5

Binary inelastic electron collisions [82], [86], [87]

When an electron of sufficient energy interacts with a target atom, molecule or ion, a significant amount of the electron’s kinetic energy can be transferred

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

69

Cl ro rn n M /| TEMPERATURE ENERGY FOR VFOR —1 loX/\ ELECTRON Vj (eV) Figure 1.4.8 Electron-ion momentum transfer frequency vei versus electron energy or temperature for singly charged ions with electron density (108n e~ + A + + e~ .

(1.4.10)

If thetarget is at rest and the incident electron has a kinetic energy E, the reaction can only take place if E ^ eVi (1.4.11) eVi (IP) being the ionization potential.

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

ELECTRON ENERGY (eV)

71

_i~

Figure 1.4.9 Ionization frequencies versus electron energy [82]. As can be seen from figure 1.4.9, the effective ionizing frequency increases rapidly once the threshold energy has been passed, as the conservation conditions are easily satisfied due to the ejected electron. The maximum values of a, are of the order of 10“ 16 cm2 and correspond, in general, to electron energies of the order of 100 eV (about 20 eV for alkali metals). After the collision one slow electron and one fast electron, which carries off the major part of the kinetic energy not used in the reaction, are generally present. The slow electrons have an approximately uniform angular distribution while the fast electrons tend to conserve the direction of the initial electron (see section 1.4.5.1). 1.4.5.4 Total ionization frequencies vt [82], [84], [86]. Our selections of total ionization frequencies u, versus electron energy are shown in figure 1.4.9. Experimental evaluations found by different authors are combined to give V; for electron energies up to 2 x 104 eV in He, H2, N2 and Ar. Some of the experimental results have been extended to higher energies through the use of the Bethe-Born theoretical expression: q i ( x — \n E

or

v / a —| ^ l n £ .

(1.4.12)

The ionization frequencies of figure 1.4.9 are total values which include the production rates of all possible charged species. In a unique collision singly

72

SPECIFIC ELEMENTS OF PLASMA PHYSICS

ELECTRON ENERGY (eV)

Figure 1.4.10

Ionization mean free path versus electron energy [82].

charged ions are in general produced much more often than multiply charged ions. Therefore the singly charged ion is the basic ingredient of the ECRIS plasma. Mean free paths are shown in figure 1.4.10. The effect of a Maxwellian distribution on v, is shown in figure 1.4.11. For that we have integrated the values of v, for Ar and H 2 over a Maxwellian electron distribution to give the curves of 00

n~(Te) -

J

f ( v )v j(v )4 n v 2 dv.

(1.4.13)

0 vj demonstrates the importance of ionizing collisions for Maxwellian plasmas even when the electron temperature (eV) is well below the ionization threshold. 1.4.5.5

Total excitation frequencies.

The basic reaction is

e~~ + A -* e~ + A + + hv.

(1.4.14)

if the target is at rest and the incident electron has a kinetic energy E , the reaction can only occur if E ^ eV+. (1.4.15) However, the probability of excitation remains very low close to the threshold energy E s, since it is difficult to fulfil the condition of conservation of angular momentum.

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

ELECTRON { jgM PERATURE

73

Figure 1.4.11 v,-, ionization collision frequencies in H2 and Ar versus electron energy; vi9 ionization collision frequencies in H2 and Ar versus electron temperature [82].

Electron excitation of ground state atoms and molecules is a very difficult phenomenon to analyse due to the multiplicity of possible final excited states, secondary transitions, the presence of metastable states and the occurrence of other inelastic processes. Thus, it is not surprising to find that the experimental data on excitation are rather limited. However, we are interested in the total excitation frequency over an electron energy range large enough to permit a meaningful evaluation of the relative importance of excitation in practical ECR plasma experiments. Figure 1.4.12 presents a compilation of excitation frequencies versus electron energy for He. We have chosen to present excitation measurements for He since they give one a feeling for the orders of magnitude of the phenomena [99]. The combined excitation curves are compared with vtot and v, in figure 1.4.12. Elastic collisions obtained by subtracting v, and vexc from vt are also presented. Vi and vexc are found to be quite important in the medium-electron-energy range where elastic collisions decrease substantially. Even with the uncertainty in the absolute values of vt and vexc, figure 1.4.12 shows that v, is dominant but suggests that vexc is at least as important as ve# for electron energies above about 200 eV. This suggestion indicates the limits of influence of excitation collisions. They do not play a leading role in the plasma behaviour of ECRIS but their presence

74

SPECIFIC ELEMENTS OF PLASMA PHYSICS

ELECTRON ENERGY

(eV)

Figure 1.4.12 Comparisons of collision frequencies in helium: vtotau ^elastic> ^ionization and vexcitation against electron energy [82].

explains some RF power absorption and the presence of optical radiations issuing from ECR plasma. 1.4.6

Momentum transfer collisions and runaway electrons [82], [88]

In addition to the binary collisions, one has to consider the collective long-range Spitzer collisions which are expressed by vei ~ 2 x 10“ 6nez(ln A ) / r / /2

(1.4.16)

where In A ~ 15; ne is the electron density (cm-3) and Te is in electron volts; z is the average ion charge (see section 1.3). We are now in a position to expand our discussion to the combined effects of all the collision processes treated herein. In particular, we shall consider two important points: (i) momentum transfer due to all electron collisions and (ii) the relative importance of electron collisions with respect to the other characteristic frequencies of a plasma. The effective momentum transfer collision frequency vm for a plasma can be deduced from the presentation of the combined binary collision frequencies and the electron-ion Spitzer frequencies versus electron energy as illustrated for H2 in figure 1.4.8. When electron energies are below a few tens of electronvolts, the momentum transfer from the forward motion of the electrons is entirely determined by electron-neutral and electron-ion collisions.

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

75

The momentum transfer collision frequency is equated simply to the sum Vm+ Vei (f°r a monokinetic electron beam) or (vm) + (vei) (Maxwellian electrons) evaluated by inserting measured values of electron (or ion) density, neutral pressure and electron energy or temperature directly into the appropriate figures. At higher electron energies, we must consider the momentum transfer ascribable to both elastic and inelastic collisions. Inelastic collision frequencies become comparable to the total collision frequencies at higher electron energies, signalling a marked decrease in elastic collisions. In addition, with increasing electron energy, the ‘forward scattering’ diminishes the momentum transfer collision frequency relative to both elastic and inelastic collision frequencies. This is true even though the ionizing collision contributes to the momentum loss of a fast electron without necessarily producing an angular deflection, because this loss is small with respect to momentum loss at higher electron energies. Therefore, we are led to conclude that the effective electron momentum transfer frequency will decrease with electron energy at the higher energies and that ‘electron runaway’ can occur to some extent for all ECR plasma conditions under which fast electrons are present [88]. The consequence of electron runaway is that, without the strong friction due to the momentum transfer collisions, a family of fast electrons can be decoupled from the bulk of the colder Maxwellian electrons of the plasma. This situation leads then to a two-electron-population plasma which in turn can generate the well known beam/plasma instability (see section 3.2.7.7). As, due to the ECR, the fast electrons are permanently produced, a permanent state of instability can be maintained. Note that for a heavy-ion plasma under good confinement conditions, the fast-electron family can lose some of its energy in multiply charged ion production. These inelastic binary collisions between electrons and ions can take away a part of the electron energy in a single encounter. However, as we will see later, their collision probabilities are not as high as those presented in this chapter and thus they do not change the basic plasma collisions. Finally, we must accept the idea of the presence of decoupled high-energy, runaway electrons in ECRIS plasma as soon as the gas pressure is lower than 10-3 Torr. Their number increases with decreasing pressure and increasing RF power. They are the generators of x-rays in the source, and as they do not feel the effects of collisions their diffusion is weak and their lifetimes are long. Their contribution to the plasma equilibrium is not always clearly established. An important question therefore remains: are the fast electrons in the tail of a Maxwellian type velocity distribution, in which case they are already the byproduct of the beam plasma instability, or are they really a separated group of electrons? The last suggestion is the most probable (see figure 1.2.3).

1.4.7

Quasi-collisionless confinement and anisotropy [82]

To demonstrate the utility of the figures of vc and k c, let us now apply them to a simple magnetic bottle ECRIS plasma obtained at 10 GHz and ascertain the

76

SPECIFIC ELEMENTS OF PLASMA PHYSICS

relative importance of collisions. The plasma is produced through the cyclotron interaction of electromagnetic waves with electrons in a static magnetic mirror. The plasma electrons are given a transverse energy and they then spiral along the gradients of the magnetic bottle. Typical operating conditions for less highly charged ion ECRIS are for instance an RF power of ~ 100 W at 10 GHz in a hydrogen gas at pressure po ~ 10~3—10~4 Torr, and a static magnetic field Bo which varies in the active region of the plasma from ~ 5 x 103 to ~ 2 x 103 G; corf and coce corresponding to B0 are in the region of 1010s_1. They are always higher than any collision frequency. Thus this plasma seems ‘quasi-collisionless’. The cyclotron acceleration of electrons occurs over a small axial distance in the ECR zone where a)RF — (oce. Downstream from this interaction region, the energized electrons are magnetically confined and can ionize the background gas. From figure 1.4.8, for H 2 , we find that v{ ^ 2 x 106 s-1 for po ^ 10-3 Torr, corresponding to a mean free path of ionization of A./ ^ 300 cm (figure 1.4.10). Thus Vi/(a)/2n) = 10~4 and ionization should practically never occur during the ECR and have very little effect in the interaction region. However, due and only due to the magnetic confinement fields the spiralling path of the mirroring electron can exceed the ionization mean free path. Then only, we would expect a background plasma to accumulate, which, in fact, is the case. We can also say that, due to the magnetic confinement, the electron lifetime in the plasma becomes longer than (v,-)-1 = r* ~ 5 x 10-7 s. Thus ionization can occur and a plasma can be created. For lower RF frequencies and higher gas pressures the conditions are easier. But it then follows that for gas pressures X times lower than 10-3 Torr the electron confinement has to be X times longer. This illustrates the necessity of better confinement, and ultimately more sophisticated magnetic systems for very low-pressure ECRIS (such as the multiply charged ion sources) are required. Let us reconsider the previous plasma at p = 4 x 10-4 Torr, with the following typical characteristics at steady state: n ~ 1011 cm-3 and Te ~ 10 eV. According to figure 1.4.8, the momentum transfer frequency vm < 106. As vce = cocel2 n we find vm/ v ce < 10-3 . The electrons will gyrate around the magnetic field lines ~ 1000 times before making a momentum transfer with an atom, and ~ 10000 times before suffering a Spitzer collision. Thus during a few microseconds the electron conserves the energy acquired in the ECR, and subsequently its velocity remains perpendicular to the B field lines. If the electron lifetime is only a few microseconds the electron trajectories will not be randomized (as expected in a classical plasma) and a strong anisotropy 1) will be observed. According to figure 1.4.8, for decreasing gas (v±/v\\ pressures and increasing electron energy, the anisotropy will even be stronger and thermalization of the electrons will not be reached, and this is what one observes experimentally. However, in some cases one also observes a threshold above which the anisotropy disappears (see section 1.3.7). The resultant isotropy (u_l ~ v\\) is accompanied by plasma noise and strong localized fluctuations

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

77

(AV) in the plasma. Then AV, due to some nonlinear processes, replaces the momentum transfer collisions, and rapidly thermalizes the electrons. Thus figure 1.4.8 serves only as a minimum indication of real momentum transfer since nonlinear effects are neglected whereas one knows that anisotropic velocity distributions are conducive to instabilities. Only in very stable multimirror ECRIS should the momentum transfer collisions intervene in the plasma balance. In such a case the Spitzer collisions are always efficient for cold electrons. For warm electrons when vsp A -\-h v — >A* + hv.

(1.4.19)

In the first reaction a cold electron is captured into the ground level and a photon is emitted. The electron may also be captured into an excited state. Recombination with double excitation. e~ H- A +* — ►A + e~ — > A + hv + hv .

(1.4.20)

During the first stage, the incident electron is drawn into an excited state of the atom and the energy available raises another electron of the same atom to another excited level (cf Auger effect or autoexcitation). After a certain time has elapsed, one of these electrons is ejected leaving the ion in its initial state (first possibility), or the two electrons fall to the ground state emitting two photons (second possibility). Figure 1.4.13 shows plausible values of radiative recombination rates a r for aluminium ions with different charge states from Z = 1 to Z = 13, compared with corresponding ionization coefficients S). Recombination in the presence o f a third particle.

~e + A+ + X

A+ X

(1.4.21)

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

79

Successive ionization rate coefficient S, and radiative recombination coefficient arec for aluminium from Z + = 1 to Z+ = 13 versus electron temperature CTe). Figure 1.4.13

eV

10 —

Figure 1.4.14

collisions.

—

(ocrec) ■ rad

100

1000

(o c rec +oc rec) rad dielectr

Recombination coefficients in oxygen [106]. The effect of dielectronic

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SPECIFIC ELEMENTS OF PLASMA PHYSICS

1.4.8.3

Ion-neutral collisions— charge exchange recombinations [89], [90].

If an electron encounters a particle X in the neighbourhood of an ion A+ , it may communicate its energy to this particle and slow down sufficiently to recombine with A+ . Instead of being emitted in the form of photons the recombination energy, E k + of this reaction is used to accelerate the third particle X. The probability of this occurring obviously depends on the nature and density of the X particles. The most considered process is dielectronic recombination (with X being a second electron). The corresponding recombination coefficient is ad- Figure 1.4.14 shows a r + against (Te) for oxygen.

A+ + B

A + B+

(1.4.22)

A captures an electron and B loses one. Thus, in general An+ + B m+ _ A(n—1)+ + B (m+\)+^

(1.4.23)

Here, A and B can be either atoms or molecules. Energy balance. Taking the above reaction as an example, the energy balance equation may be written as follows: total initial kinetic energy + ionization energy of A = total final kinetic energy + ionization energy of B.

(1.4.24)

In general, the ionization energies (£, ) differ little; as a result, the total kinetic energy varies very little in the course of the reaction. Furthermore, there is little exchange of impulse in the laboratory coordinate system, each particle more or less conserving its initial velocity. The condition defines a threshold energy

Es - ( E j ) B

{E j)A |

(1.4.25)

When (E t)B > (E t)A, the reaction can only take place above a certain minimum value of the relative velocity of the two particles. This is the case, for example, with H+ in molecular hydrogen H 2 (figure 1.4.15). The effective cross-section for neutralization (capture of an electron), designated by o\o or cr+o, thus increases to a maximum, which is usually fairly high (10“ 15 cm2 or more), and then decreases as the relative velocity of the particles increases. This type of charge exchange is particularly important for accelerated ion beams in a poor vacuum but it is not important inside an ECR plasma since the ions there are cold.

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

81

Figure 1.4.15 Non-resonant charge exchange cross-sections for H+ + H2 (experimental) (ions + molecules) versus ion velocity; resonant charge exchange cross-sections (theoretical) for He+ + He, 0 + + O, Ne+ + Ne, Ar+ + Ar, H+ + H, K+ + K (ions + atoms) versus ion velocity [90] (a0 = 5.3 x 10_9cm).

In ECR plasma another type of charge exchange occurs when ( £ /) * < ( £ « ) * .

(1.4.26)

In this case the energy threshold Es is zero, and under these conditions the cross-section a \0 is very large even for an ion with kinetic energy Ek = 0. This is true for instance for He+ in all gases (since the ionization potential of He is greater than that of other substances), and for any atomic ion in its atomic gas (Es = 0 ) which is the general case of ECRIS plasma. This charge exchange is called resonant charge exchange (figure 1.4.15) [90]. In this case, the variation in internal energy during the reaction is A E = Es. The time for this transition is t « h /E s. If a is the mean radius of the particles and v is their relative velocity, then a maximum probability for the reaction (that is, a maximum effective cross-section) would be expected at t / r = aE s/v h « 1.

(1.4.27)

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SPECIFIC ELEMENTS OF PLASMA PHYSICS

Experiments show that the relative velocity corresponding to omax does vary significantly with Es\ in particular, when Es ^ 0, this velocity is zero and then the colliding particles have all their time to make a charge transfer and the orbiting electron of the atom can jump to the ion and neutralize it. In conclusion, direct recombination of electrons and ions in ECRIS plasma is very rare, but the high cross-sections associated with charge transfer make this process one of the most important in ionized gases. One of the experimental difficulties arising due to this phenomenon is that, when heavy particles have been neutralized by charge transfer, they fly out to the walls since they can no longer be controlled by electric or magnetic fields. In the last example the loss is not dramatic because a cold A+ ion is replaced by an even colder B+ ion and if A+ and B+ are of the same gas the situation is not changed radically. However, when one considers a highly charged ion A z+ colliding with a neutral B, it loses its high charge and therefore the charge exchange becomes a crucial issue in multiply charged ECRIS where the highly charged ions are the ultimate goal. This point will be developed in more detail in the next section. 1.4.9

Collisions of multiply charged ions with electrons and atoms

1.4.9.1 Ionizing collisions. In ECRIS plasma, multiply charged ions (MI) are obtained with the help of two types of ionization. They can be produced by electron-ion collisions, where in each collision one electron is removed from the outer shells (the multiple-impact process, also called step by step ionization). In this case the impact energy has to be higher than the binding energy of the last electron to be removed. The other possibility is that a high-energy electron removes an electron from an inner shell, in which case a multiply charged ion can be produced by Auger processes and electron shake-off which are single­ impact processes. (IP) Ionization potential. An atom is composed of a central nucleus of positive charge surrounded by a cloud of electrons. These electrons are grouped in consecutive shells called the K shell (two electrons), L shell (eight), M (16), N (32) and so on. Each shell is divided into subshells. An electron belonging to an external shell is only weakly bound to the positive nucleus, owing to the screening effect of the internal shells, and a low energy is sufficient to eject it into the continuum and to transform it into a ‘free electron’. For such an electron the corresponding IP is of the order of a few electronvolts, IP are higher for bound electrons belonging to internal shells, and increase progressively from external shells to the K-shell. In the same shell, IP values of the different electrons are close together; from one shell to another (the external shell being empty), discontinuities appear in the IP scale. In a collision an incoming electron transfers energy only to one bound electron, and if the transferred energy exceeds the binding energy W , ionization occurs. W and the ionization potential (IP) = W /e are functions of the nuclear charge (e Z a )

83

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

50

100

z

Figure 1.4.16 Ionization potentials of elements [91]. The nuclear charge is plotted on the X axis and the ionization potential is plotted on the Y axis. The numbers on the curves indicate the ion charge multiplicity.

and of the quantum state of the electron. For example, the energy W of an electron of a hydrogen-like ion is eV ~ 13.6Z^. It varies within wide limits from 13.6 eV for hydrogen to 115 keV for uranium. The ionization potential for an outer electron is, according to Bohr’s theory,

(1.4.28) where R is Rydberg’s constant and a is the screening parameter of the nuclear field by the electron frame, which is a function of n and i, whose values are known, n , the principal quantum number (1, 2, 3, a positive integer), roughly defines the total energy of the electron and its mean distance from the nucleus. t is the azimuthal quantum number: 0, 1, 2, . . . , n —i roughly defines the orbit eccentricity. Formula (1.4.28) allows the outer-electron ionization potentials of all elements of the periodic system to be calculated. A famous example of such a calculation is shown in figure 1.4.16. It was derived in the 1960s by Carlson et al at Oak Ridge [91] and it gives the IP values of all elements, and charge states from 1 to 100. Discontinuities between successive shells of an atom can easily be seen as well as the discontinuities between rare gases and alkalis. We may also remark that an ionization in the K shell necessitates an energy of about 900 eV for Ne, 3.2 keV for Ar, 14.3 keV for Kr and 35 keV for Xe. 1.4.9.2 The partial ionization cross-section. The partial cross-sections characterize the different possible ionization channels. Let us consider collisions with z+-times-ionized atoms A z+. In addition to the classical single ionization model another possible mechanism of single-ionization— excitation and subsequent decay of the auto-ionization state—proceeds in two steps,

84

SPECIFIC ELEMENTS OF PLASMA PHYSICS

Figure 1.4.17 A conceptual Auger cascade leading to Xe20+ after ejection of a K-shell electron ([92]).

Az+ + e~ ^

(A z+T + e~ rilu (Az+) * A (z+l)+ + e~.

(1.4.29(a))

In this process, an incoming electron excites one of the inner electrons to a vacant level with higher n , leaving an unfilled ‘hole’ at a level with lower n. The decay of this strongly excited (auto-ionization) state is accompanied by ejection of one of the electrons. Another process yields globally a z-times-ionized atom in one collision with an electron A + e~ -> Az+ + (z + l)e~. (1.4.29(6)) Two such channels are known; Auger ionization and shake-off ionization. The former process is similar to excitation and decay of an autoionization state, except that, with Auger ionization, an inner electron is not transferred to one of the higher bound states but is detached. Excitation energy is removed by transition of one of the outer electrons to an inner vacancy. The energy that is liberated here is expended in detachment of one or more additional bound electrons. For instance in an Auger process one inner-shell vacancy produces two vacancies in the higher shell. Each new vacancy will in its turn be filled by transitions from still higher shells until all vacancies reach the outer shell. Such a vacancy cascade results in a multiply charged heavy ion [92]. A conceptual Auger cascade is shown in figure 1.4.17. An estimate of the contribution of the Auger process to stripping of argon ions by an electron beam with an energy of 20 keV made in [93] shows that this channel reduces the time required to attain an Arz+ by a factor of four to five. However, this case seems rather exceptional.

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

85

An additional helpful process is ‘electron shake-off’ in which outer-shell electrons are excited to the continuum due to a sudden change in the central potential as, for instance, caused by inner-shell vacancies [95]. Not much is known about the cross-section oz(E e) for the production of such an ion by an electron with kinetic energy E e in a single-impact collisions. Some crosssections have been measured by Schram et al and van der Wiel and calculations have been performed by van der Wiel et al and van der Woude [94]. They show that the relative abundance of the highly charged ions decreases rapidly with increasing charge. A K-shell vacancy becomes less effective for producing multiply charged heavy ions if we go to higher z. Finally, the hope for efficient ionization rates with single electron impact vanished after 1972. A review on K-shell ionization cross-section is given in [95]. 1.4.9.3 Ionization cross-section^(ICS) fo r successive collisions. Suppose that we are able to maintain an ion in a plasma system for a long time r where it is bombarded continuously by electrons of energy Ee of a few hundred of electronvolts. The ion suffers several successive ionizing collisions, each of them ejecting one peripheral electron, Az+ + e~ -► A(z+1)+ + 2e~

(1.4.30)

where z is the ion charge state. As a result of this process, the ion charge is increased by one after each collision. Thus, despite a weaker electron energy Ee, very high z may be obtained; all electrons having a binding energy less than Ee can be ejected. Early experiments performed by Redhead [96] have demonstrated the possibility of producing ions Xe10+, Cs10+ and Ba10+ with an electron beam of only 250 eV energy. Later Donets et al gave accurate ICS for N, C and Ar around E e = 2.2 keV [97], [98]. It then became clear that the successive collision ICS is much greater than the single-collision ICS (see figure 1.4.18) and therefore successive collisions are the basic ingredient for multiply charged ion (MI) production. Many theoretical works have been devoted to the computation of cross-sections cr(Ee) for successive ionization. Recently, experimental data on electron impact ionization cross-sections for atoms and ions ranging from hydrogen to uranium were compiled and given, in graphical form, as a function of the electron impact energy by Tawara and Kato [99]. Some selected theoretical data were also included. Thus hundreds of data are now available. A comprehensive review of the subject of electron impact ionization was published recently [100]. To handle the ionization processes more easily, a number of empirical formulas for calculating the ionization cross-sections have been proposed by different authors. In particular the formula derived by Lotz for removal of a single electron in successive ionizations is now widely used [102]. Younger and Mark in [100] have reviewed empirical formulas of ionization cross-sections. Other convenient formulas are proposed by Muller et al [101].

86

SPECIFIC ELEMENTS OF PLASMA PHYSICS

O cm2

Figure 1.4.18 Single-impact ionization cross-section cr0z compared to successive-impact ionization cross section zz~i,z against electron energy (argon). It has recently become recognized that on increasing the ionic charge of the ions, other ionization channels tend to play a certain role. Among them, the excitation auto-ionization and resonant recombination double auto-ionization processes contribute significantly to the total ionization of heavy alkali-like and alkali -earth-like ions. In such cases the choice of the dominant ionization channel is difficult; otherwise the step by step ionization is overwhelming. 1.4.9.4 The multiply charged ion (MI) production criterion and the dominant ionization channel [103]. As seen, each of the ionization channels (seen in 1.4.9.2 and 1.4.9.3) can be characterized by cross-section c r ^ 2(ve), so that the transition of an ion from charge state z\ to charge state zi through a given channel requires, on average, a time = [ n e ^ l ( v e)ve] - 1

(1.4.31)

where ve and ne are the electron velocity and density and x indicates the type of ionization channel. ECRIS electrons in the simplest case have a Maxwell velocity distribution, and, since the reaction cross-section is a function of ve, to obtain the reaction time for a given channel, formula (1.4.31) should be averaged over the Maxwell distribution with electron temperature Te. As a

ATOMIC PHYSICS BACKGROUND IN ECRIS PLASMA

87

result, the average reaction time becomes a function of the electron density and temperature, and can be expressed through the ionization coefficient S (see section 1.4.1): ^ S ^ 2(Te)

(1.4.32)

=

(a ™ (v e)ve)Te.

(1.4.33)

Thus, according to (1.4.33), the ionization time r* Zj for a given channel is determined by ne and Te. If the confinement time of ions in theplasma r, is such that rtrMf > z ^ 2, the transition z\ -*■ Z2 takes place and we obtain as condition for the process zi zi

nert > [S% 2(?;)]

-1

(1.4.34)

called the MI production criterion which fixes the required plasma parameters ne, r,• and Te. For a hot and turbulent plasma, single collisions might be the strongest channel for relatively less highly charged ion production whereas for ECR plasmas, with long particle confinement, the step by step ionization channel provides very highly charged ions. In this last case, which is paramount for ECRIS, we can omit the superscript (x) since we choose the ionization channel with successive charge increase z z + 1. Thus, we have to determine only the value of SZlZ2(Te) which is commonly referred to in the literature as ^z\zi^Te) — Sziz+\(Te)

or Sz- \ —z(Te)

or Sz(Te).

(1.4.35)

1.4.9.5 Analytical approach to the step by step ionization criterion [102], [103]. Let us consider the so-called Lotz formula proposing a total ionization crosssection where the summation is made over all subshells and which leads for many practical cases to a somewhat simplified value of the ionization coefficient SZlZ+\(Te) expressed in cubic centimetres per second and Te in electronvolts

[ 102], N

SZlZ+l(Te) ~ 3 x 10-6r - 3/2

(.qj/R j)[ei(-R j].

(1.4.36)

7= 1

In formula (1.4.36), j is the number of the subshell in the outer shell, Rj = W j/T e is the ratio of the binding energy in the y'th subshell to the electron temperature, et is an integral exponential function, qj is the number of equivalent electrons in the j th subshell, and N is the number of subshells in the outer shell. A calculation based on equation (1.4.36) of the dependence of the ionization rate of oxygen on Te is shown in figure 1.4.19. As can be seen from the graphs, the ionization coefficient has an optimum electron temperature T°pt, increasing with the desired ion charge z and, even at the optimum temperature, the ionization

88

SPECIFIC ELEMENTS OF PLASMA PHYSICS

Sz,z+1, cm3 sec-1

Ionization rate of oxygen versus Te. The numbers on the curves indicate ionization multiplicity. Figure 1.4.19

rate drops sharply with increasing z. In any case one needs a plasma electron temperature that is optimum for the highest required z. Generally this is obtained with an electron temperature of the order of five times the threshold energy T °p
as shown in figure 1.5.4. Limiting our considerations to fields with small curvature the field at any nearby point can be approximated as Bz & Bzo = Bz(z = zo) (1.5.23)

Small curvatures implies After some developments, one finds the drift velocity of the guiding centre along the curving field line, and in particular, the drift velocity of the guiding centre in the direction perpendicular to the plane in which both the field and the curvature vectors lie. This result can be generalized to 2W\\B x R c Vr = --e B 2R?

(1.5.24)

The curvature drift is oppositely directed for ions and electrons, producing a net current and charge separation.

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SPECIFIC ELEMENTS OF PLASMA PHYSICS

Figure 1.5.5 E || B: no magnetic effect on the electron motion. Without collisions, the average electron velocity is in quadrature with E. No wave-electron energy transfer occurs. By analogy with (1.5.22), the centrifugal force that drives the curvature drift is

2W\\(B • V)B

2W\\Rc

eB4

e B 2Rc '

(1.5.25)

This force arises from the v\\ motion along the curved field line. 1.5.3

Motion in coordinate space containing RF fields and magnetic fields

1.5.3.1 RF fields parallel to uniform magnetic fields (figure 1.5.5). In this case, B does not act on the electron and the case is similar to B = 0. The motion is parallel to E with an initial velocity i>o || E. F = m x i = eE sin cot + 6 x\ = uo H

eE [cos 0 — cos (cot + 0)] mco

yielding

X \

=

X o

+

vo H

eE mco

cos t

t -

eEo [sin ^ — sin (cot + 0)] mco*

B X l = A + [ v o + ( U ) ] t - — [(pf(t)]. coz The elongation is due to an average velocity (U) plus an oscillation term proportional to 1/co2 with phase dependence. It is very important to note that (U ) is in quadrature with the force F. Thus the electron cannot absorb any RF power! This is the main problem of RF heating. In order to energize the electron one has to somehow change the

MOTIONS OF CHARGED PARTICLES IN ECRIS PLASMA

101

Figure 1.5.6 E _L B: motion of interest takes place in the jcijc2-plane. A cyclotron resonance becomes possible. The orientation of the field vectors.

Figure 1.5.7 The electron orbit in a low-frequency electric field perpendicular to a static magnetic field, co 0 can

102

SPECIFIC ELEMENTS OF PLASMA PHYSICS

then be written

where

and for convenience

^ 3

Q = e B /m

(1.5.26)

i)\ = —l>2£2

(1.5.27)

i)2 = oc sin cot + v\Q

(1.5.28)

qE a = — m has been written as Q.

(1.5.29)

Figure 1.5.8 The electron orbit in a high-frequency electric field perpendicular to a static magnetic field co Q. That magnetic field is directed out of the page. The analogue computer solution of equations (1.5.27) and (1.5.28) for the case when co/Q = 10. The major motion is circular at the cyclotron frequency Q [110].

Figure 1.5.9 The electron orbit in a sinusoidal electric field perpendicular to a magnetic field co « Q. The magnetic field is out of the page. The analogue computer solution of equations (1.5.27) and (1.5.28) close to cyclotron resonance [110].

MOTIONS OF CHARGED PARTICLES IN ECRIS PLASMA

103

Figure 1.5.10 The electron orbit at cyclotron resonance co = Q. The analogue computer solution of equations (1.5.27) and (1.5.28) at cyclotron resonance [110].

(1.5.27) and (1.5.28) can be solved simultaneously to yield

where 0 is relative to the initial conditions. The jci- and ^-com ponents of the orbit can be found by integrating (1.5.30) and (1.5.31) to give jcj = x? + — sin Qt + — (cos Qt — 1) 1 Q Q (1.5.32) x 2 = x? + — sin Qt -b — (cos Qt — 1) 2 Q Q (1.5.33) Now the first three terms on the right-hand side of (1.5.32) and (1.5.33) are concerned only with the initial displacement and velocity of the charged particle. In order to consider a specific case, let us pick the inital displacement and velocity of the particle so that we consider only the last terms in equations (1.5.30) to (1.5.33). We can then rewrite these equations in the form (1.5.34) v2

=

— —r (cos Qr — cos cot)

(1.5.35)

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SPECIFIC ELEMENTS OF PLASMA PHYSICS

a f £2 \ — 7 3 7 ( — cos Q t cos cot I (1.5.36) co2 - Q2 \ Q co ) oc ( o) . ^ \ x 2 = —7— 7 3 7 I — sin Q t - sin c o t ). (1.5.37) co2 - Q 2 \ Q / In order to discover the major characteristics of the orbits described by (1.5.34)(1.5.37), we will consider various ranges of the ratio co/Q. Low-frequency electric field co + Q)t

2aco

1

(1.5.40)

1

s ,n 2 {“ ~ m ‘ c o s 2 (" + a>L

( l '5'41)

MOTIONS OF CHARGED PARTICLES IN ECRIS PLASMA

105

The orbit described by (1.5.40) and (1.5.41) is a circular gyration at the frequency (q) + Q )/4 tt whose radius varies sinusoidally at the beat frequency (co — A typical orbit is shown in figure 1.5.9. 1.5.3.3 The appearance o f the gyromagnetic or so-called cyclotron resonance [110]. When co = Q, the solution of the equation of motion given by (1.5.30) and (1.5.31) becomes indeterminate. It is therefore necessary to go back to the original equations of motion and resolve the problem for this case. If we set co = Q in (1.5.28), we can write the equations of motion as v = — t>2 =

ol sin

(1.5.42) (1.5.43)

£2t +

By solving these equations simultaneously, we obtain v\ = i>? cos

— d? sin £ l t

oc

(sin Qt — Qt cos Qt)

(1.5.44) (1.5.45)

Integrating (1.5.44) and (1.5.45), we obtain for the displacement of the particle

After a sufficient length of time the last terms in (1.5.46) and (1.5.47) become dominant and the charged particles move in circles of ever increasing radii. 1.5.3.4 Energy gain in the resonance. During this spiral motion the velocity of the particle continually increases. Since its kinetic energy increases the particle absorbs energy from the RF electric field. This is the most important result of this oversimplified case. A typical resonant spiral is shown in figure 1.5.10. In practice the size that the spiral attains will be limited by physical factors explained later. 1.5.4

Electron motion in time space

In this paragraph we tackle the single-electron motion in the ECR with more details. As the issue is very complicated we start with the simplest cases and gradually introduce more complexity. Hence at first we reconsider the motion in the ECR plane, then the ECR in a homogeneous magnetic field (V B = 0 ) with phase conditions between the

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SPECIFIC ELEMENTS OF PLASMA PHYSICS

gyrovelocity and the E field. Then we introduce the relativistic mass effect and finally we consider the more general case of ECR in a magnetic gradient (V # / 0), i.e. in a magnetic trap. For this very involved case we try to summarize the theoretical approaches developed between 1962 and 1970 in the ECR group of the CEA (French Atomic Energy Commission) headed by Consoli. We will consider in particular Canobbio’s analytical theory of a single passage of one electron through the ECR zone (which is no longer a plane but a slab) [111], [112].

1.5.4.1 The importance o f the phase between the electron gyrovelocity and the right-hand component o f the RF field. In section 1.5.3 we saw that inside the resonance plane (* 1 * 2 ) when corf = ^ = coce the electron velocity continually increases and thus the electron absorbs energy from the RF field in the resonance. This is possible when the spiralling electron motion and the RF field are contained in the jcjX2 -plane, but this is particularly true when the gyrovelocity and the rotating RF field are in synchronization, and the electron gyrates in the same direction as the RF field. We will see that such a situation is obtained when a right-hand polarized RF wave (R wave) propagates along * 3 with a phase velocity v^ equal to the thermal velocity of the electron (because in this case the electron moves in the frame of the wave) and the gyrovelocity and the rotating wave field E are always in the same plane X\X2 . Another equivalent situation is obtained with a standing (R) wave and an electron with no thermal velocity along * 3 . In both these cases, if the gyrovelocity is in synchronization with the rotating wave and the phase between them is fixed and favourable for acceleration, the electrons are speeded up and this is precisely what happened in the previous paragraph where V± increased linearly with time and independently of the phase 0 inside the ECR plane (0 was supposed fixed for ever). However, these favourable circumstances are not realistic because, for different reasons, after a while, the phase 0 can change and the acceleration of the electron will then be altered. For instance we know that for 0 = 7r / 2 (force and velocity in quadrature) the electron does not absorb any energy of the E field. Even worse in phase opposition n > 0 > 7r / 2 the electron will be retarded instead of accelerated. Thus the resonance conditions described in the previous paragraph are incomplete and the phase conditions have to be taken into account; another description of the ECR with another coordinate system (where 0 is explicit) must be considered. This will be obtained with a system of rotating coordinates.

1.5.4.2 The wave fields in rotating coordinates [113]. Let us replace the Cartesian coordinates Ex, E y, Ez representing the complex amplitudes of an (R) wave whose vector is E by the rotating coordinates £+ , £ _ , E z.

MOTIONS OF CHARGED PARTICLES IN ECRIS PLASMA

107

E+ = Ex + i E y E - = Ex — i E y E\\ = Ez. The rotating E of the plane xOy is such that the component Ex is advanced by 0 = 7r/2 with respect to E y meaning that £ _ = 0 and the new coordinates are represented by one single component E+ (if the component £ _ exists, it would represent a rotating field in the opposite sense, in the plane JcOy, which means a left-hand polarized wave, which cannot energize an electron (see section 2.1.1)). The conductivity tensor a is then simply expressed by

a = Go

— 0 0 tORF—O^c 0 — 0 (*>RF~U>c 0 0 1

and when we consider the resonance co = coce the longitudinal field E\\ and the E - field have no effects. Only E+ rotating in the positive sense is effective. It then rotates in the sense defined by the vector of rotation coc• In figure 1.5.11 we have represented the velocity vectors necessary for the new description of the ECR. 1.5.4.3 Electron motion in the ECR in a homogeneous magnetic field (V B = 0): the role o f the initial electron velocity Vo. Let us characterize the E field by the dimensionless expression eE 8 = -----mcoc and let us follow Delcroix’s study of the ECR in a homogeneous B field in the presence of an RF electric field E — E cos cot [113]. The RF field is the resultant vector of three field components: E+, the rotating transverse RF field represented by a vector rotating in the same sense as coc (R wave); (ii) E - , the RF field that rotates in the opposite direction of the electron (L wave) and (iii) £||, the longitudinal component. (i)

As E _ and E\\ have no action on the ECR, they are negligible. trajectory with the right-hand rotating RF field E + has a velocity vector V =

^ E +t-\(1)

ooc x rc+ (2)

The

V\\ (3)

Term (1) represents a spiralling motion with angular velocity co — coc\ term (2) represents a rotation at the same angular velocity (synchronization); whereas term (3) represents a translation parallel to B. The initial velocity determines rc and V...

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SPECIFIC ELEMENTS OF PLASMA PHYSICS

->

lb )

(a) The composition of the velocities in the resonance a)c) = coRF. is the Larmor radius r c [113]. (b ) As for (a), where Er is the E _L B component rotating in the same sense as the electron. r c is the Larmor radius and the gyrofrequency is d)c = £2.

Figure 1.5.11

p

(i)

If the initial velocity is zero the motion is reduced to a spiralling component where _

V = — E+t -± x . rc = E m B The velocity vector and the radius vector vary proportionally with time. Thus we obtain the same result as in the previous case with Cartesian coordinates (section 1.5.3). No phase conditions intervene in the motion. (ii) If the initial velocity is not zero and has a transverse component (general case) the composition of the spiralling motion and the rotation coc x rc will depend on the initial phase 0 between cdc x r c the gyrovelocity and (q /m )E + the R wave field. This is new with respect to section 1.5.3.3 and has immediate consequences. Assuming that after a given time t, both velocity vectors have rotated an angle coct and have kept the same 4> (figure 1.5.11), Delcroix has shown that the velocity is given by It t 21 1/2 cos 0 + VI (0 = — £ + f0 1 H m to *0 -I

MOTIONS OF CHARGED PARTICLES IN ECRIS PLASMA

109

V±(t) 4

3

2

2

3

4

Figure 1.5.12 The influence of the initial perpendicular velocity Vm at resonance ^ ( = eoc) = corf [113]. with m Vx(o)

= ------q E+ Let us now consider three typical initial phase conditions: 0 = 0; 0 = 7r/2 and 0 = n and let us plot (V±/Vo) against (t/to ) (figure 1.5.12). When 0 is between 0 and 7r/2 (favourable phase), V±/Vo i.e. V± increases permanently with time (graph A), but when 0 is between 7t/2 and 7T, the velocity decreases at first (graph B). It even tends towards 0 for 0 = n at the beginning and if we stop the RF at t/to < 2, the ECR has decelerated the electron. However, if we consider long RF duration (t/to > 1) all the electrons are eventually accelerated proportionally with time and independently of 0. Then V±o and V± = (q /m )E + t = gccot. The reduced energy becomes

The result shows that in the case of ECR withjong-duration pulses, in the frame system linked to gyrovelocity and rotating E fields, the electron is finally accelerated as if E+ was a continuous electric field (but this result is not valid for very short ECR pulses). 1.5.4.4 Cyclic energy pulsations in the ECR located in a homogeneous magnetic field (relativistic ECR effects). When the relativistic mass variation is not taken into account, we can write

110

SPECIFIC ELEMENTS OF PLASMA PHYSICS

keV \N± A

2 > 0,05

t (JS

0,1

Figure 1.5.13 Energy pulsation at gyromagnetic resonance versus time [115]. Typical values: E = 90 V cm-1; coc = 2tt2A5 x 109 ra d s '1. The acceleration acts as if the electron were permanently accelerated by a uniform electric field £+. We will now see that the relativistic mass variation will modify the process because the ECR condition given by eB CO RF =

y m 0c

(1.5.48)

will be perturbed if the relativistic factor y = [1 — u2/ c 2]-1/2 becomes smaller than 1 (i.e. when, due to the acceleration, v becomes nonnegligible with respect to c). The effect of the relativistic relationship between the mass of the particle and its energy in the ECR has been analysed by different authors [ 115]—[ 117], who found that if the electric field is that of an R wave propagating along a homogeneous magnetostatic field then the particle energy happens to be a pulsing function of time, so the particle is periodically accelerated by the electric field and afterwards brought to a halt by the field itself. The result is shown in figure 1.5.13. Time fo r phase changing [116]. After reaching the maximum energy defined by w max (keV) = 18.8

(1.5.49)

due to the relativistic mass variation, the electron changes its phase 0 in such a manner that acceleration is replaced by retardation until the particle energy falls to zero. After that the resonance acceleration is restored again with a new value of 0 which can be optimal since then the electron is at rest (i>o = 0). Thus in this model, promoted by Golovanivsky, the phase is allowed to vary in the resonance. In general the times necessary for these phase variations are longer that the ECR transit times in non-uniform B , which justifies Canobbio’s stationary phase condition during short time intervals (see section 1.5.5). However, in homogeneous fields (V B = 0) this time is long and energy pulsation does occur. Rephasing time. Note in the figure 1.5.13 that reacceleration after the retardation time is not immediate, showing that the adequate rephasing only occurs after a

MOTIONS OF CHARGED PARTICLES IN ECRIS PLASMA

111

Figure 1.5.14 The Gyrac effect [116]. An autoresonance is maintained in a time growing magnetic field yielding highly relativistic electron energies. given time rPh depending essentially on the values of the E field (i.e. g value) and the particle energy W±. The rephasing time is given by ~ (y - l ) 1/2g -1

y = 1+ - ^ . m 0cz

Orders o f magnitude. For g ~ 102 (corresponding to co ~ 2 x 1010rad s-1 and E ~ 3 k V cm -1 or co = 6 x lO ^ ra d s’ 1, E ~ lO kV cm "1 and W± ~ 100 eV, the rephasing time lasts a few cyclotron revolutions. For the same g value but Wj_ ~ 1 MeV, the rephasing time lasts hundreds of gyroperiods. 1.5.4.5 Golovanivsky’s auto-resonance in a homogeneous but time growing magnetic field B (t)— the Gyrac effect. In 1963, Consoli and Mourier emphasized the occurrence of highly relativistic electrons in ECR discharges [119] and proposed explanations which were further developed in 1964 by Weenink and Hakkenberg [120] and others. Let us imagine that, during the ECR process, when W±(t) increases B also grows versus time: B = B(t). When W± has reached a given energy, due to the relativistic mass effect and its subsequent energy pulsation (which is also a function of time) the retardation process starts. However, if then the increased B (t) field becomes such that it compensates the increased electron mass, the gyroresonance can be reignited and the electron is again accelerated. This cyclic acceleration and retardation process leads to a global energy increase versus time with superimposed energy oscillations, which are small with respect to the global energy (figure 1.5.14). Finally, this process can lead to highly relativistic electron energies. Actually, the relativistic gyromagnetic resonance supports itself in such a manner that the particle energy automatically oscillates in a bound interval making the values of coc and corf close during a given time. This means the process obtains a character of auto-resonance.

112

SPECIFIC ELEMENTS OF PLASMA PHYSICS

Thus, the gyromagnetic auto-resonance may support itself in the case when the magnetic field has an increasing in time character. If this happens, a simple increment of the magnetic field in time according to any arbitrary law, for example, a 100-fold increment (in the course of gyromagnetic auto-resonance) would have as a result a 100-fold increment of the particle relativistic mass. In other words, it means an acceleration of particles reaching the megaelectronvolts range. This nontrivial result is called the Gyrac effect. The Gyrac effect was studied theoretically and experimentally by Golovanivsky [115], [116] who has shown that the ECR in a time growing magnetic field is automatically self-maintained in such a way that the relativistic cyclotron frequency is always equal to the RF field frequency, so eB /

= constant.

(1.5.50)

So, the kinetic energy automatically follows the magnetic field which is growing in time from B q (initial field) toward higher values

1

= 0.51

MeV. 1

1

1 O S' * 1 1

1

1 O S ^ i i

WeJ_ - m 0c2

However, the speed of the B (t) function should not exceed a slope given by — < 2coE dt

(1.5.52)

which is easily satisfied. Auto-resonance in space growing magnetic fields o f an ECRIS. Note that the Gyrac effect would yield 500 keV electrons for a 10 GHz system when B{t) grows from Bres = 3.6 kG to 7.2 kG in a few microseconds. However, electrons bouncing inside an ECR magnetic mirror system can also be subject to a spatial Gyrac effect since the equivalent d B /d t ~ 109 is generally smaller than 2(2;r x 101 0) £ . This mechanism is then a candidate for the production of very energetic electrons in ECRIS plasmas. 1.5.5

Electron motion and acceleration in an ECR slab with VJ3 ^ 0— Canobbio’s theory

The basic assumptions—generalities. Between 1966 and 1970, Canobbio developed an analytical theory for a single electron whose motion is not impeded by any collisions or stochastic kicks (v coc) and which passes once through

MOTIONS OF CHARGED PARTICLES IN ECRIS PLASMA

113

a resonance zone located in a magnetic field gradient. At first he stipulated that during ECR the time dependence of the magnetic moment of the electron

X — cot

— (r) = fi(r)

(1.5.53)

(obtained by analogue calculations) is close to that of the Fresnel integrals and it should be possible to write it in analytical form: 2

o

(1.5.54) r

The method, which includes non-adiabatic effects, takes account of the ECR by assuming that the grad B seen by the electron is weak [vzd\Bo\/dz] [u>cBq] and that E c/V

1 + (coc/v ) 2

0

COcV

0

1 + (cOc/vY

1 1 + ((Oc/v ) 0

0 1

Alas, let us stop further developments of this classical collisional diffusion in magnetoplasmas, since it appears that the model is not applicable in most experiments. The electric fields involved in the classical collision processes are not always the main particle scatterers in magnetoplasmas. Fluctuations inside the plasma have shown that they are more efficient. Thus the parallel drawn between collisional gas theory and collisional magnetoplasma theory was surely over-idealized. 1.7.6.3 Diffusion in finite-size magnetoplasma [143]. Simon suggested that the diffusion across B may not be ambipolar and may be due to a plasma short-circuit effect which does not imply plasma fluctuations. He postulated in 1955 that the charge separation between radially spaced plasma regions could be cancelled through electron fluxes circulating firstly along the B lines and later through the metallic end walls of the plasma container. The transverse diffusion coefficient would then be essentially that of ions and D± ~ D±+ » D±_.

(1.7.19)

This diffusion coefficient leads to somewhat better agreement with most experimental observations. However, in special experiments where the length of the plasma was two orders of magnitude larger than the radius (which should eradicate the longitudinal short circuit)—the diffusion losses were not radically decreased [144]. Therefore, the classical collisional diffusion concept became

THE DIFFICULT MODELLING IN MAGNETOPLASMAS

139

less and less accepted, and turbulent diffusion was more and more invoked and especially in RF discharges [146]. 1.7.6.4 Bohm diffusion (or turbulent diffusion) [145]. As already said, most experiments indicate a diffusion rate in excess of that predicted by collisions. Even worse, the experiments show that the diffusion is not even proportional to l / B 2. Diffusion proportional to 1 /5 in a plasma is called Bohm diffusion, after David Bohm, who first proposed that collective nonlinear processes, such as instabilities or fluctuating fields inside a turbulent plasma, might lead to another diffusion coefficient where collisions are ignored and replaced by fluctuations. In practical units this coefficient is given by

D±Bohm (cm2 s !) ~ j g ^ k G ) (

e *) W

yielding a diffusion time xsec ~ R 2/D ± Bohm where R (cm) presents the radius of a cylindrical plasma column with length L R. It is remarkable that these formulas indicate increased diffusion losses for hotter electrons, which is in total contradiction with collisional diffusion, where the scatterings decrease with Te. Bohm’s formula was proposed [145] in 1949 and is still nowadays strongly debated, though it seems more realistic than the idealized collisional diffusion. It gives apparently better orders of magnitude for very noisy and turbulent overdense ECR plasma even when the length L R, but it also holds for the usual plasmas in simple mirror ECRIS. However, it seems too pessimistic for min-B ECRIS with ‘weakly’ turbulent plasma. In this type of ECRIS, containment times better than the Bohm time are obtained. Let us recall that some of the current literature concerning experiments on plasma containment by magnetic fields refers to the containment time in terms of Bohms, i.e. the number obtained when the experimental diffusion coefficient is divided by the Bohm diffusion coefficient. In his proposal (as in the kinetic theory of gases) the diffusion coefficient is D = Aid/3, but the electron motion across a uniform B is the drift due to an electric field E'. We have seen in section 1.5 that the drift velocity is then given by Vp (cm-1) ~ 108 E' (V cm-1)/B (G)) where E' is the component perpendicular to B , of the fluctuating field. Bohm then replaces A, the mean free path of collision, by an undetermined path A' of the electron between two kicks delivered by the fluctuations and D L becomes proportional to A'E '/B . Further approximations (not derivations) lead to formula (1.7.20). 1.7.6.5 The effervescence T and the diffusion coefficient in the magnetoplasma o f ECRIS. The classical diffusion coefficient is defined by

140

with

SPECIFIC ELEMENTS OF PLASMA PHYSICS

| \

D \ \ b

~

3

V coi iX mf p

D ±B ~ \VcollP]

where pe = m v± /eB . As seen in section 1.3.7, if we take vcou = va)p we can write that the plasma oscillations at cop are conducive to a coefficient

V ± ~ &(JF corf ~ coce), the magnetic mirrors are inefficient and most of the plasma diffuses along the axis. Thus the measurements of the axial losses can lead to some experimental evaluation of D\\ in coordinate space. In min-B ECRIS with quiescent ECR plasma, the analysis of the loss cone flux behind the axial mirrors allows also some quantitative approaches provided —3/2 that only Spitzer collisions (vei a znT e ) are considered, that the radial losses along the cusps are neglected and that the diffusion of very energetic electrons is ignored [147], [148]. Correlated measurements implying relationships between the loss cone and velocity distribution have also been launched [149], [150]. 1.7.7.1 Correlated diffusion. In the new diffusion models in coordinate space, the coefficient D is not linked to a collision mean free path but to an unpredictable distance between two scatterings; in addition it is not related to a simple collision time xcou depending on cross-sections, but to a so-called correlation time xcor (or coherence time) which is supposed to be deduced from the spectrum of stochastic fluctuations. If AC is the displacement of the

THE DIFFICULT MODELLING IN MAGNETOPLASMAS

141

guiding centres of the particle random walk during xcor the elementary radial shift A r _L B versus time will be given by D r1 = (A C2/x cor)t with the equivalent diffusion coefficient D = (A C2/Tcor) and the diffusion time defined as always by td ~ R 2/D \ td is the time after which Ar becomes equal to R, the radius of the cylindrical plasma container, whose length L » R. As for the value of xcor, it depends on the type of fluctuation and it has to be deduced from experimental observations of local plasma relaxations or conspicuous noise spectrum frequencies. In other words xcor is no longer predictable. It changes with each type of experimental magnetoplasma, it can even alter versus time for the same plasma, and vary from point to point. Note that the above expression for D works in coordinate space with real distances such as R, Ar and AC. In velocity or momentum space the diffusion equation is d f/d t = S (p ) + VT where f ( p ) is the distribution function which can also change during the diffusion process and T = —D V / where T is the velocity space loss flux and S (p ) the source term. For instance, it seems possible to measure T\\ on the axis of an ECR plasma (behind the mirror) and then to deduce the distribution function with the help of an energy analyser. On the other hand we can assume that D = A pA p/ A t where A p is a momentum impulsion due to some electric fields generated by the unknown ‘scatterers’. Only kicks perpendicular to B yield diffusion through B and A p = A p± = (m A v±), thus A p also yields impulsions of electron energy (m A v \ ) and momentum ( m A v \) /B gained during the correlation time A t. This image then corresponds to stochastic heating (see section 2.3). Hence in momentum space, the loss flux, the distribution function, the electron heating, the energy storage etc are linked to D. Measurements of these parameters could in principle help to determine D and, according to these new ideas, the diffusion should be approached experimentally. Subsequently some plasma thoreticians have dropped the purely speculative and generalized calculations of D, and recommend experimental guiding supports; unfortunately the measurable parameters are not easily linkable to the diffusion concept without many further assumptions. Nevertheless they give some hope for more realistic solutions with a semi-empirical approach based on nonglobal plasma transport. 1.7.7.2 RF diffusion in min-B ECRIS [150]. As seen until now, diffusion is described by successive 90° particle scatterings, in velocity space as well as in coordinate space. In velocity space when one considers kicks in the loss cone one finds / ^ IXbounce

V

^-L

J

c o llisio n s

V

^90°

142

SPECIFIC ELEMENTS OF PLASMA PHYSICS

However, only few of these scatterings seem applicable to hot-electron ECRIS in min-Z? structures where fluctuations and 90° collisions are minimized. Therefore we consider now the possibility of RF diffusion, which might play an important role in ECRIS when a stochastic heating is assumed. Theoreticians have surmised that stochastic ECR heating can also be treated as a diffusion process since heating and scattering are generated by RF stochastic fields which dispatch random kicks to the electrons. One then finds that in the presence of any RF field the kicks are such that ~ \

V ±

/

R F

— E rf A trf 171

where A rr f is the time spent by the electron in the stochastic RF fields and E ± is the amplitude of this field perpendicular to B. Amazingly enough, such small E r f as lO V cm -1 at 10 GHz have the same randomizing effects as 90° Spitzer collisions with \ m v \ = 30 keV. For low-energy electrons with a randomizing factor (A) ~ 1 one finds then [150] r f

»*'

- (£) ~

W

)

( ^

) 2w>-

For energetic electrons, one needs experimental correlations in order to evaluate Ap. In a more general case A p 2 is the increment of perpendicular momentum due to the presence of RF fields during the time of interaction A r. Many assumptions are necessary for the estimate of A p but measurements during A t with adequate diagnostics are feasible and they can sometimes lead to the evaluation of Ap. Great efforts are now dedicated to this approach, which is very complex and not immediately rewarding. Thus, for hot electrons V r f can be approximated by experimental methods where one tries to link Ap to measurable ECRIS characteristics such as E r f patterns, Te measurement via x-rays and diamagnetism, density gradients etc. However, the measurements include the effects of all RF fields present in the plasma (i.e. cavity fields, RF fields due to instabilities, wave conversions etc). Hence V r f includes all RF scattering phenomena occurring under specific conditions in the ECRIS plasma. Even if V r f is not easy to evaluate quantitatively it is the only diffusion method showing that the stronger E r f is in the ECRIS then the stronger the heating is and the stronger the diffusion losses are. It then happens that for hot electrons when the classical collisional diffusion becomes absolutely negligible and when no turbulence appears RF diffusion might dominate the loss mechanisms. ECRIS losses in min-B structures are then linked to V RF. In this case, the V RF values are much smaller than D Bohm but still orders of magnitude larger than the elusive collisional diffusion coefficient. RF diffusion might then explain the minimumRF-power principle in min-Z? ECRIS (see section 2.3), stipulating that increasing RF power above a given threshold does not improve either the plasma density or the electron energy but simply increases the losses and the noise.

THE DIFFICULT MODELLING IN MAGNETOPLASMAS

1.7.8

143

Intuitive utilization of the diffusion coefficients by ECRIS experimentalists

We will consider four typical ECRIS plasmas; all of them are strongly ionized, and RF fields, and Spitzer collisions as well as fluctuations can preferentially describe the diffusion. A priori the ECRIS experimentalist cannot predict the diffusion coefficient. He has to analyse the conditions: (i)

A long cylindrical 10 GHz plasma is contained in an ordinary double mirror configuration with (B ) ~ 5kG, (n) ~ 10n cm-3 , {Te) ~ 500 eV, the plasma is underdense: cop < corf. The argon gas pressure is ~ 10-5 Torr; the shape of the cylinder is R = 5 cm, L = 50 cm. The extracted ion current exhibits a broad-spectrum noise. The modulation ratio, noise/signal ~ 50%. The extracted ions are not highly charged but not only singly charged. Assuming Bohm diffusion let us evaluate the diffusion characteristics of a turbulent plasma (high noise level): 105K T 105 x 500 ^ r j i D± b ~ ---------- = -----~ 6 x 10 cm s ±B 16eB 16.5 R2 5x5 5 tB ~ — = ----- — ~ 4 x 10 s. Db 6 x 105

(ii) Assuming a classical diffusion, looking for vei in the figures of section 1.4 one finds vei ~ 103 and with p L ~ 1.5 x 10-2 cm one obtains: D l ~ p 2L vei = 2.2 x 10“4103 = 0.2cm 2 s-1 . Between the two diffusion models the disagreement is six orders o f magnitude! Even for the author, whose modest ambitions in plasma physics are restricted to struggling for acceptable orders of magnitude (see section 1.2), the situation is vexing. Before dropping one of the diffusion models let us compare the numbers with two experimental observations. As incidentally mentioned, the plasma is very noisy. In such a case the losses are better described by a turbulent type of diffusion and we recommend the Bohm formula. In this case the particle lifetime r is probably of the order of microseconds (i.e. r < tD/ 10 = 6 x 10-6 s) and this time would then explain the absence of highly charged ions which need confinement times of the order of 10-3 s in order to allow step by step ionizations. (iii) The second case is a 2.45 GHz ECRIS plasma contained in a similar cylindrical volume but (B) ~ 1 kG, {Te} ~ 50 eV and (n) ~ 1012cm~3 (overdense). The plasma is very noisy and the ions are only singly charged. As (op > coc and the end mirrors are not efficient, strong axial plasma leaks are present (see section 1.6). Taking as previously a Bohm diffusion one would find D b ~ 10_5cm2 s_1 and tB ~ 10-5 s. To explain the singly

144

SPECIFIC ELEMENTS OF PLASMA PHYSICS

charged ion production we can assume that Te ~ 50 eV is not sufficient for more highly charged ions, though tB is rather better than in the previous example. (iv) The third case is an overdense 2.45 GHz ECRIS contained in a short cavity with L < R ~ 10 cm. Such ECR sources are very popular since they are utilized for ion processing. With Te ~ 10 eV and (n) ~ 1012cm-3 the diffusion losses are essentially along the axis through the ends of the cylinder, and the perpendicular diffusion losses are smaller than the parallel ones. In such a case the ambipolar diffusion is controlled by the slower particles, which are the ions, and D ~ (t>+ )A+/3. (v) Let us now consider a 14 GHz ECRIS in an L = 10 cm, R = 5 cm container but with a min-Z? multi-mirror confinement. The gas pressure is about 10“7 Torr, the density (n) ~ 1012cm3, (Te) ~ 5 keV and (B ) ~ 8 kG. The ion current is not noisy, with a modulation of less than 10%; the extracted ions are multi-charged peaking for instance at Ar10+. The Bohm diffusion would yield D B = 105 x 5 x 103/16.8 ~ 4 x 106 cm2 s-1 and td ~ 25/4 x 106 ~ 6 x 10-6 s whereas the collisional diffusion would give, with p i ~ 3 x 10-2 cm and vei = 5 x 102, Dj_ ~ 0.5 cm2 s-1 , hence td ~ 25/0.5 = 50 s. In this case the disagreement is seven orders of magnitude—but the Bohm diffusion seems necessarily too pessimistic, since the presence of Ar10+ cannot be explained if the particle lifetimes are so small. We will see (section 6) that r ~ 10-3 s is a more realistic time and thus a diffusion time of 10-2 s looks more probable. We see that in this type of sophisticated min-Z? structures the diffusion time is probably 1000 bohms (which means that the confinement system is very high-performance) but even then the diffusion time is still much worse than the misleading classical diffusion time. Thus ECRIS with minB structures are dominated neither by classical collisional diffusion, nor by turbulent Bohm diffusion. Maybe RF diffusion is now assumable, with its semiempirical approach. However, the four examples above illustrate the inability to predict quantitatively an overall diffusion rate. Only the experimentalists can tell a posteriori whether the plasma is strongly or weakly turbulent and which approach yields a ‘decent’ order of magnitude. Therefore, the estimate of the effervescence (see section 1.3.7) is a very valuable guide.

1.7.9

Diffusion time,

to,

particle lifetime, r , and energy lifetime,

ten

Diffusion time and particle lifetime have different meanings and should not be confused. For instance, in a quiescent mirror plasma, the particle lifetime is given by r ~ r90° log Bmax/B min and one 90° collision is sufficient to send the particle into the velocity space loss cone and its lifetime is over. Thus the B field of a mirror has a weak influence on r since \ogB max/ B min is nearly constant.

THE DIFFICULT MODELLING IN MAGNETOPLASMAS

145

On the other hand the diffusion time to involves many scatterings in space configuration over a distance including a random walk between the plasma and the walls, to is strongly dependent on the magnetic field B and it represents a time for particle transport to the wall (i.e. for losing the particles on the wall). Thus tD is a deconfinement time and not a lifetime. It is longer than r: tD ~ A t with A ~ 10. If the particles are energetic they will transfer their energy to the wall in a more or less short time, equal to to, meaning that the injected power must compensate during to the lost power in order to maintain the steady-state plasma. Thus the diffusion time is strongly linked and proportional to the energy lifetime of the plasma, Ten •

Te

n

oc to

Note that mirror diffusion (velocity space diffusion) and cross- B diffusion (coordinate space diffusion) have to be added for the evaluation of the overall diffusive losses.

1.7.10

Conclusion of section 1.7

We have emphasized that the classical collisional diffusion may be applicable for quiescent ECRIS when the plasma is neither dense nor hot. In all other experimental situations classical diffusion has never been evidenced. When the plasma is hot and dense (or overdense), Bohm diffusion is a mediocre model but no simpler and better one exists. It also gives an order of magnitude of D± for ECRIS plasma in simple magnetic mirrors since in this case different instabilities are always present (see section 3). However, in this case a To)p gives more flexibility. For stabilized min-Z? ECRIS with hot electrons only, none of the previous diffusion types are applicable and the so-called RF diffusion is nowadays invoked. This shows that the diffusion losses increase with RF power injection but no numerical formulation of the losses is possible without preliminary experimental determination of some parameters. Thus the electron lifetime seems limited not exclusively by the Spitzer collisions but also by RF diffusion. As seen, the energy lifetime in plasma devices depends strongly on the diffusion time tD. The poor understanding of the real nature of the scatterers therefore hinders a clear prediction of the energy lifetime in all plasma devices. The gloomy image of the diffusion processes is currently the most serious handicap for a planned development of large plasma devices where megawatts of power are injected and are rapidly diffused towards the walls, leading to many undesired heat effects. Very fortunately, these catastrophic power losses do not really concern ECRIS engineering since the injected RF power is in the kilowatt range and the power dissipation on the walls is experimentally mastered. Subsequently the diffusion issues in ECRIS are not paramount except for the theoreticians who cannot determine the power balance equations, which eventually impedes progress.

146

SPECIFIC ELEMENTS OF PLASMA PHYSICS

On the other hand, for very highly charged ion production very hot electrons are needed. Therefore the energy lifetime (which is essentially equal to the hot-electron lifetime) ought to be sufficient, otherwise wall cooling problems arise. Finally after detailing the difficult modelling of the diffusion processes in ECRIS plasmas we return to the preliminary considerations of section 1.2 where we emphasized the struggle for the right orders of magnitude and deplored the fact that no satisfactory theory of diffusion exists to date.

2 WAVE-PLASMA INTERACTIONS

2.1

2.1.1

BASIC ASPECTS OF SMALL AMPLITUDE EM WAVES INCIDENT ON A COLD MAGNETOPLASMA

Generalities

Though a cold plasma with Te ~ 0 is a purely theoretical concept, we have to consider it, because it is at present the only case for which a clear-cut coherent model exists. Fortunately, we can partly utilize this model for a rough understanding of the problem of EM wave penetration into a plasma, which is especially important for ECRIS, because all the energy available inside the ECR plasma is transported there by the incident waves, and their behaviour should be known as much as possible. However, we should keep in mind that the conditions for wave power deposition (resonant or non-resonant electron heating) as well as wave propagation are not identical for cold and warm plasmas, but there are some common tendencies which help us to envisage what may happen in the warmplasma case. Incident waves and self-generated waves in the plasma. It is important for the sake of clarity to separate the externally created incident EM waves from the internally self-generated waves inside the plasma which will be described briefly in section 2.1.2. Both kinds of wave may be absorbed, propagated or reflected. The conspicuous difference between them is that the first are generated and controlled by an external wave generator and exhibit generally only one frequency chosen by the ECRIS builder, whereas the second may present many different sporadic frequencies and magnitudes which do not depend on the will of the ECRIS builder but depend on the capricious properties of the plasma. Whatever the capricious internal waves, the ECR plasma properties depend mainly on the incident waves. 147

WAVE-PLASMA INTERACTIONS

148

2.1.2

Small incident waves propagating inside the magneto-plasma— wave perturbations

Outside the plasma, if we suppose a total absence of electrical charges, the wave propagates unperturbed as in a vacuum; however, at the plasma edge and inside the plasma, the propagation can be strongly perturbed if the medium contains many free electrons. For microwaves at high frequencies (> 1 GHz) only the electrons respondjo the wave field, the ions having too much inertia. On the other hand, only E , the electric field component of the wave, acts on the electrons, the magnetic wave field component being generally negligible with respect to the static magnetic field of the magneto-plasma (B Bo). In addition, we have seen that a magneto-plasma has different properties along or perpendicular to the magnetic field lines. This feature reveals an anisotropic medium, which means that the transport coefficients of the magnetoplasma such as the particle diffusion coefficients and electrical conductivity are affected by this anisotropy because the motions of charged particles are not equally possible in all directions. We now can understand that E the electric field which interacts with electronic clouds inside the plasma can be locally altered by their anisotropic behaviour, particularly when E is perpendicular to B. In this case, the plane of polarization of the propagating microwave can be changed by the electron displacements; thus not only are the electrons affected by electric microwave fields but also reciprocally the microwave fields are affected by the electron displacements. However even for E\\B when the force e(v x B) is not involved (or in the absence of a magnetic field) the jplasma electron density alone is capable of changing the propagation of the E field. Under this condition, we can predict that E fields which are neither perpendicular nor parallel to the B field, but have different angles with respect to the magnetic field lines, will create very complex situations and lead to strange wave behaviour depending (i) on the incident wave polarizations, (ii) the propagation angles, (iii) the magnetic field strength, (iv) the plasma electron density etc. As a result of the above-mentioned facts there are some properties which we will now recall.

2.1.3

Wave modes in the magnetoplasma

2.1.3.1 A short review o f the possible wave perturbations due to the magneto­ plasma. The cold plasma electrons can (i) (ii) (iii) (iv)

change the plane of polarization of the incident wave, stop the propagation and reflect the wave (cut-offs), stop the propagation and absorb the wave (resonances) or stop the propagation and transform the wave (for instance from an EM wave into an ES wave).

BASIC ASPECTS OF SMALL AMPLITUDE EM WAVES

149

If the electrons are warm, as we will see later, they can also change the frequency of the incident waves, damp the waves, amplify the waves, create plasma instabilities and plasma heating and generate many kinds of internal plasma waves. 2.1.3.2 The fo u r principal wave modes inside the magnetoplasma and their dispersion equations. For the propagation of electromagnetic waves in a plasma where E\\B or in an unmagnetized plasma, the dispersion relationship co2 — co2 = k 2c2. Here eop = cope is the plasma frequency or more precisely the electron plasma frequency also called the cut-off frequency (see section 1.3), where k is the propagation constant which enters the term exp i(kx — cot) representing a wave of angular frequency co propagating in the + x direction with a phase velocity co/k and group velocity dco/dk. For the dispersion relation k is imaginary whenever co < copj implying a total reflection of radiation incident on a plasma. In this case expi(fcjt —cot) = exp(—x /S )e x p (—icot) representing an evanescent oscillation whose amplitude in the medium decays exponentially with a characteristic distance called the skin depth (figure 2.3.6) S = c /(w 2p - c o 2) l/1. We see that microwave frequencies are required for the penetration of plasmas of densities of interest for ECRIS sources. When co < cop, except for values close to cop, the penetration depth uh =

{0 > p e

2 \ 1/2

+ W« )

called the upper hybrid frequency. The quantity (Dce = eBo/m is the electron cyclotron or gyrofrequency at magnetic field BoTo describe the propagation of electromagnetic waves through a magnetized plasma requires two other characteristic frequencies as well, c o l and c o r , defined by o >l

/r

=

\

[(< w « +

4 ( ° 2p ) i / 2 ±

" « ]

150

WAVE-PLASMA INTERACTIONS

z

z

Figure 2.1.1 Vector diagrams of the various polarizations possible at 0 and 90° with respect to the magnetic field, (a) and (b ) are with k || B and (c ) and (d ) are with k _L B (cold plasma).

which are deduced from the permittivity tensor e given in the next paragraph. According to the value of e , the behaviour of electromagnetic waves in a plasma can be given in terms of the parameters cope, coce, a>i and cor. We summarize the situation in table 2.1.1. Whatever the modes of the waves outside the plasma, inside, in the magnetized plasma, there are only four possible waves: the ordinary (O), extraordinary (X), left-hand polarized (L), or right-hand polarized (R) wave (also called the Whistler wave at lower frequencies) (figures 2.1.1 and

2 .1.2).

2.1.4

Useful relations between plasma and wave parameters

Arguments about wave propagations in plasma look inextricable for non-experts because plasma physicists base their reasonings on miscellaneous wave/plasma parameters. Let us try to correlate a few parameters used such as N , k , e, e0, sr , v

108 per caviton (x ~ 4/3(A /))3/2)n with n > 1012 cm-3 . To evaluate roughly the energy acquired by electrons during the LCC one can use the value of the electrical field inside a caviton before it begins to collapse and we saw in section 1.3.4.5 that Ep over a few Debye lengths is about a few kilovolts per centimetre. Inside the caviton, the wave energy is then \soEp (4 /3 A /))3 which is distributed among more than 108 electrons. With this image of caviton collapses one should again find reasonable values of electron temperature in the kiloelectron volt range. Certainly this kind of speculation makes the process irreversible, and Buneman’s paradoxes of section 2.2 are discarded, but, once more, to what extent can we trust a model which ignores basically the presence and the effects of the magnetic field B1 Thus L cavitons are not a sufficient explanation. Therefore, Golovanivsky proposed recently a revisited concept including magnetic effects, where the electrons are trapped in the E field of large-amplitude Bernstein waves and accelerated perpendicular to the K vector of those waves and to the static B field lines [73]. 2.3.8

The global heating model [55]

It is obvious that, up to here, section 2.3 deals with ‘big science’ but questionable concepts. Therefore, having emphasized the difficulties of analysing the ECRH in detail, let us come back to a simple, global model. In this approach we ignore the electron motions in the ECR, the nature of the waves and the linear or nonlinear behaviour of the interactions. Considering only the coupling efficiency r] between the RF power P r F and the electrons, one can simply write r)PRF ~ (VI)

(2.3.15)

196

WAVE-PLASMA INTERACTIONS

where {e V) is the average energy acquired by the electron in the ECR assimilated to a potential drop (V) and (/) the average current of the accelerated electrons. For instance with r ] = 0.1 and 10 kW of P one can obtain 0.1 A of 10 keV electrons or 1 A of 1 keV electrons etc. This brutal assumption gives immediately the orders of magnitude of the possible electron densities n and temperature T by setting r f

I ~ N ev

N = n (Vol)

KT V ~ ----e

2eV v = J V m

(2.3.16)

where N is the total number of accelerated electrons, K the Boltzman constant, v the electron velocity and Vol the volume occupied by the electrons. The upper limits of the power transfer are now clearly defined when rj ~ 1. Though the present approach is absolutely oversimplified, ignoring all the internal plasma processes it leads to a global electron energy (comparable to that of an electron passing through a difference of potential equal to V) versus the injected RF power. Expressed in plasma parameters we can write that ~ energy contained in the electrons n K T (Vol) rip RF = ------f j - . T“7 j 7------------ = — lifetime of the electrons xe

(2.3.17)

and with PRF (W), xe (s), n (cm-3) one obtains T ev ~ 0.6 x \ 0 l9rjPRFxe/n (Vol) where n K T , the stored energy density of the spiralling electrons, is equivalent to the plasma diamagnetism (the ion diamagnetism remains negligible in ECR plasmas). At steady state all this energy is lost on the walls after a time re, which is the electron confinement time of the system; in other words this energy has to be reinjected in the system in a time span equal to xe in order to maintain the plasma. The above formula allows one to draw a major conclusion: the heating is a question not only of RF power but also of confinement. When by increasing P rf one creates turbulence r] and xe will decrease and the heating process worsens. Therefore P r f should be handled with experimental care. However, this model needs an evaluation of xe to be practical, and plasma physicists know how difficult it is to approximate xe (xe ~ 10-3 s in min-B ECRIS and 10-5 s or less in ordinary mirror ECRIS). Moreover the assumption of an average temperature T in an ECRIS plasma is oversimplified because there are generally at least two populations: the thermal electrons with many collisions and the hot ones which are nearly collisionless [284]. This global model can be developed in a more detailed manner when one adopts the two-electron-population hypothesis: a thermal one with density

ELECTRON HEATING IN THE ECR PLASMA

197

Pincident Pioniz P reflected >

Plai Pwall losses Pradiated

▼ Pnon absorbed

Figure 2.3.9 Global wave power transfer to the plasma. nth and average temperature T th, and a hot one with average temperature T h and density n h. Each of these electron populations has a specific lifetime in the magnetic trap, xth and x h, before leaving the plasma. The lifetimes of each group can be limited by different types of loss and different scatterings in the loss cone of the mirror. One can even add a potential 0 for the thermal electrons, and take into account an ion potential well A0/— in addition one can assume that the electrons have to spend power for the ionization of the atoms, W j being the average ionization energy. We can now write a more sophisticated balance equation where the RF power must be such that E P , the total power sink, is E P = r]PRF (power loss through scattering of hot electrons into the loss cone after collisional or turbulent diffusion)+(power loss through thermal electrons scattered into the loss cone after collisional or turbulent diffusion)+(power required to ionize the atoms)+(power radiated)+(RF power reflected)^ . . . (figure 2.3.9). Again, here, r) is the efficiency of the coupling of the RF to the electrons (an unknown quantity with 0.1 < r] < 0.8). For the power loss from scattered hot electrons, of temperature T h (eV) from a volume Vol we obtain . ]C)T hnh (Vol) power = 1.6 x 10” 19----- ~ — - (W). xh is generally long (~ 10-3 s) because hot electrons give long 90° collision times (r h a P ~ 3/2) and are not very sensitive to slight turbulence. For thermal electrons lost from a well of depth 0 we have power** = 1.6 x 10”

19( 4 > - r ,V ' i (Voi) Tth ^ ' r

198

WAVE-PLASMA INTERACTIONS

xth is much shorter than r h in ECRIS plasmas which are nearly fully ionized. One can then assume that the ei collisions are the scattering mechanism and xth is the effective lifetime for thermal electrons calculated by the 90° Spitzer collisions; but xth can be much shorter in the presence of fluctuations (see plasma effervescence section 1.3.7). The power required to maintain the ionization up to the ion charge Z, is power1™ =

(Vol) x 1.6 x lC r19(W) l i

The first and the last power sinks are important for highly charged ECRIS. The other two power sinks are important when operation is in a poor vacuum (> 10-5 Torr), i.e. for less highly charged ECRIS. As for the power radiated out of the plasma, usually this source of power loss is small relative to the other power sinks. The reflected RF power may be large but it is possible to measure it with adequate RF equipment. Thus the present approach is utilizable if we have some ideas about the lifetime of the electron populations in the confinement system. Note that the electron lifetime is roughly equal to the energy lifetime of the ECRIS plasma, and therefore this global model makes sense. Finally the global approach is the most popular one, because it provides orders of magnitude and allows speculations and sophistications without entering in the hazy theories of waveplasma interactions. If we put numbers in the formula for min-Z? ECRIS with xe ~ 10"3 s and n e ^ 1012 cm-3 one can reasonably find an average temperature of Te < < 1 keV with P rf ~ 100 W. For simple mirror ECRIS with the same plasma density, volume and coupling efficiency, due to the instabilities and shorter electron lifetime, 10 kW of RF power would be required; as in most ECRIS, only 1 kW of RF is available: this entails the density of 1 keV electrons being 10 times smaller ( ~ 10u cm“ 3) and only the cold electrons being dense (1012cm-3 ). However, it would be a mistake to believe that according to (2.3.18) Te increases steadily with P r f . Therefore we introduce the following principle. The minimum-RF-power principle in ECRIS. Let us forget all the previous ‘plasma arguments’. Pragmatic observations in all experiments of ECRIS show that the best overall results are obtained when the injected RF power is kept as low as possible (one supposes that all the other parameters are optimized). This indicates that an increase of PRp above some experimental thresholds always augments the diffusion losses towards the walls but never increases either Te or ne (see figure 6.6.3 below). Nonlinear phenomena are not only words. They unfortunately limit the global heating model. Big science remains necessary. 2.3.9

ECRIS heating conclusions

At a first glance, ECR is a very impressive, always successful heating method,

ELECTRON HEATING IN THE ECR PLASMA

199

but when one tries to determine the heating rates one meets numerous difficulties. The heating process can be understood on the basis of single-particle orbits in specified microwave fields E or on the basis of linear and nonlinear wave damping. Energy deposition calculations including self-consistent wave fields and quasi-linear effects have not yet been performed. If codes were developed, they would be required to keep track of the spatial distribution of energy deposition. Absorption of parametric and harmonic resonant zones also needs to be included in the codes. Theoretical work on developing the joining relations across cut-offs and resonances and the task of mode conversion problems have barely begun. This is the area which will require the most analysis before an adequate code can be used to calculate complicated energy deposition processes. A complete investigation of the ECR heating, including wall effects, mode conversions, tunnelling, etc, must still be considered a long-term project: Concerning the wave accessibilities we note that energy propagating from the high B field side of the resonance is eventually absorbed, but cut-off prevents extraordinary mode energy launched from the low-B -field side from propagating directly to the fundamental cyclotron resonance. An equilibration between waves modes occurs due to mode conversion at wall reflections and finally most of the modes are absorbed after being converted into R and X modes. Thus the deposition of EM energy in the resonance is basically possible. The transfer mechanisms of the EM energy from the resonance towards the electrons are less obvious. The physical picture of what happens during ECR heating is visualized as follows: in the underdense plasma generation (when electron orbit theories are applicable and some quantitative heating formula are available), it seems that the absorption is proportional to the electron density and the interaction is localized around co = coc. Canobbio’s single-passage and Lichtenberg’s multiple-passage formulas may be applied with caution. Unfortunately, the E fields in the ECR can only be guessed (because they are not calculable). As the density increases, the high-density regime of the X mode can be reached. Then the absorption at the resonant layer co = coc decreases and at some stage the X waves start to propagate towards the upper hybrid layer. This process seems important in small devices such as ECRIS. At the upper hybrid layer the waves can convert linearly into electrostatic Langmuir and Bernstein-like modes but probably convert rapidly into nonlinear modes, near the upper hybrid layer. Hence in all cases strong absorption is expected to occur in the broad region between the upper hybrid and the cyclotron layer. In many cases, fluctuations degrade the plasma quiescence, which is unfavourable for highly charged ion formation. Moreover, if we adopt the Russian nonlinear hypothesis, the always nascent Langmuir waves provide possibly a heating channel illustrated by transformation of plasmons and cavitons.

200

2.4

2.4.1

WAVE-PLASMA INTERACTIONS

WAVE LAUNCHERS AND COUPLING STRUCTURES

The needlessness of selected wave modes

To sustain efficiently a magneto-plasma with electromagnetic energy one has first to determine the zones of wave absorption. Though inelastic collisions are essential to the avalanche process sustaining the plasma, at low gas pressures they contribute only weakly to the electromagnetic energy absorption. As discussed in section 2.2, we need a wave with an adequate polarization, namely R and/or X waves. In practice, however, such a wave cannot be launched selectively since the presence of boundaries does not allow one to propagate pure transverse EM waves. Thus the wave electric field always possesses an axial component which does not contribute to ECR absorption. The non-absorbed waves are reflected somewhere in the device; they penetrate the plasma again with a modified polarization and are again partially absorbed. Once more the non-absorbed fraction is reflected back into the plasma and so on. After a few such passes through the plasma, most of the wave energy will be finally absorbed. Thus, to produce ECR plasmas, one does not really need to select the wave mode but concentrate rather on the design of an efficient coupling structure and matching system in order not to waste the incident wave power in the transmission line. Note that the wave absorption in the plasma through nonlinear processes, and the mode conversions changing the wave polarization at the walls, are rather modern concepts. However, in 1966, at the beginning of the ECR studies, selected polarized R waves were launched into the plasma [201]. Special R wave polarizers and antennas were utilized for this purpose, until the day when the author mistakenly inverted the wave polarization and did not notice any dramatic changes in the behaviour of the ECRIS, proving the needlessness of selected R wave modes. 2.4.2

The usefulness of matching systems and efficient coupling structures

[202] In all cases, in order to protect the wave generators and to save EM power, the system should be optimized to minimize the reflection of incident power at the field applicator where the wave-plasma energy transfer occurs (which is not the location where the wave energy is absorbed). The microwave generator is generally protected by a circulator. A directional coupler monitors the forward and the reverse microwave power. A three-stub tuner allows the impedance of the microwave line to be adjusted dynamically to match the inevitable variations in the impedance of the plasma-filled chamber. The microwave introduction system consists of two parts: (i) a transition system made of dielectric material (and whose shape is either a disc or a tube or a cap, etc), which serves as a

WAVE LAUNCHERS AND COUPLING STRUCTURES

201

Figure 2.4.1 The cylindrical cavity and coordinates (the origin is at the centre of the cavity).

vacuum window and has dimensions close to those required for the matching of impedances of the microwave transmission line and (ii) an ECRIS cavity of whatever shape containing the plasma. For 2.45 GHz wave launchers, the technical optimization has not yet been achieved: a great variety of systems exists, and improved devices are always being proposed. For higher frequencies, the solutions are much simpler and the best structures are now well known. Figure 2.4.2 shows a typical system [202]. 2.4.2.1 Wavelengths smaller than the plasma chamber dimensions. Concern­ ing ECR plasma operating at frequencies above 6 GHz, we observe that the vacuum wavelength A.0 is smaller than the size of the plasma chamber L. Under these conditions, the waves can be simply introduced into the plasma chamber through a disc-shaped dielectric microwave (/xw) window though more effi­ cient systems have been invented for example: Jacquot’s coaxial feeder, (see section 2.4.6.3). In any case, the principle of the coupling structure remains extremely simple: a hole in the plasma chamber is generally all that is needed, provided that the launched waves can propagate towards the ECR zone. In most cases it is interesting (i) to include in the /xw feeder a system allowing one to minimize the reflection of incident power and to match, if necessary, the plasma loading and the window via adequate /xw tuners, (ii) to locate the holes at a spot where the waves can propagate along a decreasing B field towards the ECR and (iii) to locate the window at a place where no energetic plasma particles are streaming or, even better, where no plasma is present at all. 2.4.2.2 Wavelengths larger than or comparable to the plasma chamber dimensions. In this case, technological tricks are necessary to fill the chamber with EM waves, and the passage from the outside to the inside of the chamber

202

WAVE-PLASMA INTERACTIONS

ECR

PLASMA SOURCE

POWERFLOW: P, - INCIDENT PR -REFLECTEDATTHE SOURCEINPUT PA - TRANSFERREDTOTHE - PLASMA P. - LOSTWITHINTHE 5 MATCHINGNETWORK P$" - LOSTWITHINTHEAPPLICATOR

Arrangements of the RF powerline from the RF generator to the ECR plasma: (a) a general scheme; (b) typical elements [5].

Figure 2.4.2

becomes a major problem. This is generally the case when 2.45 GHz waves are utilized (A.o ~ 12 cm), but because of the low cost of 2.45 GHz magnetrons, many ECR devices utilize this frequency, which, in addition, only needs lowcost magnetic field structures (B ~ 875 G). Also noteworthy, the 2.45 GHz range is officially free for various applications. Nonetheless, one can wonder if the low-cost 2.45 GHz technology is always worthwhile when one considers that in order to obtain large volumes of dense plasma (in fact overdense) one has to deal with turbulent plasmas whose energy

WAVE LAUNCHERS AND COUPLING STRUCTURES

203

lifetime is mediocre and which necessitate large amounts of RF power input. In turn this entails the use of high-power technology with strong cooling. Thus for 2.45 GHz ECRIS various techniques have been proposed and tried and are still studied. However, considering the worldwide efforts and successes in this field we recognize that some of the developments are very rewarding. In what follows, we describe some typical set-ups proposed to meet ECRIS requirements. 2.4.3

Coupling structures at 2.45 GHz

The main difficulty of the low-cost launcher is the introduction of high-power, long-wavelength radiations into a small plasma container. Different types of launcher are currently used, which include the cavity launcher, the waveguide launchers, the slow-wave launchers, the coaxial launcher, the horn launcher, the antenna launchers and combined systems using simultaneously some of the above-cited launchers. The variety of the systems proves that many intuitive /zw engineers have studied the topic, but the ideal, universal, solution has probably not yet been found. 2.4.3.1 Empty cavity excitations; the T E m mode in ECRIS (figure 2.4.1). In such systems a cylindrical cavity, excited for instance in the TE m mode, is located in a decreasing B field such that the value of B in the centre of the cavity yields c o e c r equal to the resonance frequency of the cavity. The first ECRIS, built in 1965, used this type of coupling and amazingly, 30 years later, this system is still used even for overdense ECR plasma! In this section, we briefly recall relations between the electromagnetic fields and the input power derived for a cylindrical cavity, excited in the TEm mode. In general there holds (2.4.1) v where P is the input power, Q the effective quality factor, and W the electromagnetic energy density:

The integration is over the field volume V. This implies that when E and H are in time quadrature, E is given by (2.4.3) where G is a geometrical factor. It is possible to calculate the Q of the empty cavity theoretically, and work out (2.4.3) with this Q. One would then find, for

204

WAVE-PLASMA INTERACTIONS

the electric field amplitude E q of the empty cavity in the ECR plane,

(2.4.4) Zo being the length and a the radius of the cavity (figure 2.1.4). 2A.3.2 TE modes in a cylindrical cavity containing a plasma. The empty cavity formulas are also applicable when a tenuous plasma is contained in the cavity. When the plasma is such that it cannot longer be neglected, we can imagine two approaches. One is to consider that Q is replaced by Q' such that \ / Q = 1/ Q vaCuum + ^ / Qplasma and try to determine experimentally the global value of Q' by measuring the broadening l / Q = Aco/co of the system. Such empirical approaches would give a vague idea of the value of E q in presence of the plasma by utilizing formulas (2.4.4) with Q instead of Q. (ii) A more intellectual approach consists in considering that if the permittivity s of the cavity medium is changed the frequency change is given by

(i)

f ( 8 e \ E \ 2 + 8 n \H \2) d V 0 (0

y

~

/ (s\E \2 + n \H \2) dV

(2A 5)

V

The above expression holds for small perturbations. However for plasmas, which may be magnetized, the anisotropy of the permittivity has to be taken into account. The permittivity tensor is given by * = *0

( 1

\

+ - ^ ICOSQ)

where the plasma conductivity o is given in section 2.1.4. As a depends on the density ne, it has been shown by Bers [203] that (2.4.5) can be written in the form 8(0

1

f

— = — / ((ek) - ( e d))n e dV co W J v where (e*) is the time-averaged kinetic energy of an electron, and (ed) is the time-averaged energy of the magnetic moment of the gyrating electron in the magnetic field. The total change of kinetic energy of the system is given by the integral of (£*), but only the integral of (s* —ed) is really contained in the oscillation [203].

WAVE LAUNCHERS AND COUPLING STRUCTURES

205

It follows that the field pattern in the plasma is perturbed and thus the TEm cylindrical cavity mode which is used in the experiments is degenerate; two orthogonal modes with identical resonant frequencies fit in. This implies that a magnetized plasma not only shifts the resonant frequency, but also rotates the modes of excitation which finally become degenerate modes. 2.4.3.3 Cavities with degenerate modes. To avoid further unnecessary complications of the treatment, let us say immediately that the theoretical model of such a coupling becomes inextricable. However, this does not mean that the coupling does not work. Globally it works very well. It allows considerable power transfer to the cavity and, through a quartz tube, to the plasma electrons. Numerous experiments have proved the efficiency and reliability of the system. Moreover, even overdense plasmas are easily obtained with this coupling system. In some cavity ion sources at 2.45 GHz /zw power up to 5 kW is used, yielding very overdense plasma. This entails the presence of some nonlinear wave conversions from the degenerate TEm mode to internal plasma waves, probably excited near the cut-off zones or ECR zones where wave energy may be concentrated. However even for less dense plasma it now becomes easy to understand that the genuine TEm mode is no longer of vital importance. In practice, the coupling to the plasma is achieved with degenerate modes from TE m up to TExyz, where jc, y and z can become large numbers 1). Thus we anticipate the possibility of multi-mode cavities, which play a leading role in the development of ECRIS at frequencies above 5 GHz. However, at 2.45 GHz, other cavity couplers were studied and their starting point was precisely that no definite mode configurations have to be preserved in cavities partially filled with plasma. Thus pre-calculated mode excitations are not indispensable. Moveable sliding shorts and antennas are sufficient to excite the adequate cavity modes. The coupling structure is no longer a theoretical problem but becomes an engineering art where the empirical approach prevails. Thanks to the flexible situation it becomes easy to generate the ECR plasma since its size, density and temperature are adjustable with the help of external RF structures and no theories are required. 2.4.3.4 Adjustable cavity couplers (figure 2.4.3) [204]. Interesting perfor­ mances are obtained with cavities excited by movable antennas and adjustable sliding shorts. ECR plasma sustained by such versatile resonators, where the cavity volume is changeable, were primarily studied during the eighties by Asmussen and coworkers at Michigan State University (MSU) (see section 5.4). In order to achieve good /zw plasma coupling to high-density discharges over a wide range of pressure and input power operating conditions they invented the concept of internal cavity matching. Internal cavity matching, which consists of adjusting both the discharge-loaded cavity coupling to the external transmission line and the cavity size itself, allows the perfect matching of the discharge to the /zw power oscillator over a wide range of pressures, gas types and input power

206

WAVE-PLASMA INTERACTIONS

B rass Cavity

Sliding S h o rt Movable sliding short step per m otor control L, Microwave probe sam ple ports

A djustable coupling probe step p er m otor control Lp.

Microwave power m eter

Pi

x= 0 cm

x = 1 cm

V acuum Pum p

Figure 2.4.3 A cross-section of a multi-polar ECR /xw plasma source and vacuum chamber with adjustable coupling [204].

Figure 2.4.4 The structure of the launcher. The /xw is introduced into the vacuum chamber through the conventional gauge port and fed by the antenna into the cavity, inside which the /xw power is confined [205].

conditions. These two variations, which are usually realized by variation of a cavity sliding short length and by a change in coupling probe depth or coupling loop orientation or size, allow the impressed electromagnetic energy to follow a single-mode-excited, plasma-loaded cavity from discharge ignition to a very

WAVE LAUNCHERS AND COUPLING STRUCTURES

207

high-density operating condition. This high-density operating condition, which efficiently focuses /zw energy into a bounded high-density discharge volume, either is pre-chosen from experience or is determined from theoretical intuition. Thus, MSU now utilizes internal cavity matching in all of their plasma/ion source designs, and they consider the use of this coupling/matching technique an important fundamental principle of /zw plasma source design (see section 5.4). In the late 1970s and the 1980s these coupling techniques were applied to low-pressure ECRIS (including broad-beam sources) and large-area processing sources. In Japan, an even simpler system was described recently [205] using only a moveable monopole antenna. The system has two sets of matching mechanisms: a set of two plungers for matching the waveguidecoaxial converter and the antenna, the length of which is adjustable inside the plasma cavity. A small vacuum tight quartz cap covers the antenna to separate the plasma from the water-cooled wave launcher.

2.4.4

Waveguide-plasma couplers for 2.45 GHz ECRIS

The most common 2.45 GHz ECRIS use rectangular or circular waveguides, operated preferentially in the fundamental mode (TEio mode for rectangular waveguides and TEn for circular waveguides). The ECR type plasmas sustained by an incident wave propagating in a rectangular waveguide were primarily studied during the 1960s as plasma sources for space propulsion. Let us stress that the main advantage over other ECR set-ups at 2.45 GHz stems from the fact that electromagnetic energy is being transported in waveguides instead of coaxial lines. This allows the use of much higher power levels. Powers of several kilowatts can be carried at 2.45 GHz without any significant heating of the waveguide but the windows are heated due to plasma bombardment and /zw losses. Thus specific window technology became necessary (see section 5.3.3.3). A typical set-up is shown in figure 2.4.5; the waveguide is often separated from the plasma chamber by a multilayered dielectric window (fused silica, alumina, boron nitride, beryllium oxide etc). The source, usually of cylindrical geometry, is surrounded by magnetic coils or permanent magnets that in most cases yield an adequate axial B field. The ECR zone is located at least at a few millimetres from the window (this last precaution is valid in all ECRIS types). The EM wave propagates in the circular waveguide in the fundamental TEn mode, which means that it has no axial component of electric field. When coupling a wave to the discharge chamber through a dielectric window, all field components tangential to the window must be continuous across it. In the present TEn-m ode case, a transverse electric field should thus persist once the plasma is present in the chamber. However, from the theory of wave propagation in waveguides one knows that the electromagnetic modes guided by circular waveguides filled with a magnetoplasma are all characterized by the existence of an axial electric field component. Consequently, a rearrangment

208

WAVE-PLASMA INTERACTIONS

CHAMBER WALLS VACUUM WINDOW^ RECTANGULARTO CIRCULAR MODE CONVERTER

'TEv

TUNING SCREWS COILS RECTANGULAR WAVEGUIDE

TE10

MODE

Figure 2.4.5

A schematic diagram of a waveguide ECR source (adapted from [252]).

of the E field necessarily occurs at the plasma-dielectric window interface, generating an axial field component on the plasma side. As seen in section 2.2 waveguide modes cannot propagate in an overdense plasma and cannot be responsible for generation of high-density plasma in the overdense regime, but they are at the origin of the underdense regime. The transition from the underdense to the overdense regime would occur at some wave power level, leading to a conversion from a waveguide mode to an internal plasma mode, which would explain the sudden change in plasma conditions observed when wave power is increased above some level (figure 2.4.6). As already mentioned in section 2.4.5, experimental results show that absorption can occur at lower and at higher B0 fields than the value given by the co = coce condition (see section 5.3.3). Modification to the waveguide technique is provided when one uses a waveguide to transport electromagnetic energy but the wave coupling to the discharge chamber is realized through a coaxial antenna rather than through a dielectric window; thus mode configuration is not preserved. Other techniques are described in section 5.3.4 which utilize linear wave applicators inside multipole magnetic fields. 2.4.5

Slow-wave structures

Slotted Lisitano coils [206], [207] are also used to generate ECR plasma. The originality of this system is that the excitation device is located directly within the plasma. The drawback is that the coil can contribute to the introduction of impurities into the system especially when the system is used with reactive gases. Moreover, there are problems of wave accessibility to the system as well as limited power transmission. Nevertheless, slow-wave structures (SWS),

WAVE LAUNCHERS AND COUPLING STRUCTURES

209

n(crrr3) /K

0

50

100

150 _

INCIDENT POWER (W)

200

P

Figure 2.4.6 High-mode (overdense) and low-mode plasma (underdense) in waveguide (2.45 GHz) ECRIS. The variation of ion density in a waveguide ECR plasma as a function of wave power (adapted from [187]).

such as the helical coil and slotted line antenna (SLA) (figures 2.4.7(a) and (b ), respectively), have been found to play a very effective role for high-density plasma production. An SWS, as the name implies, slows down the phase velocity of the wave considerably ( v p h < c); v p h , the phase velocity of the wave, can then be of the same order as the thermal electron velocity. This implies a much more effective wave-particle interaction and hence a more efficient plasma production. Another important property of a slow-wave structure is related to the slow-wave mode. It turns out that the fields of a slow-wave mode decay very rapidly from the antenna surface. This implies a very high concentration of RF energy close to the antenna surface, so the RF power utilization can be more efficient, but it thus introduces nonlinear effects via wave potential trapping (see section 1.3.4.7). Therefore, SWS generate many non-classical ECR plasma interactions. Moreover, the oblique slow waves can interact with ion motions and favour ion excitations such as the lower hybrid resonance, which will occur for o ) R F = o ) l h r = \ f ( D C e Q i i*e. at B l h r Be c r . The excitation of a slow-wave mode is an important factor while using an SWS in a bounded medium. When an SWS is placed inside a conducting guide, it can also excite undesired fast waves (vph > c). In order to selectively generate the slow-wave mode one then excites the SWS from its broadside by injecting the central pin of a coaxial feeder into a slot of the structure. Thus the accessibility is critical. In addition at high cw power ( ^ 500 W) operation, coaxial line coupling is not efficient due to the following factors. The waveguide-coaxial adapter transition leads to more insertion losses in the transmission line. The impedance matching of load to the line has to be made for each operation using a ‘lossy’ coaxial tuner. Also, elaborate water cooling is required for the tuner and the coaxial line. Baskaran et al [208], [209] have developed a very interesting improvement of the method. In order to handle more /xw power, the coaxial line coupling has been replaced by a hybrid launcher containing a £ -plane horn for exciting the SWS. The slow-wave mode is then generated by the £-plane

210

WAVE-PLASMA INTERACTIONS

n o . OF SLOTS 5 PITCH A N G L E (y-);'0 .7 °

(b)

(a)

HORN ANTENNA

(C)

Figure 2.4.7 A schematic diagram of the experimental system with Lisitano coil inside an ECRIS. {a) Dimensions of a helical coil antenna, (b ) an SLA, (c) an £ -plane horn antenna and (d) the excitation of the SWS by the horn antenna. horn antenna yielding stable tuning and no requirements for water-cooling of any of the components of the /zw transmission line. For this successful system

WAVE LAUNCHERS AND COUPLING STRUCTURES

211

Figure 2.4.8 A compound multi-mode cavity of whatever shape with the usual elements. a quartz plate protects the E horn. To explain the wave transmission, let us recall that in a rectangular waveguide for the TEio mode, the electric field component is oriented only along the narrow faces. The radiation field from the E-plane horn antenna excites the Er component in the case of the SLA and the Ee component in the case of a helical coil. Figure 2.4.7(d) schematically shows how the SWS is excited using an E-plane horn antenna. 2.4.6

Coupling structures for frequencies above 5 GHz (multi-mode cavities) (figure 2.4.8)

2.4.6.1 Generalities. Classical wave generators at these frequencies are rather expensive as compared to the 2.45 GHz magnetron. As they are sophisticated, they need more protection and switches. Very efficient /xw power transmissions utilizing waveguides, with circulators, matching gears and nearly all the /xw components are commercially available. However the dielectric windows necessary for the injection of kilowatts of /xw power into the cavities are not easy to obtain. Very special dielectric materials, such as beryllium oxide, are sometimes utilized instead of quartz and alumina. Fortunately large amounts of /xw power in cw are rarely needed for ECRIS purposes at these frequencies when multi-mode cavities are employed. In any case, when the size of the cavity becomes large as compared to the wavelength, multi-modes are automatically excited in the cavity whether the cavity is filled with magneto-plasma or not. In essence this corresponds to an isotropically distributed wave energy inside the cavity. Technical definitions of the modes are TEX>,Z or TM xyz with x , y, z » 1. Multi-mode cavities are generally not mentioned in /xw text books because the electric field patterns are not calculable. Thus they are ignored by the teachers as if they were unnecessary. However, the ECR community very early recognized their merits [210]. They even found that they are the best solution for

212

WAVE-PLASMA INTERACTIONS

high RF power in dense and hot plasma because they are very easy to match and rather difficult to dismatch. Even when they are filled with a variable plasma, the multi-modes can jump from x y z to x ' y fz"f but the global effect on the /zw line remains generally weak because xy z and x ' y f'z'f/ are always much greater than unity and the Q L of the loaded cavity remains small. Thus the matching issue is minimized, and stable behaviour is obtained thanks to the overlapping of the multi-modes. In general, in order to feed the multi-mode cavity with EM energy, holes preceded by adequately shaped dielectric windows are located on the cavity walls. However specific coaxial feeders are also utilizable. The transmission from the wave generator towards the cavity is generally made with good quality waveguides, a few tuners and also a k / 4 waveguide break for electrical insulation. After being correctly introduced into the cavity, one does not care about further wave propagation inside the box. When the waves pass through a resonance they are partly absorbed expecially if they exhibit R or X mode components. If they do not pass through a power sink, they are randomly reflected and repolarized at the cavity walls, until they are absorbed in the resonances or wave conversions. Thus even if cop > coRF the waves provide electron heating and plasma generation because the cavity remains filled with EM power though the absorption zones may have changed in space and efficiency. Moreover, the cavity may be of any shape provided that the vacuum wavelength A.o remains small with respect to C which is a characteristic length of the cavity. This amazing property enables one to shape the cavity in the most advantageous way not only for optimal cooling, pumping, gas feeding and magnetization, but also for the best ion extraction, /zw power injection, secondary- or primary-electron emissions etc. The materials of the cavity, and their thickness, are not critical (aluminium, copper, stainless steel, tantalum etc). The size of the cavity can be shaped to contain simultaneously the first and second plasma stages and even electron guns. In short, it is difficult to imagine a simpler and more versatile solution. Also all ECRIS working with frequencies above 5 GHz (i.e. A.0 > 6 cm) are equipped with multi-mode cavities. Note that large cavities would also be adequate for 2.45 GHz; however the cost of a large-size magnetic min-Z? field has to be considered. 2A.6.2 Multi-mode cavities and stochasticity via multiple-pass conditions. Very often ECR absorption is referred to as either strong, ‘first-pass’ coupling or weaker multi-pass or cavity heating. During first-pass absorption, the EM wave field is strongly absorbed near the ECR zone and beyond it its amplitude is smaller than the vacuum intensity (cold-plasma approximation). Thus the EM power remains strong between the wave window and the resonance. The first-pass absorption can pump 20-50% of the injected power depending on the ECR area with respect to the geometry of the wave pattern. The remaining

WAVE LAUNCHERS AND COUPLING STRUCTURES

213

power is availaible for multi-pass heating. Thus, with reflecting walls the cavity becomes an important power sink. Note that the loaded Q i depends on the ratio of multi-pass to single-pass absorption. The quality of the cavity walls is important. If they are too absorbing (a carbon layer for instance), the multi-pass coupling drops strongly and the cavity coupling is diminished, so only firstpass coupling with power absorption prevails. Experiments have proven this behaviour. Let us recall that we deal with single and multiple passes of RF waves through the ECR for wave coupling and also with single and multiple passes of electrons through the ECR for electron heating. These situations should not be confused. However, one should keep in mind that, in both cases, the multi-pass condition leads to stochastic heating because wall-reflected RF power is incoherent. Thus two waves that reach the same point along optical paths differing in length by A x arrive with a phase difference A 0 = k A x. For 10 GHz, when A x = 0.5 cm, one obtains A(p = 1 rad. Thus, cavity fields will produce in any case some stochastic heating and can contribute to RF diffusion (see section 1.7). 2A.6.3 Multi-mode cavities with Jacquot's coaxial feeder (figure 2.4.9) [211], [212]. Though dielectric windows on the walls of multi-mode cavities provide absolutely reliable technology, Jacquot proved that one can still improve the best ECR coupling structure. Around 1984, he designed and experimented an original /xw coupler feeding the waves, through an optimized coaxial line into the multi-mode cavity. The exceptional merit of this coupler is to take account along the transmission line of all the critical parameters of the multiply charged ECRIS. Jacquot’s coupler addressed the following issues: (i) (ii) (iii) (iv)

creation of a miniaturized first-stage plasma; injection of the first-stage plasma into the second stage; maintenance of a gas pressure gradient between the first and second stage; optimization of the magnetic field gradient between the first and second stage; (v) plasma injection on the magnetic axis; (vi) /xw propagation along a decreasing B field in the multi-mode cavity; (vii) heat dissipation of the /xw power and plasma losses; (viii) secondary-electron emission of the end of the quartz tube; (ix) absence of plasma bombardment of dielectric windows; (x) efficient cooling of vacuum seals and rare earth magnets etc. All these issues can be solved separately with other couplers but never in such a concentrated manner and optimized space. In figure 2.4.9 we see Jacquot’s wave launcher with details, feeding the multi-mode cavity of the CAPRICE 10 GHz ECRIS. Note that the coaxial wave propagation can be maintained along the quartz tube, because the conductivity of the cylindrical first-stage plasma replaces the conductivity of the coaxial metal

214

WAVE-PLASMA INTERACTIONS

Bmax

Figure 2.4.9 Jacquot’s coaxial injector: CAPRICE ECRIS. 1, hexapole; 2, magnetic coils; 3, iron nozzle; 4, quartz tube; 5, water cooling; 6, /xw guide; 7, gas inlet; 8, pump; 9, copper tube, inner coax line; 10, first-stage plasma; 11, /xw window; 12, second-stage plasma, 13, outer coax tube; 14, axial magnetic field profile.

tube without changing the diameter of this tube. If we were to insert the quartz tube inside the metal tube the coaxial inner tube would change its diameter and the wave propagation would deteriorate and the overall performance of the system would drop. Though not really indispensable, but convenient for optimizations, the coaxial coupling developed for CAPRICE has an adjustable tuning short in the transition of the waveguide-coaxial section, which may allow some mode control [213] especially when imperfect multi-modes are excited. Another pecularity is that the end of the quartz tube, which is at a negative floating potential, is also a very efficient secondary-electron emitter, contributing to the optimum plasma regime. If one were to replace the quartz by a glass or copper tube the overall performance of the system would drop, etc. 2.4.6.4 Imperfect multi-mode cavities. For different economical reasons the ECRIS are built as compact as possible. Thus the multi-mode cavities are

WAVE LAUNCHERS AND COUPLING STRUCTURES

215

presently reduced as much as possible in size. Such reductions decrease the values of x y z in the TE*^ and TM xyz modes and, hence, may introduce critical wave patterns in the structure. For instance it has been noticed that small changes in B , entailing small displacements of the ECR zones, lead to changes of the performance. This behaviour has been studied by Delaunay et al [214] and further commented on by Lyneis [215] who thinks that the /xw modes of the plasma chamber are spaced close together and depending on their loaded Q l several modes may be excited at one time. In addition, the dielectric constant for the plasma depends on the density so the cavity modes are shifted in frequency roughly as (0 = Q)0 + (Op where a>o is the mode frequency in vacuum and cop is the plasma frequency. Plasmas jump back and forth between two states, suggesting that /xw fields in the chamber shift between two modes. Mode shifts in turn can lead to different plasma characteristics, i.e. to different steady state regimes as shown in section 3.2. Thus, the cavity should not be too compact. Let us nevertheless emphasize that not only are modes overlapping, but we will see that many ECR parameters can disturb the steady state regimes and cause plasma jumps exhibiting hysteresis (see section 3.2.6.2). 2.4.7

Wave coupling structures— conclusions

We have reviewed only a few systems employing waveguides, coaxial lines, antennae, cavities, etc. Today the wave launchers and coupling structures for ECRIS are routine systems. They provide in most cases reliable technology and acceptable efficiency. The research for better structures at 2.45 GHz is still under way. For frequencies between 6 and 18 GHz the necessary techniques are now well known. However, further development is expected when higher frequencies will be employed. In any case the theoretical approaches are not valid when the boundaries (i.e. the walls of guides or cavities), perturb the wave modes. Fortunately the lack of theoretical support has encouraged empirical engineering with adjustable /xw equipment. Thus, today, for the ECRIS needs, the wave plasma coupling structures are mainly based on an empirical approach which works fine and to my knowledge structures which are totally precalculated are not utilized. As for the /xw components utilized for wave launchers (/xw generators, windows, transmission lines, flanges, waveguide-coax transitions etc) they have been described by Bourg in the Handbook o f Ion Sources [213].

3 THE ECRIS PLASMA STATES—BREAKDOWN, STEADY STATE AND AFTERGLOW

3.1

3.1.1

ECRIS BREAKDOWN AT LOW PRESSURE IN A VACUUM CAVITY [216]—[218]

Generalities

Let us consider ECRIS breakdown in a cavity in TEm mode. In this case, we have seen that it is possible to evaluate the amplitude of the RF field involved in the process, whereas in multi-mode cavities E is not determinable. It is well known that a gas in a magnetic field can be broken down by very weak RF fields if the frequency of those fields is at the electron cyclotron resonance. Whilst below the Paschen minimum in general the electric field strength necessary to break down a gas rises steeply with decreasing pressure, at cyclotron resonance the field hardly rises at all. This peculiarity has been found both for breakdown in a quartz tube in a cavity [216] and for breakdown in a vacuum cavity [217]. One can consider the breakdown problem in terms of the equation of continuity for the electron number density (see section 1.7) ^ = Vine + D V 2ne > 0 at

(3.1.1)

where v, is the average frequency of ionizing collisions for one electron, while D is the diffusion coefficient. In general, the equation contains more terms, representing losses and gains such as recombination, and secondary emission from the walls, but these are small at the low pressures and relatively high ECR electron energies (W± > 10 eV). Breakdown then of course requires a positive growth rate for the electron density: the ionization term has to outweigh the loss term. Note that breakdown involves the creation of a very weakly ionized gas— hence neither Spitzer collisions nor strong turbulent fluctuations are involved and the electron-neutral collisions should in principle guide the process. Thus even 216

ECRIS BREAKDOWN IN A VACUUM CAVITY

217

a classical diffusion approach (section 1.7) remains acceptable. In the B field the diffusion term can be split into D L and D\\ components and D V 2ne = D ± S72± ne +

o zL

(3.1.2)

where, according to Allis et al [151] D J D ^ v 2ol/ ( v 2col + Q2ce).

(3.1.3)

In any case, D±/D\\ being a ratio, it is not necessary to evaluate numerically each of the coefficients and specify the nature of the collisions. Here vcol is a kind of average collision frequency and Qce = e B /m is the cyclotron frequency. As equation (3.1.3) indicates, for sufficiently low pressures and strong magnetic fields, parallel diffusion is the main loss term, so anything which counteracts this diffusion in a pressure-independent way could account for the data. For instance one has to exclude any electron trapping inside the potential well of the RF field itself. Such trapping is possible in very strong E fields but should be negligible in the present E fields whose amplitude for breakdown will not exceed ~ 10 V cm-1 . As for the collisions in a weakly ionized plasma, ven, the electron-neutral impact, seems the most probable term. The strong parallel diffusion and negligible perpendicular losses lead to the following rationale: only those electrons remain in the discharge region whose parallel velocity is low enough for them to be reflected by the relatively small magnetic mirror forces. With the high perpendicular velocities acquired in the ECR field, the role of collisions is then to convert perpendicular momentum into parallel momentum and so to take away electrons from the confined population by scattering them into a loss cone. This effect is proportional to collision frequency and pressure. The continuity equation (3.1.1) then becomes d ne — = Vitie - venn e at

(3.1.4)

where ven is the frequency of collisions which increase the parallel momentum so much that the electron is lost. Equation (3.1.4) can be rewritten as d ne = (icfiVe) n 0n e - (crenv e) n 0n e at

—

(3.1.5)

where n0 is the neutral density and where (oiVe) and (crenve) are reaction rate coefficients, averaged over the velocity distribution, for ionization and scattering respectively. From equation (3.1.5) it is clear that, when these conditions hold, breakdown, i.e. d n j d t ^ 0 , is reached when (criVe) ^ (aenve>, which is independent o f pressure. This explains the observed constancy of breakdown power at low pressures as will be seen in section 3.1.3.

218

THE ECRIS PLASMA STATES v a c u u m c a v it y

Figure 3.1.1

3.1.2

The experimental arrangement for breakdown measurements [217].

The experimental arrangement and procedure

Schrader’s experiments were performed in hydrogen in a cylindrical vacuum cavity, excited in the TE m mode at 3.4 GHz. A schematic representation of the apparatus is given in figure 3.1.1. Some efforts were made to ensure constancy and uniformity of 1 0 - 4 of the magnetic field. The microwave oscillator had a maximum output power of about 60 mW. The frequency was measured with a transfer oscillator and frequency counter. The inner radius a of the cavity was 3.45 cm, the length zo was 6.4 cm, yielding for T E m mode (see section 2.4) kL = 1.841/a = 0.534 (cm-1) /I'll = 7i I zo = 0.476 (cm-1) SO k = (k2± + k j y /2 = 0.716 (cm-1).

(3.1.6)

This gives for the theoretical resonant frequency /o = k c /2 n the value 3.417 GHz. The observed resonant frequency of the cavity was 3.4075 GHz. The value of the loaded Q of the experimental cavity was obtained from measurements of the standing wave ratio as a function of frequency and it was found to be Q lo a d e d

^ 4.2

X

10 .

With this figure for Q i and known attenuation factors the electric field strength E0 in the centre of the cavity was calculated: E0 = 4 .3 0 ((2 l^ )1/2 (v ^m-1) = 2.7 x where P is the input power to the cavity. right-handed component (R) standing wave.

102

P 1 /2

(3.1.7)

E containsonly the field of the

ECRIS BREAKDOWN IN A VACUUM CAVITY

219

The base pressure in the vacuum system was about 3 x 10- 8 Torr. The electron plasma resulting from breakdown damps the cavity resonance and shifts the resonant frequency. Both effects change the standing wave pattern on the transmission line; a sudden change of the voltage on the detector could thus be taken to indicate breakdown. The oscillator was used in cw mode. The measurements were made with a continuous stream of gas and continuous pumping. After setting the pressure, a certain RF power was chosen whereupon the magnetic field B0 was turned on and slowly increased, until the gas in the cavity broke down. Bo was then further increased, until the discharge was extinguished, and thereafter decreased again, until breakdown was again obtained. The RF power was then lowered and the same procedure repeated. In this manner, at each electric field value an upper and a lower value of the magnetic field where breakdown was just reached were obtained. The procedure was continued down to the power level where breakdown could be obtained no longer. 3.1.3

Experimental results for ECR breakdown in TEm mode in a constant B field [217]

Curves such as those of figure 3.1.2 resulted from the measurements. From each curve, the RF power and the magnet current at the minimum were taken, converted into the electric field amplitude parameter and plotted against pressure. The results of the figure 3.1.2 also show that breakdown occurs for magnetic fields in the ECR which are very close but somewhat higher than the theoretical resonant fields. This point can be explained by the relativistic mass increase of the electron in the ECR which can be compensated by a corresponding increase of the magnetic field. We also observe that breakdown is obtained for a narrow range of magnetic field values. Results given in figure 3.1.3 show that breakdown could be obtained at arbitrarily low pressures without significantly increasing the RF power. This type of behaviour differs radically from the usual behaviour of either DC or RF breakdown which strongly depends on gas pressure. Thus the classical diffusion equation explains at least this outstanding result. Note the small E fields (5 V cm-1) involved in ECR breakdown. Finally it was also observed that the breakdown, i.e. the presence of a plasma inside the cavity, shifted a little the resonance frequency (plasma-loaded cavity) and one could by this method evaluate the plasma density near breakdown. It was found that n ECRhrrMown ~ 1 0 7 (cm-3) which is a very small number as compared to ECR plasma densities at steady state. Thus between the breakdown and the steady state ECR plasma, dramatic plasma multiplication phenomena have to take place. Thus, according to the experimental results the mechanism of cyclotron resonance breakdown in the low-pressure region can be understood as follows:

220

THE ECRIS PLASMA STATES p=Vixio-3

0.7

/-s r ,,

\ 0.6 i

7, 1x10" ^ ( A)

/B ,1 *1 0 ^ (0 )'

0.5 e

‘ 7 (x)

Q_ aj

0.A

?

CL QJ

>

0.3

O o

0.2 z:

0.1

jeB 3 S.00

35.10

35.20

M agnet cu rre n t (A )

Figure 3.1.2 Cyclotron resonance breakdown curves; magnetic field at four different pressures [217].

breakdown power versus

uE > E LxJ

O D H E o p

*0

4)

Figure 3.1.3 Minimum RF power for breakdown as a function of gas pressure. The combined results of seven runs of measurements are given. The electric field given is the amplitude in the centre of the cavity [217].

electrons are accelerated transversely to the magnetic field; as there are virtually no collisions, the resulting parallel velocities are small. An electron population with such a highly anisotropic velocity distribution (in the case studied here, W\\/W± ~ 10-3 ) can be trapped by very small forces parallel to the magnetic field and the process should even be more conspicuous in a magnetic trap. The infrequent collisions can then either scatter an electron from this population, or make a new electron-ion pair. As both loss and gain are thus proportional to pressure, the regime is pressure-independent.

ECRIS BREAKDOWN IN A VACUUM CAVITY

221

P min

Figure 3.1.4 Minimum breakdown RF power against magnetic field in ECR simple mirrors, (a), ECR in the centre of the TEm cavity; (b ), ECR near the end walls of the TEin cavity [218].

3.1.4

ECR breakdown in magnetic mirror configurations [218]

In the previous studies the B field inside the TEm mode cavity was kept as uniform as possible. Recently Gulyaev et al have made measurements under similar conditions but the TEm mode cavity was located inside a magnetic mirror trap. They then observed a much broader range of possible magnetic fields for min-E breakdown and for deep symmetric mirror traps at least two microwave power minima are obtained for variable^ B. One min-E coincides with the ECR in the midplane of the cavity (where E is maximal) and the other when two ECR zones are near the edges of the cavity (figure 3.1.4). The edge minima are explained by a possible increasing of the electron energy due to a stochastic ECR heating which is supposed to compensate the decreasing E field near the resonator edges in the TEm mode. 3.1.5

ECR breakdown in multi-mirror configurations and multi-mode cavities

For more involved cavity modes and particularly for the popular multi-mode cavity the experimental conditions for ECR breakdown become less clearly defined and the detailed analysis becomes more and more difficult. In particular, when a multi-mode cavity is located in a multi-mirror configuration, one observes that the ECR breakdown is possible over very large ranges of B and gas pressure. These easy and noncritical breakdown conditions are due to the presence of different zones of ECR located in the cavity, with possibly various local E fields and gas pressures. When one ECR zone disappears another, located somewhere else, is capable of breaking down the gas. Only when the ECR condition is nowhere fulfilled inside the plasma container does the low-RF-power breakdown disappear and then, for gas breakdown, one has to increase substantially the RF power and/or the gas pressure (but in this case the breakdown is no longer an ECR process). Thus for ECRIS the breakdown conditions are always easily fulfilled even at very low pressures and very low RF power provided that ECR zones exist in the plasma.

222

THE ECRIS PLASMA STATES

P a.u.''

a.u.

\ j r \ * £=------------------ ^— > C

2* O

t a.u.

CD

O rt ^ 7n ID CO 0) CO

CD


V Figure 3.2.3 Plasma regimes in arc discharges n versus applied voltage V.

£ Primary — Figure 3.2.4 The coefficient of secondary emission. population with Te ~ 150 eV at low pressure (< 10- 5 Torr) and high density (n > 1 0 11 cm-3 ). Such a regime ruled out volume ionization as the unique source of electrons in the ECR discharge because the ionisation time (v~ln ~ 10- 3 s) was obviously longer than the electron lifetime. Thus other mechanisms had to provide the electrons, for instance secondary electron emission from the walls. In DC arc discharges the plasma build-up and maintenance is due to volume ionization (a regime) and secondary emission from the electrodes— occasioned by the primary electron and ion bombardment (y regime). The a + y regime might trigger an electron avalanche (figure 3.2.3). In RF discharges without magnetic fields similar phenomena are observed— the y regime triggers an important density transition. We have also seen in section 1.3.9.1 that multi-factor phenomena are possibly present which amplify the secondary electron effects and help to maintain an RF plasmoid. In ECR discharges, multi-factor and y regimes are also plausible. They are due to secondary electron emission from the metallic or dielectric cavity walls. It is impossible to separate the multi-factor effects from the usual secondary emission because the angles of incidence of the electrons as well as their phase conditions are difficult to track. However many ECR plasmas have illustrated the importance of the wall conditions. For instance, wall coating with materials

ECRIS STEADY STATE DISCHARGES

225

having a high secondary electron emission led to impressive improvements of the steady state discharges (see chapter 6 ). Therefore let us recall some of the ECRIS wall properties. 3.2.4

The influence of the walls, secondary emission

3.2.4.1 Action o f electrons. When a beam of electrons is incident on a solid wall, the latter will emit electrons, some of which will simply be the primary electrons reflected without loss of energy. However, the walls also eject a certain number of secondary electrons per incident electron, the average value of this number being greater or smaller than unity. The secondary electrons, for the most part, have an energy of the order of 10 eV. Thus they are energized in the ECR in the same way as volume-produced electrons. The coefficient of secondary emission, 8, is defined as the ratio of the total number of electrons leaving the walls to the number of incident electrons. (Secondary emission therefore, by convention, includes reflected electrons as well as true secondary electrons.) The elementary process of secondary emission is still not completely understood. Nevertheless, experiment has verified that a threshold energy equal to the work function of the surface bombarded, Es = e 1 ) and for insulators (8 10) than for other substances. The maxima occur at energies in the range 100-1000 eV. An important effect is obtained by changing the angle of incidence. Secondary emission is more intense for greater angle of incidence of the primary electrons (figure 3.2.5), but is does not depend on the temperature. Finally, the time between the arrival of the primary electron and the departure of the secondary electrons does not exeed 10“ 12 s. The majority of these experimental results can be explained if one accepts that (i)

the incident electrons penetrate to a greater or lesser degree depending on whether they are incident at a smaller or larger angle of incidence; (ii) over the whole of their paths in the solid they impart energy to electrons, which are scattered in all directions; (iii) those of the secondary electrons which have gained a sufficient quantity of energy at a sufficiently small distance from the free surface are able to escape from the latter; it has been shown that secondary electrons originate from depths less than about 30 A. Finally let us quote the Maker effect.

226

THE ECRIS PLASMA STATES

2,6

2.4

2,2 2,0 1,8 1,6

Cu Mo Ni W

1.4

1,2 1,0 0,8

C

0,6

0,4 80 60 40 20 0 20 40 60 80

>

0°

Figure 3.2.5 The variation of 8 as a function of the angle of incidence of the primary electrons. Values of 8 greater than 1000 can be obtained by lightly oxidizing an aluminium surface (producing a thin film of AI2 O 3 ) and then depositing on it a layer of CS2 O. The latter becomes positively charged and strongly attracts the aluminium electrons. Unfortunately the Maker effect is difficult to utilize in plasma because the particle bombardment rapidly destroys the thin films and the effect is limited in time. However different wall oxidations are obtained when oxygen is introduced into the source and ECRIS improvements are then observed. Some scattered data on secondary emission are gathered in [2 2 0 ]. 3.2.4.2 The action o f ions, secondary electron emission and gas supply. Ions, like electrons, may cause secondary emission from surfaces on which they are incident. However, they differ primarily in that the threshold energy of a singly charged ion is double that of electrons: Es ~

2

ecp.

This is due to the fact that, besides the secondary electron which is liberated, the ion itself leaves the surface taking with it a second electron which neutralizes the ion. But this time the energy available for this reaction is equal to the total ion energy (i.e. the kinetic energy of the incident ion plus its ionization energy eVi, which increases sharply with increasing charge states of the ions). Thus, the yield of secondary ion emission (ylon, number of secondary electrons/number of incident ions) is generally less than unity, for energies below 1000 eV for singly charged ions. But yion increases with the total energy of the primary ion up to more than ten, this value being reached at total energies of the

ECRIS STEADY STATE DISCHARGES

227

W q (e V )

Figure 3.2.6 (a) Total electron yield y for impact of Ar8+ ions on clean W and gas-covered Ta and Pb against kinetic energy. The yield of Ar+ on Ta was measured to deduce the kinetic contribution [222]. (b) Total electron yield y for 20 keV Ar ions with charge q = 1 to 12, versus total ion potential energy Wq. order of a few kiloelectronvolts for multiply charged ions, meaning that highly charged ions even with low kinetic energy have important secondary-electron yields (figure 3.2.6) as demonstrated by Delaunay et al [222], [223]. As mentioned above, the incident ions, when they are not implanted in the solid walls leave the surface as neutralized atoms, which represents a considerable gas flow. Thus the neutral gas in the ECRIS is supplied by three sources, the external one in addition to the wall desorption and the recombined ion flux leaving the walls. 3.2.5

Links between instabilities, wall secondary emission and steady state

The plasma instabilities produce permanent or sporadic electric fields which energize the electrons before propelling them towards the walls. According to figures 3.2.3 and 3.2.4 the secondary emission can then yield values of 8 > 1. Thus the instability increases the electron wall losses but the secondary emission may reinject more electrons than primary electrons are lost, and if 8 becomes greater than unity an avalanche of electrons becomes possible, leading to highdensity plasmas. The ignition of the dense ECRIS plasma can be observed with pulsed RF power (figure 3.2.1). Before the steady state plateau is established many bursts and plasma depletions are observed versus time. A theoretical approach to the transition looks impossible—too many phenomena are present. As for the steady state— illustrated by the plateau in figure 3.2.1— we will now describe it in a simplified global way, with the help of the equation of continuity. 3.2.6

The steady states and the variety of plasma regimes

When the plateau is reached let us call y the overall average secondary

228

THE ECRIS PLASMA STATES

coefficient of the ECRIS walls. We have now to introduce y into the equation of continuity for the electrons with density n (n ~ constant in steady state). As seen in section 1.7 we can write in coordinate space d n/dt = 0 =

Z)V n

VCreationn

VdestructionM

(3.2.1)

where D is a symbolic average diffusion coefficient; V2n ~ \ n / d 2]n & [A]n if we consider a density profile represented by n = n o sin (x/d ) (a simple but acceptable assumption. The term vcreation is the ionization frequency in the neutral gas yielding electrons through the a effect. We can assume that ^creation == ^ionization =: vionization) w h e r e (cfVionizafion) is the ionization rate in cubic centimetres per second and no the density of neutral atoms. On the other hand, the term vdestruction of the electrons by recombination is generally negligible inside ECR plasma. Thus equation (3.2.1) can be simplified: D[A]n ~ VionizationK' However we have seen that the flux of loss D[A]n creates on the wall a flux of reinjected secondary electrons + y D [A ]n , which counts as a source term in addition to vwnn. D[A]n = vionn + yD [A ]n _ ___ (3.2.2) D[A]n = (a ionv)n0n + yD [A]n. The above equations seem valid when we reach a steady state i.e. when we assume, that, after some experimental tunings of the pressure, the RF power and the magnetic field shape, a stable regime R\ has been obtained. 3.2.6.1 The influence o f secondary electrons on the steady state regimes. When d n /d t = 0 we are encouraged to surmise that the values of D , v and no also remain constant versus time. Then, for a short while at least, we can also assume that y remains unchanged, but we know that, without changing voluntarily the wall conditions, they will change spontantanously versus time. Due to some local plasma impacts, followed by possible outgassings, sputterings, oxidizings, polishings, heatings etc, the secondary emission y will change in some way. If yD n is large with respect to (av)no and y spontaneously increases by a few per cent, the conservation of the same regime R\ is now possible by decreasing voluntarily the neutral gas pressure and vice versa. Always for the same regime R\ considering equation (3.2.2) if one keeps n0 unchanged, this variation of y makes it possible to change (pv) (i.e. the electron velocity) by retuning the RF power. Finally the change of y also makes it possible to change the magnetic field of the structure which acts mainly upon the diffusion losses D[A]n. Many other steady state regimes R 2, ^ 3 , . .. with densities «2 » . . . and other gas densities n02, fto3 > electron velocities i>2, ^ 3 and B2, £ 3 field profiles

ECRIS STEADY STATE DISCHARGES

229

are plausible, depending on the wall conditions and their capricious properties. Therefore a great variety of steady state regimes are obtained during the first hours or days of the ECR discharge, i.e. when the wall conditions are not stabilized, and the reproducibility of the regimes is poor. 32.6.2 The influence o f the cavity modes on the steady state regimes. We have seen that different wave modes can be excited in plasma-filled cavities or wave guides. For instance the excited modes depend on the loaded Q i value especially when imperfect multi-mode cavities are utilized where the cavity size L is not much larger that the vacuum wavelength. One then observes that the plasma can jump back and forth between two states. Finally, a hysteresis is sometimes observed when a source is carefully tuned to peak at high output and then jumps back to a very different state. To recover it is sometimes necessary to reset the source parameters and work the output back up. The phenomena can be explained by EM mode transitions when the modes change, the E field patterns change in the ECR zones and subsequently the characteristics of the resonance might change, which leads to another steady state regime. Looking for a better tuning of B , no or n is then not always rewarding, because due to the persistence of the new E field pattern, the ECR condition is no longer what it was. This might explain the hysteresis. Local changes of E have been observed in the CAPRICE source [214]. On the other hand the number of possible modes in plasma-filled cavities is probably larger than in vacuum cavities. Lyneis [215] has calculated the possible modes in an imperfect cylindrical multi-mode cavity. In table 3.2.1 a set of modes are listed for a CAPRICE size cavity operating at 10 GHz. The average mode spacing is 37 MHz not counting mode degeneracies. The half-power points for cavity modes are given by A / / / = 1 /Q l .

(3.2.3)

Substituting the average mode spacing into this equation gives Q L = 270. So if the cavity modes have Q values significantly higher that this they will not necessarily overlap, while if the Q values are lower then there will be a significant overlap. Different experimental estimations indicate that QL values of the order of 200 are realistic and EM mode transitions in ECRIS cavities are then very plausible. Among the possible TE or TM type modes, some modes will couple only weakly to the electrons because their electric field patterns do not overlap the ECR surface strongly. Techniques to experimentally control the modes would include coupling schemes which preferentially excite one type of mode, using adjustable coupling, or even dynamically tunable cavities [204] (see section 2.4). Nonetheless, very stable regimes are reached in multi-mode ECRIS cavities even with imperfect modes. Long-run optimization for stable regimes is routine nowadays in high-performance ECRIS provided that the absorbed RF power and the gas pressure are controlled and kept constant. Stable regimes are then

230

THE ECRIS PLASMA STATES

Table 3.2.1

Calculated frequencies in gigahertz for all modes in vacuum between 9.5 and 10.5 GHz for a cylindrical cavity 16.28 cm in length and 6.6 cm in diameter [215]. Mode

Frequency

T E 3.1.8

9.553 94 9.591 07 9.63604 9.68456 9.713 39 9.74641 9.848 95 9.87620 9.939 60 9.975 18 9.97518 9.98665 10.0400 10.055 6

T E i.i.io

TM

3 .2.3

T E 5.1.3

TM 2.1.6 TE 2.2.1 TM o .i.io T E 2.2.2

TM TM

3 .2.4 1. 1.9

T E 0 . 1.9 T E 5 . 1.4 T E 4 . 1.7 T E 1.2.7

Mode

Frequency

T E 2.2.3

10.0888 10.1513 10.1930 10.1930 10.2185 10.2657 10.2815 10.3167 10.3172 10.3172 10.3621 10.3791 10.4793

TM TM

1 .2.0 1.2.1

T E 0 .2.1 T E 2 . 1.10

TM

2 . 1.7

T E 3 .2.9

TM TM

3 .2.5

1.2.2

T E 0.2.2 T E 5.1.5 T E 2.2.4 T E i.i.n

possible for weeks, as long as the wall conditions of the ECRIS remain in equilibrium with the plasma.

3.2.6.3 The influence o f coupling modes and internal wave conversions on the steady state regimes. Considering ECR plasmas in wave guides or single­ mode cavities, preferential mode excitations are necessary especially at 2.45 GHz. Some of these techniques based on dynamically tunable RF components have been used for scientific and commercial applications. In these sources, they adjust both the cavity frequency and the coupling strength and report significant improvements in the transfer of microwave energy to the plasma [204]. Excessive local heatings in the RF equipment must be strictly avoided, because they can result in mode jumps. Nonetheless reliable and reproducible working regimes are tunable even in the overdense plasma, exhibiting however many aspects of hysteresis (see figure 2.4.6). In any case, in spite of the generation of ES waves (Bn waves or Lm waves) and the possible presence of plasmon decays, ECR plasma can be ignited and maintained in equilibrium. In consequence the influence of internal wave conversions on the steady state regime is not necessarily catastrophic. They just change once more the wave pattern and the localization of the energy sinks. For instance the overdense plasma must be considered as one of the possible steady state regimes— where the collisional and turbulent effects are in equilibrium with the wall effects, the particle losses and creations. Thus, even if the plasma is turbulent, reliable steady states are reached in the presence of wave conversions.

ECRIS STEADY STATE DISCHARGES

231

3.2.6.4 Steady state and reflected RF power. Absorbed and reflected RF power act strongly on the plasma equilibrium. Tunable matching of the line with the plasma load is advisable; however, the power absorption itself depends on the instantaneous plasma characteristics. Thus the plasma load is dynamically changing due to spontaneous variations of wave cut-offs, local density and temperature gradients, wall emissions etc. The matching elements of the RF line cannot compensate all the rapid variations of the plasma load, and the correlations between RF power reflections and steady state characteristics are not easy to interpret. As fever reveals a disease, RF power reflection reveals that better plasma regimes should be searched for by tuning the externally accessible parameters such as pressure, magnetic field and RF power, until the ratio of reflected to injected RF power decreases to a minimum (< 20%). 32.6.5 Influence o f the velocity distribution on the steady state. consider the diffusion equation in velocity or momentum space

Let us

% = S ( P±) + V D V f

at where / is a velocity distribution and D the diffusion term which depends on A p 2/Tcorreiati(m. A p is a possible momentum kick (due to 90° collisions, turbulence, RF fields, coc acceleration or cop oscillations etc) which depends on the plasma properties and thus D has to be evaluated for each different plasma situation. The oversimplified diffusion coefficients (like classical, RF or Bohm diffusion) are not relevant for all these plasma situations. S(p±) is the source term which depends on momentum kicks (as well as the loss term). In steady state we assume that the distribution is stationary, d f / d t = 0, and all the terms are equilibrated (thus heating and ionizing are balanced by losses) but the steady state is surely perturbed if a nonlinear process grows. As V / changes, d f / d t and all the other terms might vary. A stable equilibrum is possible between two unstable tunings and vice versa. However, in order to describe different steady states, it would also be necessary to describe the velocity distribution before and after the nonlinear processes. These fundamental studies are complicated, expensive and rarely rewarding. During the last 30 years little information on experimental distribution functions has been published. Thus the questions are always the same: In the numerous possible steady states of an ECR plasma what are the electron distributions? The overall source terms S (p ) and the loss term D V / are surely not identical for different equilibria and a link surely exists between velocity distributions and steady states. Hence further fundamental research on ECRIS velocity distribution should be performed in order to provide better understanding. 3.2.7

The influence of instabilities (short review) [224]—[234], [344]

When one experimentally tunes the steady state one always notices transient, more or less destructive, unstable regimes. Each different instability changes

232

THE ECRIS PLASMA STATES

differently the characteristics of the equilibrium. As one does not study these instabilities one rather turns some knobs in order to find a more favourable tuning without conspicuous instabilities. In ECRIS mirror devices many instabilities exist: macro-instabilities, often called MHD, or flute instabilities, and micro­ instabilities which are divided into many different types. In addition RF and drift instabilities might be excited. The instabilities increase the plasma losses to the walls and therefore also act on the wall secondary emissions and desorptions, i.e. change the steady state. Moreover, in section 1.3.7 we suggested that instabilities might be driven by the nascent plasma oscillations which contribute to the plasma effervescence. In the present section let us very roughly describe the physical mechanisms of the growth of some instabilities and how energy is coupled to these instability waves. 3.2.7.1 Macro-instabilities—origins and remedies. Macro-instabilities are caused by particle density gradients in the coordinate space. They manifest themselves as oscillations or sporadic perturbations of the plasma, which, as a rule, result in fast departure of plasma to the walls. Thus they are dramatic perturbations involving MHD effects. As can be seen from figure 1.6.3, in the central part of the trap, the B field intensity on the axis is greater than that at the periphery (the lines of force have a positive curvature with respect to the plasma); therefore, an axisymmetric plasma in this magnetic configuration is in a state of unstable equilibrium. Any random perturbation of axial symmetry grows with time. In other words, in the central part of the trap, any fluctuation on the surface of the plasma leads to rapid ejection of plasma to the wall and thus limits the confinement time. In all simple mirror ECRIS this instability is supposed to exist at steady state and in effect the confinement times hardly reach 1 0 - 5 s (see section 1 .6 ). One of the most effective means of combating this instability is obtained by a field distribution of the magnetic trap such that the magnetic induction increases from the centre not only in the directions of the ends but also along the radius (which is called a min-B configuration). It can be obtained by superposition on the field of a simple mirror of an additional multipole transverse magnetic field. Thus in min-B ECRIS when underdense plasma is obtained, the macro­ instabilities are rarely observed and long confinement is generally possible, which is not the case for simple mirror ECRIS and even less for overdense plasma (see section 1.6.4). 3.2.7.2 Micro-instabilities— their aspects and origins. Micro-instabilities have a kinetic origin and are produced by nonequilibrium particle density gra­ dients in the momentum space. They manifest themselves as a sharp increase in the diffusion coefficients. The mechanism of the increase in particle flux, momentum and energy is due to excitation in the plasma of natural oscilla­ tions, which result in a sudden reduction of A t, the time step of diffusion, and, therefore, its acceleration in both the coordinate and momentum spaces.

ECRIS STEADY STATE DISCHARGES

233

A source of plasma micro-instabilities in ECRIS is the possible distortion of the momentum distribution function of the electrons, which makes this distribution anisotropic and gives rise to instabilities for v±/v\\ ^ > 1 . In section 1.6.4 we saw that the ions are trapped in a potential dip, but since this potential has practically no effect on the confinement of electrons they have a fundamentally nonequilibrium distribution function. As practically all of the plasma energy is concentrated in the electron component, the reserve of excess free energy is great and the conditions for formation of micro-instabilities are favourable. Thus small factors might trigger them—and lead to large effects. In general micro-instabilities are a result of wave-particle interaction, where the wave is one of the natural waves of the ECR plasma with characteristic frequencies. As seen in section 2.1, the waves in the plasma can be of two types: transverse (EM) and longitudinal (ES). The mechanisms of exchange of the energy of a charged particle with electromagnetic and electrostatic waves differ, since the electric field of the wave E and the wave vector k are perpendicular in an EM wave and parallel in an ES wave.

3.2.7.3 Conditions fo r the triggering o f micro-instabilities in ECRIS . Since the efficiency of energy exchange between the electron and the wave is a function of E and ve, the interaction of an electron with a longitudinal wave is maximal for ve\\k and is absent when ve _L k\ for effective energy exchange, it is necessary that the wave and electron velocities be similar in magnitude. Then a particle automatically synchronizes its motion with the wave such that their velocities are equalized: particles that overtake the wave are decelerated, intensifying it (Cerenkov effect), and particles that lag behind the wave are accelerated, attenuating it (Landau damping). If there are more fast particles than slow ones, the wave, on average, builds up, i.e. the plasma is microscopically unstable; otherwise (equilibrium velocity distribution) the wave, on average, is damped, i.e. the plasma is microscopically stable. In an ECR source, micro-instabilities can arise only in electron longitudinal modes (ES waves) that are propagated at a nonzero angle to the magnetic lines of force and that are characterized by high frequencies. Thus frequencies around ojp and phase velocities of the order of ve are particularly dangerous. The role of the ions is restricted to the creation of a stationary background of positive space charge and ions do not participate in the triggering process. The mechanism of coupling of electrons with an EM wave is more complicated than the case of ES waves. Strong coupling between electrons and an EM wave can occur only when k is perpendicular or almost perpendicular to ve and the velocities of particle rotation in the magnetic field and of rotation of the vector of the electric field of the wave are similar. Hence, an unstable electromagnetic wave in an ECRIS is a wave that is propagated along or at a small angle to the magnetic field and that has right-hand polarization and a frequency that is close to the frequency of electron cyclotron rotation.

234

THE ECRIS PLASMA STATES

Thus, anisotropy of the distribution function of electron velocity in a mirror trap makes the plasma unstable to excitation of electromagnetic and electrostatic waves propagated at an angle to the magnetic field. When the plasma density is low, these waves are not excited, since the plasma frequency is low in comparison with the cyclotron frequency and, therefore, coupling between cyclotron rotation and plasma oscillations of the electrons is absent. If the plasma density is increased so that o)pe is of the order of coce, then conditions for transfer of the energy of cyclotron rotation to the energy of natural longitudinal and transverse waves become favourable and instability arises. Note that under these same conditions (see figure 1 .6 . 1 0 ) the mirror confinement fails. With a further increase in plasma density, when cope becomes greater than coce, wave-electron coupling can move to higher harmonics of the cyclotron frequency and the plasma is unstable. However, resonance coupling between electron rotation and plasma oscillation is, probably, weakened with increasing harmonics. Experiments performed by Jacquinot [223] with hot electrons in a magnetic mirror trap show that micro-instabilities in both the electrostatic and electromagnetic modes arise when 0.1 < a)2pe/(o2e < 20. Thus hot overdense plasmas are both macro- and micro-unstable. Conversely, most of the ECR sources of multiply charged ions that are in use have Mpe/tOce < 0 . 1 and, therefore, their plasma might be microscopically stable, their mirror confinement decent (figure 1 .6 . 1 0 ), and due to good curvature of the magnetic field lines they seem even macroscopically stable. 3.2.7.4 The effect o f micro-instabilities on electron confinement and electron density. Micro-instabilities tend to reduce the electron lifetime in an ECRIS —i 3 /2 even with m in-# configuration. Then the Spitzer time [xei] = A (n e/T e ) no longer determines the electron lifetime xe. The micro-instabilities decrease xe in such a way that

1 _

1

Tei

1

oss

where xioss globally accounts for the effects of the micro-instabilities. We have seen in section 2.3 that the power balance implies the actual electron lifetime; thus An ( 1 P rf 1 I f 2+ W

= (Vol) neK T e

If we assume that the loss term increases with injected RF power (micro­ instabilities and RF diffusion are enhanced) and that it becomes comparable to the Spitzer collision term we can write that the upper limit of electron density as given by Melin [224] is

ECRIS STEADY STATE DISCHARGES

235

Thus even without considering cut-off conditions for PRF penetration, we see that the density scales with \ / P r f / (Vol). Again we see that a systematic increase of RF power is not rewarding, since it can feed the instabilities instead of improving the plasma parameters. 3.2.7.5 Forced micro-stability at steady state ? As already observed by Alikaev eta l [225], in all experiments in which strong micro-instabilities with anisotropic temperature could be studied, the instabilities were observed not during the steady state but in the afterglow after switching off the RF fields [223], [238]. It can be assumed, therefore that, in the presence of a forced high-frequency field, the weak natural waves that are self-generated are not amplified by electronwave interaction. Possibly the synchronization between the natural waves and the electrons is destroyed by forced motions of the electrons at the frequency of the external field. If this qualitative reasoning is valid, then the RF heating of the electron can simultaneously be an effective means of protection against the growth of high-frequency oscillations that are dangerous for stable plasma confinement [103]. However, on the other hand, (as seen in section 1.7), even without micro-instabilities, strong high-frequency power injected from the outside enhances also the RF diffusion coefficient. Thus losses due to the presence of RF waves are unavoidable in ECRIS. 3.2.7.6 Instabilities due to hot-electron gradients. Plasma gradients are well known troublemakers, and were taken into account in the vQ)p collision frequency (section 1.3.7). However, only recently could the growth rate and instability criterion of a plasma instability driven by density and temperature gradients of hot electrons be calculated. Pu and Halverson [226] have shown that, when hollow density and temperature profiles are developed due to strong local ECR heating, a drift wave type, low-frequency electrostatic instability may be excited. This instability transfers energy from hot electrons to the ions, thus destroying ion confinement in the direction perpendicular to the magnetic field lines. 3.2.7.7 Recapitulation o f some possible instabilities in ECRIS plasma. To finish this unsolved problem of instabilities, let us recapitulate some well known instabilities which possibly occur in ECRIS plasma. Two-stream instability—beam-plasma instability or Buneman instability [230]. An ES micro-instability which can develop when a stream of particles of one type, moving in a well defined direction, has a velocity distribution with its hump well separated from that of another type of background particles through which it is flowing. A stream of energetic electrons passing through a cold plasma can, for example, excite ion waves which will grow rapidly in magnitude at the expense of the kinetic energy of the electrons. Mirror instability [223]. An EM micro-instability which can arise in an openended configuration when the plasma particle energy component perpendicular to the magnetic field is greater than its longitudinal component. The particles

236

THE ECRIS PLASMA STATES

will then become concentrated to the mid-plane between magnetic mirrors. As a consequence the field lines will be expanded by the plasma pressure in the same plane and the mirror ratio increases. This reinforces, in its turn, the particle concentration in the mid-plane. For a sufficiently large plasma energy the expansion of the field grows at an increased rate and becomes unstable. Loss-cone instability or Harris instability [227]. An ES micro-instability which arises in open-ended systems where the deficit of plasma particles within the loss cones produces a ‘humped distribution’ in velocity space. This creates a situation similar to that in the two-stream instability. Whistler mode (or Helicon instability) [228]. This is an EM micro-instability due to a resonance between an RF wave (R wave) and a drift wave generated by gradients of n and T but which arises at frequencies near the cyclotron frequency. It is produced by electrons which exchange energy with the Whistler wave [233]. Flute instability or interchange instability. An ES macroscopic instability resulting from a charge separation due to gravitational fields or magnetic gradients (simple bottle) perpendicular to the magnetic field that produce transverse drift motions of ions and electrons. The resulting electric field generates in its turn a transverse drift by which expansion or gravitational energy is released and fed into a growing unstable motion. This instability is suppressed in min-B configurations. Cyclotron instability. An ES micro-instability in a homogeneous anisotropic plasma due to coupling between the cyclotron motion of particles and an ES wave which is associated with plasma oscillation. The ES wave is in turn coupled to the longitudinal motion of the particles. Weibel instability [231 ]. When two electron temperatures T± and T\\ are present, this electromagnetic instability tends to restore the isotropy. Universal drift instability. A class of micro-instabilities due to the plasma diamagnetic drift arising from the spatial density and temperature gradients across a magnetic field. They are universal in that they can occur in any confined plasma, regardless of the geometry of the configuration (since particle energy and density are not the same everywhere).

3.3

3.3.1

SIMPLE MAGNETIC BOTTLE ECRIS; EXPERIMENTAL STEADY STATE CHARACTERISTICS

Generalities

Let us divide the ECRIS experiments into two different types, ECRIS inside simple magnetic bottles and ECRIS inside min-B magnetic traps. Overdense plasma sources are achievable in both ECRIS types, but we rather consider them as simple magnetic mirror sources since in overdense ECRIS the mirror

SIMPLE MAGNETIC BOTTLE ECRIS

Figure 3.3.1

237

Ion current against PRF\ MAFIOS mirror ECRIS.

configuration is not an important parameter and simple mirrors with small mirror ratio do as well. The simplest characterization is obtained by observing the extracted ion beams while changing the main ECRIS parameters: RF power, B field intensities or shapes and gas pressure. In such simple experiments one evidences rapidly the variety and complexity of the steady states as analysed in the preceding paragraph. In figure 3.3.1, we see some ion currents—extracted from the early ECRIS [235] built at Saclay— versus PRF. Jumps obviously related to different steady states were observed but in the pressure range of above 10- 4 Torr these variations are not dramatic. With a waveguide ECRIS (figure 2.4.6), intense mode changes were ascertained when underdense to overdense plasma transitions were created by varying the RF power [187]. However, the most outstanding differences in the steady state characteristics occur when the gas pressure is reduced below 10~ 4 Torr and the RF power density in the plasma remains in the range of ~ 1 W cm -3 . Suddenly highly energetic electrons appear whereas the total plasma density tends to saturate below the critical density (corf > Q)p). Moderately multi-charged ions are then observed. For stronger RF power, localized overdense plasmas are achieved but instabilities perturb the steady state. Different diagnostics for density and temperature measurement were utilized; however, the most direct ones are those of electron energy deduced from x-ray spectra. They teach us about the strange behaviour of electrons in the steady state. Note that the ions have too much inertia to respond to RF fields in the gigahertz range. Therefore only electron characteristics are dramatic. The ions remain cold and just maintain the global plasma neutrality.

3.3.2

Steady state characteristics in underdense simple mirror ECRIS

Because of severe x-ray hazard, ECRIS have to be shielded with lead plates. The hard x-rays are not emitted in all the observed steady states but, as they are emitted in some of them, in order to evaluate the rates one needs specific detectors of x-ray spectra. These tools of radioprotection provided the first diagnostics for energetic electrons inside the plasma and on the walls of the container. Electron energies up to several megaelectron volts have been reported. Different simple bottle ECR plasma have been objects of theoretical

THE ECRIS PLASMA STATES

238

PLASMA VESSEL AND RESONATOR 9 .72 GHz

3db co u p le r

ION EXTRACTION AND FOCUSING

COPPER RESONATOR

60 MAGNETIC SPECTROMETER

FARADAY CUP ION COLLECTOR

PENNIN GAUGE'

gmn mm mtm .NFTIP —* ^ To gas MAGNETIC regulator MIRROR TURBOPUMP

I

TURBOPUMP

Figure 3.3.2 The Bochum experimental arrangement for simple mirror ECRIS [246], [247]. investigation with regard to heating [191]—[194], [197], [236]—[241]. Experimentally, many x-ray diagnostics of high-energy electrons in ECR discharges in simple mirror configurations were performed in Oak Ridge and in Nagoya. Dandl et al (1964) used microwaves of 10.6 GHz with an input power of up to 50 kW and deuterium as the discharge gas [242]-[244]. Ikegami et al [245] used microwaves of 6.3 GHz with an input of 2-5 kW and helium as the discharge gas. In all cases the neutral gas pressure was some 10- 5 Torr and the microwaves were fed into the resonator perpendicular to the mirror axis. Despite the different parameters in all experiments the resulting density of hot electrons was found to be between 1 and 1 0 % of the cold-electron density n c, which was about 10n -1 0 12 cm-3 . The hot-electron density appeared to be comparable to, or even higher than, the neutral gas density. Hot-electron rings were often detected. In all cases the density of the hot electrons was found to be non-uniform. Ard and Dandl [243] reported belt-shaped density distributions as early as 1965. In most ECR plasmas, anisotropic, long-living, high-energy, nearly collisionless electrons were observed— but not studied in detail. The first fundamental study of the x-ray spectra linked to the steady state of a simple mirror ECRIS was performed in Bochum in a group directed by Wieseman. This study was continued for years; its results are discussed in the following paragraph. 3.3.2.1 The Bochum experimental arrangement [246]-[248]. The experimen­ tal arrangement is shown in figure 3.3.2. A 9.75 GHz microwave generator, available up to peak powers of 2.5 kW, is used. It can be operated cw or can be pulsed with arbitrary pulse width and duty. It is transmitted to the plasma via four entrance ports located pairwise on opposite sides at the midplane of

SIMPLE MAGNETIC BOTTLE ECRIS

239

t/ms

Figure 3.3.3 The time dependence of the peak values of the x-ray spectra (150 keV and Ka-line). Ar p = 1.6 x 10~4 Torr. the cylindrical resonator. Resonator dimensions are large compared to the mi­ crowave wave length and multi-modes are excited. A magnetic mirror trap field is produced by two pairs of toroidal coils; each pair is driven by a separate current supply. Gas is fed into the vacuum chamber through a needle valve and penetrates, through a matrix of 1 mm diameter holes in the resonator wall, into the resonator. The gas pressure (5 x 10~6—3 x 10- 4 Torr) is measured outside the magnetic mirror field. The pressure reading is used to operate the needle valve in a feed-back loop to keep the pressure constant during operation. The x-rays emitted from the plasma provide the tool for hot-electron diagnostics. For this purpose a 5 cm diameter Nal (TI) crystal is used to measure x-ray spectra in the range E ^ 150 keV. For lower energies an SiLi crystal with a 7/zm Be window is used. In this way the energy range E > 1 keV is covered. Below 1 keV no measurements are made. If the magnetic field is so weak that the fundamental ECR zone lies outside the resonator, there is very little microwave power absorbed and no hot electrons are seen. As usual in all ECR plasmas when the magnetic field is increased, strong absorption starts as soon as the resonance zone enters the resonator. Simultaneously the electron energies rise rapidly, as can be seen from the x-ray bremsstrahlung spectrum taken with an Nal crystal. Heating of the electrons becomes most efficient at the strongest magnetic fields available. If one relates the slope of an observed bremsstrahlung spectrum to the temperature of a Maxwellian distribution of electron energies with the same slope, one obtains ‘apparent’ temperatures up to 100 keV. From the early bremsstrahlung measurements one could not see any deviation from a Maxwellian distribution. (If a cold group exists, the energy of these electrons must be below 1 keV.) Under obviously unstable operating conditions, however, non-Maxwellian distribution functions can be clearly detected (see below). The build-up and decay of the x-ray spectra have been measured under pulsed conditions. The results of such measurements show that the build-up of the lowenergy electron group is faster than the heating of the hot group (figure 3.3.3).

240

THE ECRIS PLASMA STATES

Ey/ MeV Figure 3.3.4 The variation of x-ray spectra with incident RF power: Xe+/? = 2 x 10- 5 Torr. 3.3.2.2 Unstable steady states in the Bochum ECRIS. Under cw operating conditions the plasma parameters are not necessarily stationary. There are two typically unstable operating conditions. At moderate and low pressures and low power, one sees pronounced relaxation oscillations on the reflected microwave signal having time periods of several tenths of a millisecond. During the absorbing state the electron temperature is high whereas in the reflecting state there is a group of low-energy electrons and a tail of high-energy electrons which have not been lost since the end of the absorbing period. At low pressures and high power the plasma is unstable in the sense that large fractions of the plasma can be lost in sudden bursts to the wall. The latter instability limits the capability of the device as a source of highly charged ions. As evaluated, the plasma lifetime is of the order of ~ 10- 5 s. For high Bmirror and ~ 2 x 10- 5 Torr, it appears that there is an augmentation of multiply charged ions as power is increased from 600 to 800 W. This is accompanied by a rapid increase of the density of highly energetic electrons, as shown in figure 3.3.4. At about 700 W the reflected microwave signal shows a transition from the region having relaxation oscillations to the stable absorbing region. Above 1200 W the plasma becomes totally unstable and a rapid plasma loss occurs. In the region between 800 and 1200 W the machine provides a steady ion output for specific values of magnetic field and pressure, and the beams contain multiplycharged ions but the charge states are limited and much lower than in min-Z? ECRIS. These result confirm earlier measurements made in Grenoble with a single-mirror ECRIS [235], [250]. 3.3.2.3 Non-Maxwellian electron distributions. In short, because of the exponential dependence of the x-ray quantum flux on photon energy, it was concluded that the distribution function of the high-energy electrons is similar

SIMPLE MAGNETIC BOTTLE ECRIS

241

to a Maxwellian distribution function. However, some earlier studies at Saclay had already shown that the perpendicular electron energies are much stronger than the parallel ones. Later, Shohet (1968) pointed out that the distribution function of the high-energy electrons is not isotropic [249]. The x-ray spectra measured by him are in good agreement with calculated spectra, if one assumes a mirror distribution function f ( E ) ^ E ±j c x p ( - E J k T ) where E± is the perpendicular energy, j is an integer; j > 0. Somewhat later Lichtenberg et al [198] showed that it is very difficult to distinguish between x-ray spectra of electrons having a Maxwellian energy distribution and of those obeying a mirror distribution function. This stems from the procedure of obtaining distribution functions from x-ray spectra (special distribution functions are convoluted with x-ray production cross sections and varied until computed and calculated x-ray spectra are in agreement. After first proposing Maxwellian distributions Bernhardi and Wiesemann [248] changed their x-ray diagnostic methods and used an improved numerical deconvolution scheme to measure the volume bremsstrahlung spectrum emitted by the high-energy electrons to derive their energy distribution function. With this new method and careful measurements, they then found that for kinetic energies below 350 keV the electron energy distribution obeyed a power law, if a cold-plasma component (JcTe < 1 0 0 eV) was present. The density of electrons with energies above 10 keV turned out to be smaller than 108 cm~3, whereas the cold-electron density was several orders of magnitude larger. In figure 3.3.5 we see x-ray intensity spectra and corresponding distribution functions. As expected by ECRIS specialists it has eventually been proved that not only are the electron velocities anisotopic but the electron distribution function inside the ECRIS plasma is not a Maxwellian one and this fact does not entail catastrophic plasma collapse. At pressures below 10- 4 Torr, the simple mirror ECRIS can reach steady states with hot electrons inside a plasma of denser cold electrons, but due to instabilities the ion lifetime is only 1 0 - 5 s. These instabilities are probably macro-instabilities (see section 3.2.7) and are not exclusively related to the non-Maxwellian electron velocity distribution. Recent measurements confirm the limits of the power law for the electron distribution at p > 10- 5 Torr. However below this pressure the relativistic electrons are capable of creating some diamagnetism, which added to the mirror configuration yields a kind of m in-# structure. Under these conditions (section 3.4) better confinement is observed [248]. 3.3.3

Steady state characteristics in overdense simple mirror ECRIS [251], [252]

3.3.3.1 Generalities. In the preceding paragraph local overdense plasmas were invoked even at rather low gas pressure (< 5 x 10- 5 Torr), but the typical,

242

THE ECRIS PLASMA STATES

|

10e

1(1) -3

cm

107 -1

5

3.510 'Torr.Ar

105

\

10s

A • .\

107

_

106 10

f(E)

s

. * 2 5 10'TorrAr

'0 7 10

10

20

50

100

Figure 3.3.5 Typical electron distribution functions f(E) (non-Maxwellian) and measured x-ray intensity spectra I (K) at different Ar pressures; PRF = 1.2 kW. The energy range is below 150 keV [248].

Figure 3.3.6 Overdense simple mirror ECRIS with 2.45 GHz microwaves. A schematic diagram of the experimental set-up. I\ and h are magnetic coil currents [251].

SIMPLE MAGNETIC BOTTLE ECRIS

243

globally overdense plasmas are obtained at higher gas pressures (> 10- 4 Torr). In addition, as the critical density decreases with the RF frequency, the most popular overdense ECRIS are obtained with 2.45 GHz microwaves. As already mentioned in the case oop > a)c the plasma is effervescent, which leads to the destruction of the end mirror properties (section 1.3.9) Thus the mirror configuration is no longer useful and quasi-uniform B profiles do as well. Under these conditions the radial losses are described by turbulent diffusion but due to the absence of end mirrors the overdense plasma leaks without restraint along the axis of the B field (which is an advantage for axial ion extraction). On the other hand the strong plasma losses reduce dramatically the plasma confinement and need more RF power injection. We emphasized in section 2.3 that in the overdense plasma strong nonlinear wave processes occur and internal wave conversions with parametric decays are expected. Thus lower-frequency waves propagate in the plasma, which might exhibit specific behaviour, and many steady states due to wave dampings and amplifications should be added to all the already envisaged possibilities. No doubt one has to face a very complicated situation. 3.33.2 A typical overdense ECRIS. In order to illustrate the complexity of the overdense steady states, we reproduce experimental characteristics as published in 1992 by Popov et al and quote some of his observations [251]. Note that similar results were observed in UHR plasmas in the 1960s [180]—[182], [236]. A schematic diagram of the source and an experimental set-up is shown in figure 3.5.6. Microwave forward power, Pf = 50-1000 W, at a frequency / = 2.45 GHz, was delivered to the plasma chamber (D = 15 cm, L = 16 cm) via the rectangular waveguide transmission line. The reflected power, Pref> was measured with a RF diode in the dummy load attached to the three-port circulator. The matching of the microwave plasma impedance with that of the transmission line was performed with a three-stub tuner installed close to a quarter-wavelength dielectric (quartz) window which also worked as a vacuum window. A radially uniform magnetic field was generated in the chamber using two Helmholtz magnetic coils. The aperture ( 8 cm in diameter) determined the initial diameter of the plasma stream ‘extracted’ with the divergent magnetic field. A thermocouple attached to the support was used for temperature monitoring and for detection of the microwave power transmitted through the plasma down-stream. Plasma parameters and their radial distribution were measured at 25 cm from the source output using a movable Langmuir probe. Nitrogen was introduced directly into the plasma chamber. A turbomolecular pump and a mechanical pump provided the basic pressure in the system of 1 0 “ 7 Torr. 3.3.3.3 Overdense and weak plasma modes versus RF power, gas pressure and magnetic field intensities. The excited plasma could be maintained at two

244

THE ECRIS PLASMA STATES

modes: (i) overdense plasma mode, ne > «cr, and (ii) ‘weak’-underdenseplasma mode, ne < ncr, which was characterized by wave propagation through the underdense plasma downstream. The transition from the weak-plasma mode to the overdense mode occurred when the absorbed microwave power was high enough to generate plasma density higher than ncr. The transition could be achieved by tuning or by the increase of microwave power, provided there was an effective mechanism of microwave power absorption. At magnetic fields below ECR, B < 875 G and gas pressures p = 0.1 3 mTorr, the transition from the underdense plasma mode to the overdense mode occurred when the magnetic field near the vacuum window, Bwv was equal 430-440 G. This transition was accompanied by a sharp increase in the probe ion saturation current, 7/o, and by the drop of transmitted (propagating) downstream microwave power, Ppr. Reflected power, Pref, usually decreased also, but the value of Pref was dependent on the microwave tuning (the position of the tuner’s stubs). The transition was observed for all investigated forward microwave powers, reflected powers, gas pressures and microwave tuner settings. The transition magnetic field, Bwv = 430-440 G, was equal to half of the ECR magnetic field, 875 G, and did not vary with plasma density, gas pressure or microwave power level. The dependences of the probe saturation current on the plasma stream axis, 7/o» and the reflected power, Pref, on the coil currents, I\ = h = /, are given for nitrogen microwave plasmas (0.7 mTorr) sustained at 300, 500 and 700 W (figure 3.3.7). One can see that at coil currents I = 35 A (B = 435 G), 7/o has a very sharp drop and then increases. The ‘location’ of the maximum of probe ion saturation current, Jm, varied with gas pressure and microwave power around I = 30-31 A (B = 390-410 G). The same behaviour of 7/o (drop and sharp increase) was observed at other combinations of coil and currents which generated magnetic fields of 430-440 G near the vacum window. The ‘location’ of Jm was also shifted to lower magnetic field, Bm = 390-410 G. The magnitude of Jm was controlled by the microwave power absorbed, the magnetic field profile along the source and gas pressure. One can see from figure 3.3.7 that the sharp increase of the probe current, 7/o, occurs also at other magnetic coil currents, I\ = / 2 = 55-66 A, in microwave plasma sustained by a forward power of 300 and 500 W. The current density ’jum p’ was not accompanied by a decrease in the reflected power, Pref, but rather by a drastic reduction of the microwave power propagated downstream, Ppr. This means that the sharp increase of the probe current, and hence plasma density, is due to the increase of the microwave power absorbed, PabS. It can be seen from figure 3.3.7 that as microwave power Pf increases from 300 to 500 W both transition magnetic fields and transition probe ion current, 7r , grow, while at higher microwave power, 700 W, where the probe ion saturation current 7/ 0 is much higher than JT, and the microwave propagation downstream

SIMPLE MAGNETIC BOTTLE ECRIS

h

=

h

245

(A)

Figure 3.3.7 Langmuir probe ion saturation current on the chamber axis. Ji0 (Z = 25 cm, R = 0) as a function of coil currents, l\ = /2 = / (axially uniform magnetic field in the source). Small arrows show the direction of the coil current changes. JTX and JT2 and ITX and IT2 are ion and coil transition currents for the 500 and the 300 W microwave plasmas respectively. Large arrows show positions of 437 G (/ = 35 A), 875 G (/ = 74 A) and 925 G (/ = 78 A). A sharp increase of Ji0 at / = 47 A (a 700 W microwave power) was caused by the drop of the reflected power, Pref ~ ® [251].

is negligible, no resonance-like increase of 7/o> was observed. At gas pressures higher than 0.6-0.7 mTorr, and absorbed microwave power Pabs > 200 W, the resonant absorption of microwave power at 430-440 G resulted in an overdense plasma mode. In this mode no microwave propagation downstream was detected. With the proper tuning, 80-90% of the forward power can be absorbed power, and the variation of the magnetic field in the source from 100 to 800 G does not noticeably affect the microwave power absorption level, and hence the plasma density, even at the resonant magnetic field Bwv = 437 G. This is illustrated in figure 3.3.8 where probe ion saturation currents on the stream axis, and at R = 12 cm, JiR, are given for the overdense plasma at 1.4 mTorr, 850 W, as functions of coil currents, I\ = I2 = I. One can see that with the exclusion of the ECR zone (I > 69 A), both Ji0 and IiR increase with the magnetic field from 75 G ( 6 A) to 820 G ( 6 8 A). It is worth noting that the ratio 7/oM/? is practically constant as the magnetic field changes, with the ratio 7/oM/? being about two. This means that in the

246

THE ECRIS PLASMA STATES

Figure 3.3.8 Probe ion saturation currents on the chamber axis, and at R = 12 cm, JiR, as functions of magnetic coil currents, 1\ = /2 = /. The nitrogen pressure was 1.4 mTorr. The forward microwave power was 850 W, and reflected power varied with coil current within 60-120 W [251].

overdense mode the plasma radial profile is not affected by the magnetic field strength, at least within the range from 100 to 800 G. The sharp decrease of the plasma density at / > 68-69 A (B > 820 G) was accompanied by the sharp increase of the microwave leakage power downstream, while the reflected power remained constant or even decreased. Microwave propagation through the plasma causes the drastic drop in the microwave power absorbed, Pabs> and hence in the decrease of the plasma density. The appearance of the microwave power downstream can be explained as follows. When the magnetic field in the absorption area near the window approaches the ECR field of 875 G, the thickness of the evanescent zone (ne > ncr) near the window shrinks, allowing some of the left- and right-hand polarized waves to tunnel through the evanescent zone and propagate downstream without absorption. The dependences of the probe ion saturation currents 7/o on the microwave absorption power, Pabs = Pf — Pref, are shown for different combinations of 7i and h in figure 3.3.9. One can see that JiQ increases practically linearly with Pabs. This means that, in the overdense mode, the microwave power does not propagate downstream, and all the ‘nonreflected’ power is absorbed in the plasma. The high value of 7to, and low value of JiR, at B > 875 G can be explained by the formation of a narrow plasma stream with a maximum plasma density along the chamber axis, revealing the creation of another type of plasma (see section 5.3.2). Overdense microwave plasma at B < 800 G ( / < 6 8 A) could be maintained down to pressures as low as 0.5-0.7 mTorr. At pressures lower than this

SIMPLE MAGNETIC BOTTLE ECRIS

247

Figure 3.3.9 Probe ion saturation currents on the axis (Z = 25 cm, R = 0), / /0, measured in overdense microwave plasma streams in different magnetic fields (different coil currents, I\ = /2, from 10 to 78 A), as function of the microwave power absorbed, Pats. The nitrogen pressure was 1.4 mTorr [251].

Figure 3.3.10 Probe ion saturation current, *//q, and reflected power, , as functions of pressure for two coil current combinations, I\ = / 2 = 32 A, and 1\ = 56 A, I2 = 7 A. The magnetic field near the vacuum window was 400 G. JT is the mode transition ion current; Jext is the lowest ion current at which the underdense microwave plasma can be sustained [251].

248

THE ECRIS PLASMA STATES

transition pressure Ptr the plasma density began to decrease, and even the reflected power decreased (figure 3.3.10). This decrease was accompanied by the increase of the microwave power propagating downstream, Ppr. As gas pressure decreased further, plasma density continued to decrease, until at pressures of 0.2-0.3 mTorr (Pext) both reflected and transmitted power abruptly increased and the plasma was extinguished. The two transition pressures, Ptr and Pext, are probably associated with cut­ off plasma densities for L and R waves, which the maximum plasma density in the source passes as gas pressure gradually decreasses.

3.3.3.4 Summary o f the experimental observations in overdense ECRIS. (i) Two modes of magnetoactive microwave plasma were found: low density (,ne < ncr) with microwave propagation downstream and high-density (ne > ncr) with possible standing waves formed between the plasma surface where ne = n i tCUt.0f f and the microwave introduction window. (ii) Overdense microwave plasma at Pabs = 200-900 W could be maintained at magnetic fields near the microwave introduction window, Bwv = 75-800 G down to pressures of 0.4-0.6 mTorr. (iii) Transition from the underdense plasma mode to the overdense mode occurred at the magnetic field near the microwave introduction window, B wv = 430-440 G. (iv) No significant effect of magnetic field on the microwave power absorption was observed in overdense plasma at B < 875 G, but the magnetic field was still needed for plasma confinement: plasma density decreased as the magnetic field diminished. (v) A peak density was observed at B ~ 925 G, which is 50 G above the normal ECR field. This ‘off-resonance’ will be considered in more detail in section 5.3.

3.3.4

Practical conclusions about simple mirror ECR plasma

High pressure ECR plasma. Many nonclassical ECR effects are evidenced. Hot electrons are rarely observed in the pressure range p > 10~ 4 Torr, overdense (cop > c o r f ) rather turbulent plasma is achieved. In steady states one finds generally low electron temperatures (Te < 2 0 eV) and only singly or less highly charged ions are extractable. Many tunings of the magnetic field are possible, some of them yielding reproducible steady states allowing the extraction of intense ion beams. In these, a priori, unpredictable regimes, the end mirrors are not efficient. Due to strong incoherent diffusion losses, and to capricious RF power absorption, the plasma density versus magnetic field intensity exhibits strange peaks which are not yet explained. However, it seems that they are linked to nonlinear processes connected to ECR and UHR (see sections 2.3.3 and 5.3.2)

MIN-B ECRIS: STEADY STATE ELECTRON CHARACTERISTICS

249

The most outstanding result of this overdense plasma is that it can be maintained at off-ECR conditions. Low-pressure ECR plasma. At lower pressures, (p < 5 x 10~ 4 Torr) the end mirrors provide a better confinement and the electrons bounce between the mirrors and exhibit high ratios of v±/v\\. When RF power is increased some of the electrons reach strongly relativistic energies and seem to be decoupled from the bulk electrons. The electron distribution functions are not Maxwellian in spite of relatively quiescent steady states. A more detailed observation shows that bursts of instabilities occur— limiting the confinement to some 1 0 - 5 s and thus hindering the production of very highly charged ions. The electron density remains generally underdense; however localized overdense plasma might exist in the discharge. The electron heating mechanisms as well as the losses are not yet clearly formulated, but the steady states are reproducible. The proportion of energetic electrons is generally less than 10%. When RF power is increased, thresholds of severe instabilities are observed which destroy the steady states and strongly perturb the electron velocity distributions. Because of severe x-ray hazard, the ECR discharge must be efficiently shielded. 3.4

3.4.1

MIN-jB ECRIS: STEADY STATE ELECTRON CHARACTERISTICS Generalities

M in-# ECRIS work generally at very low pressure (p < 10- 6 Torr) and exhibit clear ECR effects. In section 1.6, we emphasized the positive actions of m in-# structures: stabilization of turbulence, suppression of MHD instabilities, improvements due to multi-mirrors instead of simple mirrors, increases of confinement times, etc. Moreover, the performance of the m in-# sources is also strongly correlated to the high-temperature electron population which is generated by the ECR heating mechanism. Different plasma measurements were performed involving various types of m in-# ECRIS (hexapoles, quadrupoles and octopoles). The first global measurements were made on SUPERMAFIOS in 1974 (figure 3.4.1) (see chapter 6 ). However, the available diagnostics and the times spent for the study were limited. Cold-electron densities were evaluated with microwave interferometers and the more energetic ones through diamagnetism. Thus the total electron density could not be directly measured. Nowadays additional diagnostics such as x-rays and electron cyclotron emission track the hot component and UV radiations and loss detectors address the mildly energetic electron population, but the question of the total density still remains unsettled. The difficulties of ECRIS diagnosis have been extensively emphasized [255], [256].

250

THE ECRIS PLASMA STATES

^Arbitrary

x t^ e V o T r 3

VO^OTT3 x tfW

10

3

?

RF2 POWER (Watt) Figure 3.4.1

SUPERMAFIOS [396] (1974). Some characteristics against PRF.

M IN IM A F IO S

Figure 3.4.2

MINIMAFIOS and the diagnostics in 1993 [255].

Recent measurements were made with the MINIMAFIOS 18 GHz source at Grenoble and published between 1990 and 1994 [257], [258]. Other experimental steady states were studied with quadrupolar traps [260], [429] like INTEREM or such as the CONSTANCE facility at MIT [261]-[263] and the QUADRIMAFIOS device at Grenoble [259], [67]. However, as quadrupolar ECR plasmas have not produced as highly charged ions beams as the hexapolar ones, we prefer to concentrate our study on steady state hexapolar ECRIS. In particular MINIMAFIOS 18 GHz, which is nowadays among the most highperformance devices, can be considered as a typical example for characteristics of min-B ECRIS. Figure 3.4.2 shows the different diagnostics that are used now, and their location.

MIN -B ECRIS: STEADY STATE ELECTRON CHARACTERISTICS

251

25

20

o=?15 >N

to '0

c

0) c *“

5

0

Figure 3.4.3 ECE frequency (uncalibrated) spectra showing the existence of high-energy electrons (in MINIMAFIOS, 18 GHz) [253].

3.4.2

Steady-state diagnostics: electron cyclotron emission (ECE) and bremsstrahlung

A plasma immersed in a magnetic field radiates at the electron cyclotron frequency and its harmonics. The emission of a single radiating electron (velocity v± perpendicular to the magnetic field) at the given harmonic m is

T _

el(al

1- P o

6 TTSq C3

Po

where Po = P±/

30

?

2

2

CD

20

Q.

10

0

200

400

600

800

1000

rf power (W)

Figure 3.4.5 Electron ‘temperatures’ given by bremsstrahlung spectra; the small square symbols stand for data obtained at intermediate pressures [253]. pinj is a monitored pressure measured in the gas injection tube.

Figure 3.4.6 The principle of operation of the measurement of diamagnetic effect in axisymmetrical plasma [255].

A loop (N turns) surrounding the plasma can measure any variation of the magnetic flux it encloses; as the plasma is created the diamagnetic current increases and the flux decreases; this variation induces a voltage V (t) which can be time integrated (either numerically or analogically):

/vd,

= —N A4> ~ \ N n r l B

Y,nK T (B 2 / 2 /^ o )

where the sum is performed over ions and electrons, ro is the radius of the plasmas, and B the magnetic field; this voltage is therefore proportional to the plasma pressure Y,nK T . The density of 25 keV electrons was approximately deduced: ne ~ 101 2 cm-3 . It should be noted however that when the pressure is anisotropic— which is the case for ECR sources—only the perpendicular

254

THE ECRIS PLASMA STATES

Figure 3.4.7

Diamagnetic signals versus time.

Figure 3.4.8

ECE signal versus time.

pressure (with respect to the magnetic field) must be considered. Information about the plasma energy confinement can be obtained by assuming that P rf absorbed T~

/ nK TdV

The transient regime consists of having the RF power pulsed at a given constant level, but variable from pulse to pulse, in two different ways: (i) when running in the steady state regime, the RF power is turned off for about 200 ms, and then turned on again, or (ii) the RF power is turned alternatively on and off every 200 ms. In these transient regimes, the diamagnetism and the total ECE intensity signals are simultaneously recorded, the RF power being in between 50 and 1000 W and the monitored pressure in the range 4 x 10"5^1 x 10- 4 Torr; the real pressure inside the MINIMAFIOS is much lower, but unknown because the neutral gas is burnt out in the plasma. The ECE total intensity and the diamagnetic signals in the transient regime (ii) as shown in figure 3.4.7, behave approximately the same, the major difference being the rapid instability spikes superimposed on the ECE signal (figure 3.4.8).

MIN-B ECRIS: STEADY STATE ELECTRON CHARACTERISTICS

255

Figure 3.4.9 Amplitude of the diamagnetic signal versus RF power [253]. ne

Figure 3.4.10 Density deduced from diamagnetic signal against RF power [253]. One also observes a similar behaviour of the diamagnetic signal and the ECE signal versus RF power (figure 3.4.9). As the diamagnetic signal was calibrated Barue [253] found empirically that in MINIMAFIOS n

( E

e )

(keVcm

(W) W) + 390’

P h f

) - 3 x 10 13 P h

f

{

Hence at 400 W RF power the average diamagnetism is 1.5 x 1013keVcm 3 and at 1000 W it is 2 x 1013 keV cm-3 . As, on the other hand, (E e) was evaluated through bremsstrahlung measurements against (P ) and an average hot-electron density could be determined at P ~ 1 kW, it was found that the density of averaged 25 keV electrons was ~ 1 0 1 2 cm~3. For somewhat more energetic electrons Barue found the empirical scaling (figure 3.4.10) , _3 , . 1An Prf (W) n (cm ) ~ 2 x 1 0 ---------------------. P (W) + 260 r

f

Thus with comparable or even lower RF power many more hot electrons are observed in min-B ECRIS than in simple mirror ECRIS. Clearly the energy lifetime is much longer than in simple mirrors.

256

3.4.4

THE ECRIS PLASMA STATES

Conclusions on the 18 GHz MINIMAFIOS electron characteristics

The electron ‘temperature’ as given by the bremsstrahlung x-rays may be considered as a volume-averaged electron energy. Surprisingly, it does not increase much with the RF power, at least above 200 W, as one would expect according some theories of stochastic ECR heating. In fact the effect of the neutral pressure is more important. The ECE, and the diamagnetism, both sensitive to the perpendicular energy and the density of the electron population, exhibit the same behaviour. Finally, with more scientific rigour, the 1992 results of MINIMAFIOS 18 GHz resemble very much those of SUPERMAFIOS 1974. Amazingly the hot-electron density in both cases tends towards but probably does not exceed significantly the critical density as long as multiply charged ions are optimized in the plasma (i.e. when quiescence and low-gas-pressure regimes are considered). Let us recall that only low-pressure regimes yield highly charged ions. At high pressure, overdense plasmas are always feasible with a hot-electron component, but then, due to effervescence, the min-B mirror confinement is worsened, and the highly charged ion production is reduced. Thus overdense min-B ECRIS seem useless in this case. The steady state ion characteristics in min-fi ECRIS are studied separately in chapter 4.

3.5

3.5.1

ECRIS AFTERGLOW REGIMES (OR POST-DISCHARGE)

Generalities

Let us suddenly switch off the RF power. The steady state regime is replaced by the afterglow regime. Considering the diffusion equations in coordinate space, one finds that a suppression of the source term [S] necessarily leads to a decreasing of the electron density when one neglects the uncontrolled wall emission, 8n 2 ——= [5] [Vrec o m b i n a t i o n ^ \D V 7i], dt When [S] = 0 and neglecting the recombination losses as compared to the diffusion losses &n = —D ^ V t-,7 — n\ V n oc [n]. 8t 8n (see section 1.7). Hence I t

—Dn

The above equation yields n(t) = n(0) exp(—t / r ^ f f ) (with rdiff ~ R 2/D in a cylindrical discharge with radius R). Thus without specifying the value of the strongly debated diffusion coefficient we see that the plasma density in the afterglow decreases exponentially versus time.

ECRIS AFTERGLOW REGIMES (OR POST-DISCHARGE)

257

a.u. t ms

A

a.u.

0

10

20

30

t ms

Figure 3.5.1 Typical density n{t) decreases in the afterglow of ECR plasma. (i)

If the afterglow plasma is turbulent the density decrease is very rapid because the losses are governed by a kind of Bohm diffusion (figure 3.5.1, curve a) (overdense plasmas exhibit very rapid decays). (ii) If the afterglow is quiescent the decrease is very slow because the losses are mainly due to collisional or RF diffusion and recombinations (figure 3.5.1, curve b) (hot-electron plasmas should exhibit this kind of decay). (iii) If, during the afterglow, nonlinear processes are generated which expel particles towards the walls, the decay exhibits sudden drops (figure 3.5.1, curve c) (general case).

In any case the density can only drop inside the plasma during the afterglow. As the above equation deals with coordinate space diffusion the diagnostics of the afterglow should be located inside the plasma. However as such diagnostics perturb the processes only external methods (such as ECE, xrays and diamagnetic probes) are acceptable. Unfortunately these diagnostics address mainly the hot electrons. For the cold-particle component, optical line spectroscopy, soft x-ray scintillators, interferometry etc are utilizable but less popular. Hard x-ray decay can be observed in simple mirror and min-B ECRIS provided that hot electrons are created during the steady state. 3.5.2

Experimental results and discussion

In the afterglow of the MINIMAFIOS source, under certain conditions, different types of kinetic instability could be driven: figure 3.5.2 shows the diamagnetic and ECE signals recorded at the end of the RF pulse; bursts of microwaves on the ECE signal correspond to rapid expulsion of electrons (see the decay of the diamagnetic signal). Figure 3.5.3 shows the diamagnetic decay time versus RF power on the MINIMAFIOS source. Note that the decay times are the longest at low RF power and times up to 40 ms are observed.

258

THE ECRIS PLASMA STATES Phf

.900-

400

W

.700 .5 0 0 .300 . 100 2 0 . (3

60 .0

100. 140. t ( m3 )

1B0.

Figure 3.5.2 Instabilities observed in the MINIMAFIOS afterglow seen in diamagnetism and ECE.

Figure 3.5.3

Decay time of the diamagnetic signal.

On the CAPRICE source, characteristic times of the same order—though slightly lower— were obtained. (A slow decay of the hot-electron population with superimposed instabilities was also observed both in simple magnetic bottles and in quadrupole ECR plasma [260]—[263].) Considering the above-mentioned results, we obtain an idea of how the hot-electrons decay in the ECRIS afterglow. However, on the other hand, unfortunately, it is still very difficult to evaluate the decay of the mildly warm

ECRIS AFTERGLOW REGIMES (OR POST-DISCHARGE)

259

and cold electrons since the permanent magnets hinder the radial access for interferometers. We have only a few old measurements for them obtained with the SUPERMAFIOS ECRIS, which show much shorter density decays (< 1 ms); similar short decays for cold electrons were deduced from measurements of simple magnetic mirrors and quadrupole ECRIS. In any case the decay times are necessarily different for the various electron populations because for the mildly warm- and cold-electron components the physical image of the loss mechanism is different, (since Spitzer and other collisions become dominant). Thus the end mirror losses can become stronger than the losses of the coordinate space (see section 1.6). In this case we should consider the velocity space diffusion governed by the equation ? l = S(p) + V D V f where f ( p ) is the distribution function, S (p ) the source term (S (p ) = 0 in the afterglow) and D V f is the velocity space current. D is then a non-explicit general diffusion tensor D = A p A p /A t where A p is a momentum pulse due to electric fields of RF waves, turbulence, collisions etc and A t is the correlation time. Thus it is obvious that D cannot be theoretically predicted, each case being different. What we know is that in the afterglow, due to momentum impulses, the measurable velocity space current D V / = T varies. We can briefly write that

and try to measure some aspects of the velocity space current by studying the particles leaking through the axial end mirrors of an ECRIS. Thus assumptions have to be made about the distribution functions f ( p ) before and during the afterglow. According to the above equations, when the velocity space current V varies, the distribution function of the observed electron population also changes and this at least should be seen with particle detectors located beyond the end mirrors and analysing only plasma particles inside the loss cone. For this purpose one can utilize small ES detectors with retarding potentials. In addition for the ions the usual ion beam analysers including magnetic deflectors can also provide further information. Note that the analysable electrons are either initially inside the loss cone or suffer 90° rotations due to additional electrical impulses during the afterglow to be injected into the loss cone. In the afterglow, the loss hyperboloid is absent because the ECR mirror plug (see section 1.6) is switched off together with the injected RF power; this removal of the ECR mirror plug results in the release of previously trapped electrons and a sudden increase of the end-mirror losses of a given electron population is expected. We can also say that the RF removal changes the velocity distribution, which entails a change of the velocity space current.

260

THE ECRIS PLASMA STATES

F(v)

2

3

> v/v0

Figure 3.5.4 Plausible distribution functions in the afterglow for different delay times. The cold and warm electrons are expelled in the loss cone. The hot electrons remain in the afterglow plasma. The presently available experimental results are not sufficient to give a clear image of all the types of end loss versus time. However, even if the steady state electron distribution is a Maxwellian one, during the afterglow this can no longer be the case since the cold, warm and hot electrons leave the plasma with different escape rates. 3.5.3

ECRIS afterglow collapses

Let us for instance consider the ideal case of steady state when in the ECR plasma we have a Maxwellian distribution of electron speed F (v) where F (v)dv is the mean number of electrons per unit volume with speed v = \v\ in the range v + dv F (v) = 4 n v 2n Figure 3.5.4 shows such a distribution at time t = to when the RF stops. After a short while, t\ = to + 100/xs, many cold electrons have left the plasma core due to termination of the ECR plug and loss-cone diffusion whereas the mildly warm electrons have leaked weakly and the hot ones with 1 have not leaked at all. Thus we can imagine temporary speed distributions versus time as seen in figure 3.5.3. For plasma theoreticians such distributions should cause instabilities. There are so many plausible instabilities that it is even impossible to track them because, in addition to the distorsions of the orthodox velocity distribution inside the plasma, unacceptable temperature gradients and density gradients will appear (see section 3.2.7). Moreover organized hot-electron populations are also vulnerable, especially when incoherent microwave fields perturb their trajectories. For instance hotelectron puffs detected by mirror end diagnostics are observed when strong microwave pulses are injected during the afterglow. However, without any

ECRIS AFTERGLOW REGIMES (OR POST-DISCHARGE)

261

external intervention, one also observes bursts due to instabilities (figure 3.5.5) and, after each instability which tends to Maxwellianize the plasma, other unstable processes can be launched which lead to successive bursts etc. Even if electron bursts do not interest ECRIS builders, intense ion beam bursts which are subsequently generated by ambipolar forces should interest them because, as shown in the next section, afterglow instabilities might become powerful ion pulsers. 3.5.4

Intense ion pulses in the early afterglow

Before considering any theoretical models in 1988, the Grenoble group exploited the afterglow pulses [266] for increased high charged ion yields. As the method can improve pulsed synchrotron injection it rapidly became a success story. The rationale of the afterglow pulse was the following [138]. During the steady state, the loss hyperboloid allows the leakage of a certain number of electrons, which drag ions with them towards the extraction gap located behind the magnetic mirror. The extractable ion current can be written as /+ ~ \ n \ z e a L j r+

(3.5.1)

representing the ion losses leaking from the magnetic trap. Here n+ is the density of the ions of charge state z, a the extraction area and L a characteristic plasma length along the axis. is the confinement time of an ion of charge ze. As seen in section 1.6 this confinement time depends on the potential dip |A *| Tz+ ~ rbounceQ\p(ze\A 1 still remains mirror trapped and thus ions remain in the not yet destroyed potential dip ze\A\. These ions will only disappear together with the hot electrons which can still live for a while (A t ~ 10- 2 s) even in the presence of some weak instabilities. If the hotelectron density in the MINIMAFIOS afterglow remained neh ~ 1011 cm 3 = q n +, the extractable ion flux would be ( 1 0 n / 1 0 _2)L ~ 1 0 14 charges s - 1 i.e. ~ 20e ji A, but if one could recover these ion charges in 100fi s the ion pulse would reach 2 mA. (q is the average ion charge and L ~ 10 cm the plasma length.) For synchrotron injection such short intense ion bursts are needed and the problem becomes fashionable. Hence it is important to recover very rapidly most

264

THE ECRIS PLASMA STATES

of the remaining ions of the plasma column and one has to expel as rapidly as possible the hot electrons. Let us envisage two possible methods. Pulsed magnetic extraction. The Pu Ma ECRIS [270], [271]. In addition to the ECR plug the magnetic mirror field could be switched off. Unfortunately it is technologically difficult to switch off currents in mirror coils rapidly. However with special techniques this approach is feasible. It was proposed in 1989 and some positive results were published in 1992 and 1995. (ii) Artificial instability triggering. One can imagine beam injection into the afterglow plasma in order to trigger the famous beam-plasma instability. Other predictable instabilities may also be envisaged. Finally a destructive (but theoretically ill determined) instability can occur, when anisotropic hot electrons gyrate in a tenuous cold-plasma which cannot stabilize them. Thus the free energy tank is ready for a relaxation. In the afterglow after the cold-plasma release, such a situation prevails. It then happens that a short pulse of injected RF power triggers a violent plasma collapse and subsequently a strong ion burst.

(i)

3.5.6 (i)

Second RF pulses in the afterglow

Rapid hot-electron collapses following a second RF pulse in the afterglow have been observed by Ikegami et al [273] and Hokin [150]; however the interpretations of the processes are completely different. Ikegami et al observed that in simple magnetic mirror ECR plasma at 6.1 GHz strong electron bursts and electron mirror losses occur when the second pulse is applied ~ 1 ms after the removal of the RF power, (gas pressure of helium less than 10- 4 Torr). The instability is accompanied by a fast-rising x-ray signal, and a sudden burst of microwaves at 2.1, 4.2 and 6.3 GHz. It was not determined whether these wave bursts were the by-product of the instability or whether they were the driving source. The instability was identified as a electron cyclotron wave instability whose characteristic frequency satisfied the relation W ^/W ±) q)c

as proposed by Crawford and Tataronis [233]. It was also proved that the radiation associated with this instability was, as predicted, an electromagnetic R wave. (ii) Hokin’s instability was triggered in the afterglow of a quadrupole m in-# ECR plasma (figure 3.5.7); p < 10- 6 Torr [150]. During the second pulse one observes a strong loss of hot electrons as seen both in the increased decay rate of the diamagnetic loop and the increase end loss seen with a scintillator probe. When the diamagnetic decay rate and the end loss signal are plotted versus second-pulse RF power, both quantities scale with RF power up to ~ 4 kW. This behaviour gives support to a stochastic

ECRIS AFTERGLOW REGIMES (OR POST-DISCHARGE)

265

RF diffusion process which could be responsible for the electron collapse. The RF diffusion coefficient D RF — A P r f A P r f / A trf is stronger as no cold plasma is present to damp the RF electric fields. (Strong stochastic momentum pulses APj_ are then available.) Thus two completely different concepts of hot-electron losses in ECR plasma afterglow lead to the same practical conclusion: hot-electron populations can collapse when the coldelectron population has decreased. Maybe there are some other reasons. (iii) Ion bursts due to second RF pulses were utilized in the 14 GHz MINIMAFIOS working at CERN. As the short ion bursts have to be synchronized with RFQ + linac + synchrotron operation, the possibility of triggering the pulses improved the efficiency and reliability of the overall injection system. Working with sulfur S 14+ ions, the post-pulsing injector was utilized for a three week run and gave better performance than the simple afterglow pulse operation [269]. (iv) The second RF pulsing technique was also verified with Arz+ bursts in a 10 GHz CAPRICE source [272]. In this study the amplitude of the second RF pulse as well as its delay with respect to the first pulse were very changeable. It was then observed that (a) above a given amplitude, the second pulse did not enhance the ion yield, (b) the ion burst was obtained after the second-pulse termination and not during the pulse (which weakens the assumption of enhanced RF diffusion) (figure 3.5.8) and (c) the second pulse can be delayed over many milliseconds before the second ion burst begins to decrease (proving once more that the hot electrons have long afterglow times during which they trap the ions). 3.5.7

Conclusions for ECRIS afterglow regimes

Afterglow ion pulses are now very successfully utilized for synchrotron injection and have become a classical method. However, the explanation, though based on reasonable arguments, is not univocal. Certainly different conditions generate different phenomena which may be superimposed. Nonlinear effects as experimentally observed are probably a basic ingredient but the improvement of the highly charged ion current in the afterglow pulse with respect to the steady state current suggests the intervention of the potential dip. This particular point is analysed in section 4.8.5.1.

4 ION CHARACTERISTICS AND ION PROCESSES IN ECRIS PLASMA

4.1

4.1.1

ION HEATING

Ion energy

We have shown in chapter 1 that the ions remain cold because the collisional electron-ion equipartition time is much longer than the particle lifetime even in such quiescent steady states as achieved in min-Z? ECRIS. Thus the basic ion heating, which is only obtained via elastic ion collisions with the energetic electrons, remains weak. According to Spitzer [62] the ion heating rate is given by (4.1.1)

— = constant dr

where Tt and Te are the temperatures of ions and electrons in the plasma; Z is the charge of the nucleus; ne is the density of electrons; A and M are the atomic mass number and the mass of the nucleon; In A ~ 15 is the ‘Coulomb logarithm’. We see that the ion heating rate depends on Z 2 /A . In other words, even if the heating rate is weak, heavy multiply charged ions are heated faster than light ions. 4.1.2

Ion thermalization [136]

Generally, in ECR plasma without turbulence, ion thermalization is due to elastic collisions among the ions. The collision rate of ions with charge state /, mass number A, nucleon rest mass Af, temperature 7* and ion density /i, with the ions of all ion components (1 < j < k) is defined by Spitzer [62] and is a generalization of formula (1.3.18) of section 1.3.6 .3. (C G S)

266

(4 .1 .2 )

IMPROVEMENT OF MULTICHARGED ION CONFINEMENT

267

where re = e2/m e 2 ~ 2 . 8 x 1 0 - 1 3 cm and i = Z /e = zGenerally, v,-* is about 106 s _ 1 for typical ECRIS parameters and let us recall that this collision rate increases with i2 (i.e. increases rapidly in the presence of highly charged ions). In the thermal ion equilibrium, Maxwellian velocity and Boltzman energy distributions are established in the plasma during a time of about l/v a with i — k in (4.1.2). If we have two groups of particles with temperatures T[ and 7* then the rate of temperature equipartition between these groups is determined as [62] (4.1.3) These times are much less than ion confinement times, hence thermal ion equilibrium is achieved. 4.1.3

Ion temperatures

After thermalization we can suppose that the energy distribution functions of all ionic species are Boltzman-Maxwell distributions with a common temperature T[ for every kind of ion: (4.1.4) where E { is the energy of the ions. Following Shirkov [136] the ion losses decrease the total energy of the ion components but the balance condition of ion energies makes it possible to define the ion temperature

As already seen in section 1.3 and according to equation (4.1.5) one then finds Ti Te. Thus in all ECRIS, Tt remains low (a few electron volts) and experimentally all the optical plasma measurements confirm this point. Experimental studies of the resolution of the extracted ion beams also allow one to evaluate the ion energy inside the ECRIS, and once more one finds Ti « Te [279], [281]. 4.2

IMPROVEMENT OF MULTICHARGED ION CONFINEMENT IN ES POTENTIAL TRAPS

The potential trap is determined by the ambipolarity of the ion and electron currents leaving the plasma

268

ION CHARACTERISTICS AND ION PROCESSES IN ECRIS PLASMA

where xe is the electron lifetime. When xe is improved through some specific techniques, r, also increases, meaning that a negative-potential zone has been created where the ions are trapped. In section 1.6 for min-fi mirror configurations at steady state we assumed that the electrons leak mainly through the ECR mirror plug, i.e. through the loss hyperboloid in velocity space, where the electrons have been scattered by the elastic collisions with electrons, ions and neutral atoms. In consequence the electron lifetime xe is related to this rate of electron scattering and to ~ xei. With respect to the usual loss cone the loss hyperboloid decreases the electron leaks, and then r t as well as xe becomes somewhat longer. If we now accept the image of an ES ion confinement and if we suppose that the plasma has a negative potential A 0 for ion confinement, then mainly the ions with energy higher than the potential barrier will leak. The different ion charge states i have potential barriers of different value proportional to their charge (i.e. A0). Thus differently charged ions have equal temperature but different potential barriers and subsequently different loss rates. The highly charged ions have much longer confinement times r, than the less highly charged species [224]). In short we can state the following. (i)

Ions with higher charge states have longer lifetimes r { but it is more difficult for them to leave the plasma trap, meaning they will not be easily extractable. (ii) Subsequently the extracted ion beam charge distribution will have a smaller mean charge than the charge distribution inside the ECRIS plasma. This has been experimentally observed [282]. The proportion of high-Z ions is larger in the ECR plasma than in the ion beam. (iii) When ions are heated up (for instance by fluctuating fields) the potential barrier lowers and r, decreases which was also experimentally observed. A noisy plasma gives less highly charged ions but higher ion temperature. (iv) However, conversely, all possible ion coolings mechanisms would raise the ratio ieA(p/K Ti and thus increase the ion lifetimes and the mean ion charge state in the plasma [276]—[278]. This was at first experimentally observed by Antaya [283].

4.3

THEORETICAL ION CONFINEMENT TIMES WITH ELECTROSTATIC POTENTIALS AT STEADY STATE

Again if we accept the idea of an ion confinement via potential trap models then in a min-Z? structure such as MINIMAFIOS the ion lifetime is approximately given by a semi-empirical formula where Z, is the ion charge.

THEORETICAL ION CONFINEMENT TIMES

4.3.1

269

Ion confinement in West’s model [284]

The above formula is obtained by simplifying modelling calculations utilized by West in his potential trap model. These calculations yield a semi-empirical equation that can be generalized to a plasma of multiple-charge-state ions

(i)

(ii)

Putting numbers in this formula one sees that the scattering term (ii) is much smaller than the flow-term (i) where L (M ion/2T i o n ) 1 / 2 is equal roughly to the bounce time of the ion. In the above formula we have ry, the ion confinement time, R , mirror ratio, Bmax/ B min» G(R) a the factor ~ 2 , L, the effective length, Tion the ion temperature in ergs, at least for the first term, toy = 1 /v/e,, the scattering time of ions with other multi-charged ions as given by Spitzer and Zy, the charge of the ion (Zy = ze or ie). Let us recall that the term (ii) is the ion scattering time for scattering through 90°, and exp(A0Zy/7yo/I) takes into account the time for the ion to overcome the well of depth A(f> created by the mirroring electrons, whose total charges locally exceeds the total ion charges. 4.3.2

Ion confinement in Pastoukhov’s model [286]

Though only proposed for classical mirror confinement, various ECR studies utilize the Pastoukhov model for ion confinement. In this case the parallel ion confinement is dependent upon the axial profiles of the magnetic field and potential. The vacuum magnetic field is well known, but there is as yet only an assumed potential profile. The potential model shown in figure 4.3.1 is therefore proposed based on the following physical factors [263]. (i)

If the trapped electrons follow a Boltzmann distribution between the midplane and the mirror peak, with the electron density at the midplane being significantly larger, then the potential must decrease from the midplane to the mirror peak according to the relation — = e x p [( 0 m -0 )/7 ;]

(4.3.3)

where the subscript zero refers to the midplane value and m refers to the value at the mirror peak. (ii) The potential should dip in the region of the magnetically confined hot electrons. This is because the hot electrons have relatively long confinement times, forcing the electrostatic confinement of ions to neutralize them. The majority of the ions are confined in the region of the potential dip. The parallel ion confinement time in this region is given by the sum of the

270

ION CHARACTERISTICS AND ION PROCESSES IN ECRIS PLASMA

U Qi

a V4

n a (total density) —

nH

(hot e le c tro n s )

ECRRE90NWCES

Z (AXIAL DIRECTION)

Figure 4.3.1

ES ion confinement modelling. Parallel ion confinement is dependent upon the axial profiles of the magnetic field and potential. The majority of the ions are confined in the region of the potential dip [263].

long and short mean-free-path confinement times. The long mean-freepath confinement time (collision time > bounce time) is given by a term more involved than the term (ii) of (4.3.2), but the short mean-free-path confinement time (collision time ^ bounce time) which is proposed for min-B ECRIS is given by the flow formula.

(4.3.4) This value of ES confinement time for the ions is similar to the first term of West and the semi-empirical value of equation (4.3.1). A high-collisionality regime in which ion confinement is governed by spatial diffusion (and not by the loss cone in velocity space) was also proposed by Pastoukhov; however it seems not applicable to usual ECRIS plasma for highly charged ions, but rather for overdense ECRIS. (4.3.5) As for the potential dip of a cylindrical shape plasma with length i and radius r, according to [276] it can be valued as

CRITERIA FOR MULTIPLY CHARGED ION PRODUCTION [109]

271

with T being a function of Poisson’s equation

(4.3.7) Experimentally it has been observed that not merely does the ECR produce mirror-trapped warm electrons but also an enhanced flux of axial electrons appears beyond the mirror throat during the heating. Thus during the ES potential build-up the electron losses through the plug tend to be at least ten times larger than expected from Pastoukhov scaling but on the other hand the axial flux of ions has been confirmed to follow the scaling. 4.3.3

Ion confinement in ± turbulent plasma models— the need of additional electron donors— electron starvation

When considering a low pressure min-Z? ECRIS where Bohm-like diffusion is present (see section 1 .6 ) one surmises that on average the electron lifetime is shorter than the Spitzer collision time and shorter than the ion lifetime r, . As a result the plasma acquires a highly positive potential which enhances the ion losses and worsens r, in order to equalize the global electron and ion losses. Such a potential evolution would be inauspicious for highly charged ion production which requires maximum values of ner, and therefore a negative potential for ion trapping. A limitation of the processes is therefore desired which becomes possible when the electron losses are permanently ‘over-compensated’ by electron injections or ionizations inside the plasma core. Subsequently electron injections from a first ECR stage, hot filaments, biased electrodes and secondary wall emission can play the role of electron donors and prevent electron starvation, which would lead to very strong plasma instability. Addition of light gases may also increase the local ionization and thus prevent electron starvation [285]. Even a lower average ion charge due to light-gas addition, impeding the ambipolar losses, would act in the same way [287]. As for the over-compensating electron donors, they are studied in more detail in section 6 .2 .

4.4

4.4.1

CRITERIA FOR MULTIPLY CHARGED ION PRODUCTION [109]

The basic criterion. The importance of ion lifetime, electron density, electron energy and neutral gas density

In section 1.4.9.5 we derived the basic criterion and showed its atomic physics background. Let us summarize the fundamental processes and parameters for producing MI (multiply charged ions). The probability of producing them by a

272

ION CHARACTERISTICS AND ION PROCESSES IN ECRIS PLASMA

Table 4.4.1

ne/ri() < 1 ne/ n {) > 1 ne/ri() > 1

(neXi), Te < 10 eV 108 - (neXi), Te < 100 eV 1010 - ' (neTi), Te < 5 keV

ne/ n 0 » 1

1013- ' (neXi), Te > 100 keV

No MI whatever nex MI with low Z MI with totally stripped very light species MI with totally stripped heavy species

neXi is in cm 3 s. single electron impact falls off rapidly with increasing ion charge Z. Therefore the only efficient way to obtain a reasonable yield of many-times-ionized ions is by successive ionization. We are then led to increase t/, the exposure time of the ions, to a cloud of plasma containing electrons. These electrons must be hot. Their temperature Te has to be in the range of kiloelectronvolts if one wants to achieve high Z. To avoid charge exchange processes a necessary but not sufficient condition for multiply charged ion production is given by n e/n$ > 1 . The electron density n e must exceed the neutral density no inside the plasma. The basic criterion is then given roughly by table (4.1.1) where typical cases are summarized. An interesting way to look at this {neXi)Te criterion is to compare it to the well known Lawson criterion for achieving power balance in d-T fusion. The Lawson criterion is: n r > 1014 cm " 3 s, T > 10 keV, where n is the plasma density and r is the plasma confinement time and T ~ 7} ~ Te is the particle temperature. Similar electron temperatures are involved in fusion and in ion stripping but not similar ion temperatures (Te ^> Tt). Hence the ionstripping criterion is much easier to satisfy than the Lawson criterion. Therefore if impurities are present in fusion devices these devices deliver MI with high Z. (These high-Z impurities in plasmas radiate and lead to power losses which cool down the plasma.) 4.4.2

Applications of the basic criterion for MI production. The foil stripper— the ECRIS and EBIS

For multiply charged ion beam production by foil strippers, one generally injects very energetic (a few megaelectronvolts per nucleon) low-charge-state ions through thin foils whose thickness is only a few micrometres. The thin foil contains in its crystalline structure atoms together with cold electrons with density ne ~ 102 4 cm-3 . The relative interaction velocity w between the energetic ions and the cold electrons is, under these conditions, approximately equal to the transit velocity of the accelerated ions (a few 109 cm s-1 ). The interaction time will be that during which the ion passes through the foil (r ~ 10- 1 4 s) and nex will thus be about 1010 cm - 3 s. During the interaction, two types of collision are in competition: the step by step ionization

THE POWER FLUX CRITERION

273

of the incident ion and the recombination of the multiply charged ion through electron capture. At high speed w , the ionization process predominates and the ion beam that emerges from the thin foil is very highly charged. The ECRIS idea consists of inversing the process and injecting very slow ions through a stripper of hot electrons. For this, it is necessary to have a plasma of cold ions that diffuses through a plasma of hot electrons. One would obtain the same relative interaction speed if the cyclotron resonance yielded electrons of a few kiloelectronvolts. Thus one would have to create a hot-electron target plasma that presents a value of nex ~ 1 0 10 cm - 3 s similar to that of the solid stripper. In figure 4.4.1 we emphasize the perfect symmetry between ECRIS and foil strippers. For foil strippers cold ions are extracted from an ion source and accelerated through an ion cyclotron resonance, whereas for ECRIS the cold electrons are accelerated through an electron cyclotron resonance (ECR). However, one has to consider that if the value of the hot-electron density is less than 101 2 cm-3 , one needs an ionic lifetime r, ~ 10- 2 s. Such ion lifetimes can be obtained in min-2 ? structures of an ECRIS, especially when there exists an additional self-consistent ion trap of electrostatic nature. Then the basic MI production principle in EBIS is the same as in ECRIS [10], [ 1 1 ] where instead of magnetic ion confinement the idea is to use an externally applicable electrostatic ion confinement and instead of bulk electron resonance heating, the electrons are concentrated in a beam and accelerated by potential differences. The main EBIS parameter is 7 r = new r = (nex)Te where w is again the relative interaction velocity between fast electrons and slow ions and I is the electron current density. Finally the same basic criterion is valid for our three examples. However in the next section we will show that, in spite of these basic similarities, for practical reasons the necessary electron power dissipation will be quite different.

4.5 THE POWER FLUX CRITERION AND THE IMPORTANCE OF THE LIFETIME OF ENERGY IN ION SOURCES [109] t

e

n

If one begins to ponder the practical MI production in existing ion sources, sooner or later one has also to consider the lifetime of energy. Therefore in addition to long ion lifetimes, and for practical reasons, one also desires long lifetimes for the hot electrons. To explain this let us consider the flux of electron energy that is required to satisfy a given MI production during a time span equal to the ion confinement time r ,. Let us apply the following rationale. Writing ve for RMS electron velocity, this flux is given by e = (nve/2 )(K T eXi). (i)

If we assume that the energy lifetime xEN = r,-. We can write M .l

*low ion*

P)

+ + +>

" > M .l ECR plo*rrvj

iff

3>

m .i

Figure 4.4.1 The stripper and ECRIS. Top left, in stripper (a ), ECRIS (/?) and EBIS (y) the same relative collision velocity between the electron and ions with the same nwz values gives a similar charge state of the multicharged ions (MI), but the short and intense interaction in foils provides excited levels and some additional ionization. Bottom left, the charge-to-mass ratio e achievable by passing energetic ions through foil strippers as compared to a min-Z? ECRIS. Bottom right, 238U ion spectrum issuing from an N2 gas stripper at 1.4 MeV per nucleon. Top right, 238U ion spectrum issuing directly from an ECR ion source. The 238U spectra are experimental and obtained in continuous operation with a sweeping magnetic field selector.

(ii) If then te n = 1 s,

r ne cm'2

Figure 4.7.1 The burn-out possibilities in min-R ECRIS depend on the plasma size r and the nature of the gas.

4.7

4.7.1

THE NEUTRAL GAS DENSITY CRITERION FOR MI PRODUCTION IN STEADY STATE

The limitations due to the charge exchange collisions

As seen in section 1.4 all MI recombinations fight against the charge state increase and therefore it is important to recognize the most dangerous collisions. For instance we know that radiative recombinations in a hot ECRIS plasma are very rare and dielectronic recombinations, which are somewhat more frequent, can be notable in some particular circumstances. However the charge exchange of an ion with a neutral atom is by far the most important mechanism that reduces the ion charge Z inside the plasma. Therefore in the basic MI production it is specified that the ratio of electron density to neutral atom density ne/no must greatly exceed unity. We evaluated this condition greater precisely in section 1.4. We then found that n0/ n e < 103 £[7; op, r 3 / 2 A l/2z ~ l gives the upper limit of the neutral density no inside a plasma of electron density ne for reaching the charge state z where £ is the total number of electrons in the outer shell of the ion and Te opt ~ 5 IP (figure 4.7.1). These low values at no impose severe pumping conditions. One needs for instance intensive vacuum pumping of all the plasma chamber. However this good vacuum reduces the probabilities of residual gas ionization and thus necessitates an auxiliary cold-plasma injection in order to avoid electron starvation. In this case the ECRIS must have two stages with differential

THE NEUTRAL GAS DENSITY CRITERION

277

pumping as already utilized in the first ECRIS and/or auxiliary electron injectors improving the local ionization. As in most cases external pumping is still insufficient, one needs an additional ‘internal’ pumping provided by the plasma itself. Then, possibly, the neutral atoms that enter the plasma from outside are ionized so rapidly that they do not have time to penetrate deeply into the plasma. This phenomenon is called burn-out of neutral particles. The effects of the charge exchange on the MI production were numerically analysed by Delferriere (section 4.8.3) [289]. 4.7.2

Improvements due to internal pumping: the burn-out effect

The burn-out effect requires that the mean free path k A of a neutral atom with velocity Vo be smaller than the minimum dimensions of the region occupied by the ECR plasma (for example, its radius r, if the plasma region has the shape of an egg, as is usual for the ECR surfaces). Thus the condition is < r.

(4.7.1)

The mean free path k A = vqTq where r 0 is the ionization time of the neutral atom Ao. The burn-out time is obtained by two possible types of collision in the plasma: the electron impact and the charge exchange with corresponding collision times ro+ and tz-* z -i and mean free path k\ and A.2 . The process for k\ is: A0 + e -» A+ + 2e, and r0+ = [ne(ve - u o ^ o i + r 1

ve » v0

(4.7.2)

The process for A2 is A0 + B z —> A + + B z ~l , and ^z-*z-i+ = [ftz(fz+ — vo) 5 x 101V 3/2. We note that this burn-out is facilitated by the mean ion charge state q of the plasma. For instance for oxygen, krypton and xenon with q — 4, 10 or 16, respectively, the burn-out effects of electron ionization and charge exchange are of the same order of magnitude. Thus the shaded zone seems realistic when both effects are taken into account (figure 4.7.1). It is curious to note that charge exchange, which limits the step by step charge increase, has also a beneficial effect and favours the charge increase by decreasing the neutral gas pressure— no wonder that ECRIS characteristics are so complex to analyse. Finally let us note that charge exchange is not exclusively linked to charged ions and neutral atoms. Collisions between charged ions are also conducive to charge transfer. Unfortunately, reliable cross-sections are not yet available.

4.8

4.8.1

SEM I-TH EO RETIC A L ANALYSIS OF HIGHLY CHARGED ION PRO DUCTION

The batch model [290], [291]

Previously we utilized the symbols i or z for ion charge states and Z for the ion charge (Z = ie or ze). As in section 4.7.2, here we denote by q the mean charge of an ion collection: q ~ (ie) = (Z). In section 4.6 we saw that the only efficient way to obtain a reasonable yield of many-times ionized ions is by successive ionizations in a very low-pressure

SEMI-THEORETICAL ANALYSIS

279

nwx for electrons of 13.6 keV (w « 9 x 10"9 cm s-1). Note the very slow quasi-logarithmic increase of q with nw x , which slows even more for K-shell ionizations. All other elements exhibit similar behaviour because of the quasi-logarithmic decrease of the ionization cross-sections. As n0 is a constant, the graph in fact gives the percentage Figure 4.8.1 The calculated charge distribution of neon ions as a function of

of each charge state against

nwx

[291].

gas. We are then led to increase the exposure time r of the ions to a cloud of electrons of density n e and velocity w. The parameter n ewx = (nex)Te determines the achievable q in a good vacuum plasma, where the electron energy (in the kiloelectronvolt range) exceed the relevant ionization potential IP. Figure 4.8.1 shows typical mean charges q for neon ions versus n w x . They are obtained through simple calculations, which are based on the knowledge of ionization cross-sections and assume that only the ion lifetime r, limits the achievable charge (section 1.4). The ion lifetime in turn, is limited either by the confinement system (magnetic structure with or without ES potential trap) or by a charge exchange collision decreasing the achievable charge. Thus r, is considered as a parameter which is free to take a large range of possible values (10~5 s < xi < 10_ 1 s) and so is nwxi. For each achievable value of nwxi there is a corresponding charge state distribution centred around a peak value of q. No other loss mechanisms are considered. Before ionizations start, one assumes that a ‘batch’ of neutral atoms is injected into the system, yielding at time r = 0 a neutral density no, which is a finite quantity. For r > 0 the electrons ionize the batch and q, the charge of the atoms, increases gradually to yield successively different ion densities nq and different ratios of nq/no. Note the very slow increase of q with nwx. The quasi-logarithmic growth of q with nw x is due to the quasi-logarithmic decrease of the step by step ionization cross-sections versus q , which we take into account. Only when n w x exceeds 101 9 cm - 2 do highly charged ions appear (figure 4.8.1). How can one link the previous time-dependent ‘batch’ spectrum to an experimental spectrum delivered in steady state by a magnetic charge separator, analysing the ion beams of an ECR source and yielding ion intensities versus

280

ION CHARACTERISTICS AND ION PROCESSES IN ECRIS PLASMA

charge states? Let us consider, for instance, carbon with 1 keV electrons. Under the assumptions that (i) the successive step by step ionization processes by electron impact play a main role in ion production, (ii) the single-collision, multipleionization processes contribute negligibly to total ion production; and (iii) ion losses due to the diffusion and recombination processes are negligibly small, the ion production is governed by dnq - j j - = nq- \ o q = nqcFq q+\

I = e n w r,

the ionization factor

where nq is the ion density with charge q , crq,q+\ is the ionization cross-section from charge q to q + 1 by electron impact, and I is the ionization factor, which is equal to a product of electron current density (enw) and confinement time 00. The above equation can be solved under various conditions, for example that the neutral gas atoms are continuously injected or that the gas is injected under a pulsed mode. In the first case no is a constant quantity even versus time r because the batch is permanently renewed, whereas in the second case, as already mentioned, no is a constant quantity that is meaningful only for r < 0. The calculated results for carbon ions are shown in figure 4.8.2(a) using Lotz’s empirical formula to estimate the ionization cross sections. These results demonstrate that in the pulsed mode the charge distribution of ions changes with / , that ions with each charge state have a maximum intensity at a particular value of the ionization factor and finally that all ions become completely ionized. 4.8.2

The continuous gas feed batch model [290], [291]

For ECRIS in continuous wave mode, i.e. for continuous gas injection, the production of ions becomes equilibrated (dnq/ d l = 0 ) at large values of the ionization factor, n w r and their intensity ratios are given by nq/ n q- \ = r

a=

pr/p2

Figure 4.10.3 An emittance diagram of an ion beam with strong optical aberration. so deformed that it is impossible to refocus the particles from the outer regions of the beam back into the diagram that describe the acceptance of a subsequent machine or optical system: it is then better to trim the beam with an aperture because its effective emittance has been made larger than its real emittance by poor ion optics (aberrations). Thus the transformation of the six-dimensional invariant phase space volume to an invariant two-dimensional emittance by considering vz to be constant is useful but surely not rigorous [308].

4.10.3

Normalized emittance [298]

In the case of beams of low intensity, in which the internal space charge forces are negligible, and of optical systems without losses, Liouville’s theorem provides a proof that this emittance remains the same at points where the potential V(z) takes the same values. In particular, it remains unaltered along the whole extent of a drift space without an accelerating field. If V ( z ) changes, the product 7te„ = A n = — rriQC

x A(r, r') = -—

1—

, A(r, r')

(v/c)1

is now invariant, which defines a ‘normalized emittance’ sn which is very useful for comparing different ion beams accelerated to different energies issuing from different ion sources and thus determining the optical quality for further beam transport.

ECRIS BEAM EMITTANCES

4.10.4

307

Normalized brightness

For a comparison of different sources, it is better to use the ‘normalized brightness’

which includes not only the transport qualities of the beam emittance but also the real ion current I + transported in the beairi, whatever its energy.

4.11

ECRIS BEAM EMITTANCES

4.11.1 Evaluations of ECRIS emittances As pointed out by Krauss-Vogt et al [306], [315], [316] in their specific study of ECRIS emittances, the motion of a charged particle in an axially symmetric field can be described by a Hamiltonian function:

H = I m \-{pe/r ~ qAe)1 +

+ ^

(4' 1L1)

where A$ = \Bo{z)rstart, q is the charge and pe, p z and p r are the canonical momenta. The canonical momentum in the azimuthal direction pe(can) is a constant of motion, because the Hamiltonian does not depend on the azimuthal angle 0. The kinetic momentum pe(kin) can be assumed to be nearly zero (quiescent plasma) because the atoms in the plasma move with thermal velocities. When the atom is ionized in a magnetic field Z?(z), one must add a vector potential to the azimuthal kinetic momentum, and so pe{can) is now given by Pe

=

pe(kin) + q A e rst art •

(4.11.2)

For simplicity one can consider a magnetic field which is constant and decreases suddenly to zero at a certain point in the extraction zone. Then the canonical momentum of the ion is completely transfered into kinetic momentum after the passage through the ’infinitely” short fringing field. For the projection in the jc, x' phase space one finds p (k in ) = \ q B 0{z)rs,art

(4.11.3)

with rstart the radius of the extraction aperture. When the kinetic momentum is divided by the linear momentum after the acceleration in the electric extraction fields one finds for the divergence of the particles .r' = \ qBo±.z)- stun Po

(4.11.4)

308

ION CHARACTERISTICS AND ION PROCESSES IN ECRIS PLASMA

and so the emittance of the ion beam is given by s =

tcx x

= 7zrstart

1 qBp(z)rss t art 2

Mvo

M v 0 a y/qM V eext r •

Taking into account the relativistic ion speeds, but always ignoring the ion temperature the minimum normalized emittance according to Taylor [13], [309] is then limited to sn = 1.6 x 10 5( q / A ) B r 2

(Trmmmrad)

(4.11.5)

with B the magnetic field in Gauss, r the radius of the extraction aperture in millimetres and q and A are the charge state and atomic weight of the ions. The above relation of sn indicates that in spite of the magnetic fringing field sn remains very acceptable for accelerators {sn < 1 mm mrad). For min-B ECRIS it is important to state that the shape of the magnetic fringing field has no great influence on the magnitude of the emittance but determines the shape of the emittance area in phase space [306]. However, the electrical field in the extraction region shows a significant influence on the beam matching at a definite position behind the m in-# ECRIS. From the calculations described in [306] it follows that the shape of the plasma electrodes and the starting conditions of the particles have a minor effect compared to the fringing field and the electrostatic immersion lens (which consists of puller and earth electrode or special beam-forming electrodes). This may explain the low importance of the plasma electrode and the puzzling electrode suppression seen in section 4.9.3. It also shows the needlessness of a very sophisticated extraction geometry in such sources. Generally the results of the numerical ray-tracing calculations are in agreement with the experimental size and shape of the emittance ellipse. Because of this agreement it is possible to come to a reliable design of the matching between ECR source and a beam line. For this case, it is necessary to calculate the beam properties at a definite matching point between source and beam line with a numerical integration code [310]. On the other hand Xie [311] has also considered the ion temperature T+ in the plasma. He then has shown that the final emittance would be given by

(4.11.6) where # 0 is the magnetic field at the extraction radius. In obtaining the relation, he assumed that the total electric field has no azimuthal variation, and that the magnetic field due to the hexapole can be neglected within the extraction aperture.

ECRIS BEAM EMITTANCES

309

There are two simple limiting cases to this formula. If the first term dominates, then one obtains the hot-ion limit, showing a decrease of e for highly charged beams with an emittance

(4.11.7)

If the ions are cold (T + ~ 0), and the interaction of the ions with the magnetic field in the ions source dominates, then one obtains the cold-ion limit where e increases with charge state q.

(4.11.8)

4.11.2

ECRIS emittances— experimental data

The first measurements were made in 1976 on TRIPLEMAFIOS (SUPERMAFIOS with an expansion cup) [312]. At the beginning of the ECRIS development, plasma and beam theoreticians prophesied very large emittances caused by the E x B forces in the extraction zone, making the ECRIS inappropriate for beam injection into accelerators. Therefore the first measurements proving small emittances were very important for further developments. (The theoretical justifications for small s values were presented by other theoreticians some 1 0 years later.) In 1975 the first emittance measurements of a global beam containing argon ions from i = 1 to i = 10 showed total emittances of 200-380 n mm mrad when the radius of the extraction hole was increased from 3.5 to 7 mm and with the ion beam current increasing by a factor of ~ 5 in this operation. No dramatic changes were observed on varying B q in the extraction zone. Later, charge-selected beams of A r ^ - A r 10* (r = 7 mm, Vextr = 10 kV) provided s decreasing from 318 mm mrad to 204 mm mrad with increasing q (90% of the ion beam) and normalized sn around 0.5 mm mrad. Similar values were found for the axial emittance [313]. Jumping over all the numerous emittance measurements made on different ECRIS between 1976 and 1993 let us comment on the most recent emittance measurements made on the superconducting ECRIS at MSU [314]. With this high-performance source and a sophisticated and reliable emittance meter, the values of s and en are only two to three times smaller (with 99% of the ion beam). These results prove that in the meantime the ion beam optics was greatly improved (no aberrations) with respect to the primitive extraction optics of TRIPLEMAFIOS but the ECRIS emittances have not radically changed.

310

ION CHARACTERISTICS AND ION PROCESSES IN ECRIS PLASMA

Finally we can say that, according to experimental data, (i) in spite of different methods and instruments the measured emittances of ECRIS are not very scattered and comprise between 100 and 500 mm mrad in all cases when 5 < Vextr < 25 kV, with sn < 0.5 mm mrad, (ii) that the order of magnitude of the normalized emittances is roughly given by Taylor’s formula en = 1.6 x 10~5{ q /A )B r 2 (for low-charge ions), (iii) that the emittances of highly charged ion beams are generally smaller than those of less highly charged beams issuing from the same ECRIS as if they were concentrated around the ECRIS axis and (iv) one often also observes that the emittance increases with the beam current, which seems to be related to space charge effects during the beam transport.

5 SIMPLE MIRROR AND BUCKET ECRIS FOR LESS HIGHLY CHARGED IONS

5.1

5.1.1

THE HISTORY OF THE FIRST ECR ION SOURCES (1965-1973)

Introduction to the ECRIS concept and its invention

It is always difficult for an author to write about his own work in an unbiased manner. Either he is too modest or too assuming. In addition, it is not simple to describe the genesis of a new concept and its motivations without invoking a few personal experiences. So let me begin with what I think was the beginning of the ECRIS story. When I worked for my thesis (1954), I utilized an ion source containing a hot filament. As I was obliged to change the destroyed filaments myself, I became averse to the hot-cathode principle. At the same time, I worked on ion stripping with a foil stripper. As I was obliged to change the foils myself, I became averse to foil strippers and developed a supersonic condensable gas stripper [317]. This encouraged me to ponder the question of multiply charged ion production, a topic which never disappeared from my mind. Somewhat later, I worked with an RF ion source (the so-called Thoneman source) and I was delighted not to have to change the cathodes, however the high gas pressures, the subsequent charge exchange and the large gas flows created many difficulties [318]. In 1959, I worked on RF plasmoids (see section 1.3) and discovered some experimental effects relative to cop and coc resonances. From 1959 to 1963, I worked on enhanced diffusion in PIG sources. During this time, I was again obliged to change the cathodes— and from that time on I began really to hate hot cathodes and arc sources of all kinds. In 1963, I worked with Consoli at Saclay—CEA (French Atomic Energy Commission), on an ECR plasma accelerator which was invented by him. This accelerator, named PLEIADE, based on the /x grad B force, produced energetic electrons and axially accelerated ions in an ECR zone located in a magnetic field 311

312

SIMPLE MIRROR AND BUCKET ECRIS Gauss

1000

grounded Quartz

a)

b)

c) l+or I-

ECRIS No 1 [323]: (a) magnetic field profile; (b ) experimental set-up; (c) the extraction system for ions.

Figure 5.1.1

gradient [121], [319] (typical results were ~ a few kiloelectronvolts and Wj* ~ a few kiloelectron volts). Dr Consoli, who is one of the pioneers of ECR plasmas, also studied and introduced new methods of wave-plasma coupling (the PLEIADE coupling was based on the TEm cavity mode at 3 GHz). In 1964, Consoli’s group was incorporated into the Plasma Fusion Department of CEA. It then became natural to add on the other end of the PLEIADE device an opposite magnetic field gradient in order to trap the energetic plasma in a magnetic mirror system for fusion studies (figure 5.11). However, the mirror trapping of an anisotropic plasma with vj/vjj" and vi / V1 ^ 1 was on*y achieved in 1968 [320]. In the meantime, we observed that the trapped ECR plasma inside the magnetic bottle exhibited different regimes when the pressure and the RF power were changed. Among the regimes, I noticed a peculiar mode with anisotropic electrons ( v ± /v ^ 1 ) inside a dense plasma containing cold isotropic ions. As I was enthusiastic about cathodeless ion sources, at the first opportunity (in May 1965), I mounted a primitive extraction system (two ring electrodes with a target) on the existing ECR plasma

THE HISTORY OF THE FIRST ECR ION SOURCES (1965-1973)

313

Figure 5.1.2 ECRIS No 1 [323]: (a) hydrogen ion current against extraction voltage; (b) electron current against extraction voltage. and analysed the extracted particles: ions and electrons (figure 5.1.1). Though the system was very primitive and the measurements rough, the results were so striking that we immediately filed two patent applications: the first one for an ECR plasma ion source, the second for an ECR plasma cathode [321], [322].

5.1.2

The first ECR plasma cathode and the first ECR plasma ion source— ECRIS No 1 (or PLEIADE source)

In an official CEA report, No 2898, published in November 1965, I presented the first experimental data and as these data were puzzling I added a tentative interpretation of the results. An electron beam of 200 A cm - 2 could be extracted at very low extraction voltage— and a hydrogen ion beam of 40 mA cm - 2 was obtained with only 100 V extraction voltage (figure 5.1.2). These results were outstanding because they were obtained (i) at gas pressures a hundred times smaller than in the usual RF ion sources and (ii) at low extraction voltage with ion current densities well above the ordinary Child-Langmuir limit. It was necessary to justify such results. The high currents at low pressures were explained by a high ionization efficiency in the magnetoplasma and reduced charge exchange collisions, because the ECR plasma was created in a high-pressure region of a quartz tube inside the cavity (first stage) and the electrons and ions diffused towards a lower-pressure container (second stage) where the ions were extracted (the two-stage principle was retained for later developments).

314

SIMPLE MIRROR AND BUCKET ECRIS

However the high currents above the Child-Langmuir limit at low extraction voltage required a longer analysis. The phenomenon was explained by the large potential drop in the sheath formed on the first electrode E q due to ambipolar forces. The potential drop A V oc yjKT~~/ M + obtained with energetic electrons (T~ > 100 eV) could give an initial velocity oc A V / M to the ions before they enter the extraction zone, where they acquire the usual energy eVextr. The Child-Langmuir law is derived on the assumption that Vo = 0 and large initial velocites are not taken into account in the V3 / 2 formula. Thus I suggested a different formula, derived in the report, which was consistent with the observed current densities:

/+a (VAV + V (A V T ^

))3

.

If the potential drop in the sheath is in the region of 102 V, the measured ion currents at low extraction voltages are normal. This means that the ECR plasma potential is positive and well above the potential of E0. Nowadays, such assumptions are well accepted for ECRIS working at low pressures with energetic electrons. They are the basis of ES potential generation in ECRIS (see section 1 .6 ). 5.1.3

ECRIS No 2 (or CIRCE I source)

At the same time, another ECR mirror plasma called CIRCE I was built in Consoli’s group, with a quite different and original coupling technique [201]. An R wave at 10 GHz (obtained with a specific right-hand wave polarizer) was introduced to the plasma chamber via a cylindrical waveguide, an alumina window W, and through a conical antenna made of boron nitride (BN antennas are now again fashionable). On the axis of the cone, a narrow channel g was used for the gas feed, towards the ECR zone (located near the top of the conical antenna) in the B field gradient (figure 5.1.3). A plasma density of n < 7 x 1011 cm - 3 was measured with a microwave interferometer. In order to verify the results of ECRIS No 1, a movable extractor made of three electrodes with holes 0 1 cm and a grid plus a collector was mounted in the second mirror near the ECR 2 plane. The system could be located at four different positions 1, 2, 3 and 4, with respect to the ECR 2 plane and the magnetic mirror. The existence of an anisotropic electron plasma (tf[/ujj“ > 1) favoured the electron mirror trapping and the ion-electron separation. Thus it was seen that the best extractor locations were beyond the ECR mirror (positions 2 and 1) at low gas pressures (< 5 x 10- 4 Torr) (which was to become an important point for multi-charged ion production) but at high gas pressure (> 10“ 3 Torr) the best locations are reversed. The ion energy before entering the extraction gap was measured to be approximately 100 eV or less in the low-pressure regime. In figure 5.1.4, we see that Ar+ beams up to 80 mA were obtained with only 100 V extraction voltage, and hydrogen beams of ~ 40 mA could be routinely

THE HISTORY OF THE FIRST ECR ION SOURCES (1965-1973)

315

Generator CW

Figure 5.1.3 ECRIS No 2: general arrangement [201]. Note the R wave launcher with conical antenna—ABN—made of boron nitride. 100 n

mA

50

5x10"^ TORR ARGON

P0S 2

3,5x10“ 4TORR ARGON

P0S 3

3x10"4 TORR HYDROGEN 10"3 TORR HYDROGEN

P0S 1 POS 4

r 0

100

250V

Figure 5.1.4 ECRIS No 2 [201]: extracted ion currents against extraction voltage for different positions of the extractor and different gases. extracted. However the beam-plasma interface was not clearly determined and nobody in the group was able to draw conclusions at that time. Thus, the puzzling results of ECRIS No 1 were confirmed with some useful specifications concerning the plasma density and the location of the extractor but without further explanations. The question of whether the 100 eV ions were accelerated inside the plasma or in the sheath was not solved and neither were many other questions.

SIMPLE MIRROR AND BUCKET ECRIS

316

B gauss R e so n a n ce

M agn. m ir ro r

3600

Z

1000

0 mm m e t a l j Hot

-

Sheath '

■

mmm. glaSS

■

——q u a r t z Wave

guide ^

Q = 10 GHz Tight Be

w indo w

E1 E2

Figure 5.1.5

E3

E*

ECRIS No 3 [324]: general arrangement with calorimetric target E5.

As for the electrons, a current of 200 mA cm - 2 was once more obtained with 10 V extraction voltage and the belief in an ECR plasma cathode was strengthened. All these results were published in the proceedings of the Seventh International Conference on Phenomena in Ionized Gases (1966) [201]. 5.1.4

ECRIS No 3 (or CIRCE II source)

In 1967, I launched a third device called CIRCE II dedicated only to ion beam production (figure 5.1.5). In order to simplify the technology, non-polarized EM waves at 10 GHz were introduced simply with a wave guide and a microwave window into a multimode cavity (in other words in a metallic box whose size is large with respect to the wavelength). The forced R wave propagation of ECRIS 2 was dropped and we could observe that nevertheless a reliable ECR plasma with similar characteristics was ignited (thus R waves were automatically regenerated in the cavity). Different plasma regimes were obtained and in particular an overdense plasma was clearly achieved with densities 1012 < n < 5 x 101 2 cm - 3 (figure 5.1.6). The extracted ion beam currents are shown in figures 5.1.4 and 5.1.7. In order to ascertain that the ions in the extracted beam are energized by the extraction voltage and that their energy is not due to some fig rad B force as in the PLEIADE accelerator, we measured their heat deposition with a pyrometric target [325] and proved that the heat was proportional to the extraction voltage (figure 5.1.8). In parallel, we observed the corresponding Doppler shift of the optical line with recombined protons in the beam (figure 5.1.9). So no further doubt was possible: the ion currents were formed in the extractor

THE HISTORY OF THE FIRST ECR ION SOURCES (1965-1973)

n

317

cm-3 A 5 1 0 12

Te 4

10

3

2

Watt 100

> 500

Figure 5.1.6 ECRIS No 3: electron temperature and density versus RF power [324] (N2 2 x 10~4 Torr).

T+m A

Figure 5.1.7 ECRIS No 3: extracted ion current against pressure for two different positions of Ei with respect to the magnetic mirror point.

system and the device was an ion source. On the other hand, we noticed that above a certain level of RF power, even in the underdense regime, instabilities occurred, with increased plasma noise, and thus the particle lifetime was limited to some 10- 6 s (which was later confirmed in ECRIS No 4 and ECRIS No 6 ). Moreover, the role of the location of the extractor with respect to the magnetic mirror was ascertained (figure 5.1.7). All these results were presented at the First International Conference on Ion Sources (1969) [324] and also published elsewhere [307].

318

SIMPLE MIRROR AND BUCKET ECRIS V5

m A j

w atts

—O - , /f , ion cu r re n t strik in g the p y ro m ctric ta r g e t; Vs /j , e le c tr ic a l pow er d ep o sit . on the ta rg et by the beam ; - . radiated pow er deduced f f»x>m ta r g e t tem p era tu re, y

^5 p '

R wait

y

P

* O

(X

/

potential o f the

500

p y ro -

m etric target with resp ect to .Elt

1000

Vg volts

Figure 5.1.8 ECRIS No 3: calorimetric measurements of the ion beam power deposition [327]. Light

intensity

Optical Doppler shift measurements of the Hpline.

Figure 5.1.9 ECRIS No 3: Doppler shift measurements of the optical

line [327].

THE HISTORY OF THE FIRST ECR ION SOURCES (1965-1973)

5.1.5

319

ECRIS No 4 (or MAFIOS source) (1971)

In 1970, Postma suggested the use of an ECR plasma to produce highly charged ions [316]. The multicharged species were supposed to be generated with very energetic electrons yielding Auger cascades and shake-off collisions (see section 1.4). For this purpose, we shortened the device and again utilized a cavity but at 10 GHz in the TE 321 mode. Due to the Q-factor of the cavity strong EM fields were obtained in the ECR zone. In this way one obtained very hot electrons which interacted nonlinearly with the plasma and eventually produced electron populations with electron energies in the kiloelectronvolt range and decoupled electrons reaching tens of kiloelectronvolt. The extractor was located near the second mirror plane. The device was named MAFIOS (machine fabriquant ions strippes) (figure 5.1.10(a)). A cold plasma was created in the capillary quartz tube ( 0 5 mm; p ~ 10~3 Torr, n > 1011 cm 3 inside the cavity, which constituted the reservoir of electrons and replaced the usual short-lived cathode (first stage). The cold electrons immediately diffused to the ECR zone where they were energized by the available microwave power ( P < 2 kW). Due to differential pumping the pressure in the second stage was less than 10-5 Torr. A Wien filter was located beyond the extractor for analysing the Q / M species followed by an electrostatic analyser. A time-of-flight analyser could also be mounted. Though completely stripped N7+ ions were produced [328] their yield was very small. Thus, the experimental results were interesting and reliable, but not a breakthrough [327]— [329]. The multiply charged ion rates were not much better than those of special PIG sources but the longevity of the source was remarkable since no hot cathodes were utilized. Figure 5.1.10(b) shows typical xenon ion spectra, with ~ 1 0 0 /xA up to charge state 8 + and then decreasing sharply towards 2 /xA for X e12+. Nevertheless, we came rapidly to the conclusion that for a high current of highly charged ions, the single-tandem-mirror ECRIS were not adequate. Better particle confinement had to be achieved and the obvious instabilities had to be eliminated. Thus ions with long lifetimes had to be generated in order to undergo step by step ionizations, since the Auger cascades and shake-off collisions are insufficient for this task. Thus, very gradually, we came to the solution of the min-B mirror ECRIS developed in chapter 6 . r f

5.1.6

ECRIS No 5 (the Japanese source) (1972)

In 1972, Okamoto and Tamagawa published two articles describing the operation and the results of an original large-size ECRIS, which was the first ECRIS built outside our laboratory [330], [331] (figure 5.1.11). In this 2.45 GHz tandem mirror source, the wave-plasma coupling was obtained with a slow-wave Lisitano coil (see section 2.4) and the extraction electrodes, with an accel/decel arrangement, utilized multiple apertures. Large ion beams up to 500 mA of protons were extracted with 1 keV ion energy. A rather low beam divergence was obtained (0 < 2°). On the other hand, for the

320

SIMPLE MIRROR AND BUCKET ECRIS

n K T i~ 1 0 u e V cm3

i i

n K T j - 2 10U eV cm3

V 7 i/W .. p r f ~

2

KW

n K T t ~ 5 101 coRF and coce > coRF (see section 2.1). However the situation is very confusing, since, in such a case, plasma-wave interactions depend not only on the angle 0 between the propagation vector k of the electromagnetic wave and the static magnetic field but also on the presence of a longitudinal electric field component in the EM wave before the resonance is reached (whereas a pure ECR mode only requires a transverse electric field E j_). A favourable condition can be imagined for instance with an E q\ wave since it supplies both, an E\\ component parallel to the static magnetic field (mainly having a B\\ component) as well as a radial component E ± B. As for the angle 6 between k and B , unfortunately even in the simplest case (a circular waveguide with no plasma inside) it is not possible to determine this angle. Thus it seems hopeless to determine the value of 6 in wave-plasma systems with a complicated B configuration and therefore these theories look practically inapplicable. On the other hand, further theoretical support was provided by Musil and Zacek [187], Kopecky et al [188] and Nanobashvili et al [189] who reported that higher electron density can be obtained by microwave discharges at higher B fields. In this case the existence of ECR is not a prerequisite condition forj)lasm a generation. Let us also emphasize that the specific /x-wave power (P/V ol) in these ECRIS is generally much more than 1 W cm-3 leading necessarily to nonlinear interactions (see section 1.3.4.7), entailing quite unpredictable conditions. 5.3.2.3 Off-resonance plasma effervescence. A puzzling aspect observed by Sakudo in the 1980s [348] shows that the best RF power absorption in small ECRIS occurs when the magnetic field B > B ecr and even when B ecr is not present at all in the source (with B ^ 1.3B ecr )- Under these conditions, anoverdense plasma (copo)RF) is obtained with rather cold electrons (Te ^ 10 eV) and large ion beams are extracted. According to [187]—[189], in an inhomogeneous plasma, wave-plasma interactions may explain such a phenomenon (not involving ECR). However, for those who discard mathematical wave-plasma models in overdense turbulent plasma, let us try to imagine what can occur physically to an orbiting electron interacting with an R wave near the ECR zone. For this we proposed a simplified heuristic model based on the plasma effervescence of section 1.3.7. (i)

When B = B ecr and < a)ce an orbiting electron can remain for a while in synchronization with the rotating E± field. Before being out of phase, after several orbits, it acquires a substantial energy and absorbs a

334

SIMPLE MIRROR AND BUCKET ECRIS

Figure 5.3.1 R wave electric field vector rotations and electron gyrations in ECR (a) and off-ECR (b ) conditions; (c) with B > B EC r .

given power from the wave. Looking at one single orbit we can write that the T Ec r is given by (figure 5.3.1(a)) T'e

c r

= 2n IB e c r (e/m ) = T rF.

(ii) When collisions at frequency v(J)p impede the orbit (v(i)p > coce) the electron drags behind the rotating £j_. It can no longer close its (perturbed) orbit during = 2 n / B Ec r (e/m). It is rapidly outphased and a resonance then seems impossible (figure 5.3.1(b)). (iii) In order to compensate the time lost in the collisions and to maintain some synchronization with E± the electron must gyrate faster, on a smaller average orbit, such that T = lix /B ’ (e/m ) = TRF where B' > B Ec r • Hence the magnetic field must be somewhat increased but not too much (figure 5.3.1(c)). In any case the electron will not reach a high energy level but during its invervals of synchronization it can reach just enough energy to maintain an overdense plasma with singly charged ions. In this case it absorbs energy from the wave which is damped. Thus the RF power absorption peak at B > B Ec r represents an experimental compromise between the best angular velocity co' = 2jx/ T ' and a sufficient energy gain for the existencejDf the discharge. This energy gain can be acquired by the electrons in a E'L field which is relatively large with respect to non-resonance conditions but still small with respect to the theoretical field (E _l / oo) of a collisionless ECR. From the above-given heuristic explanation, we suggest that the so-called ‘off resonance’ is not in conflict with a weak, viscous, collisional, broad-band ECR.

OVERDENSE ECRIS AT 2.45 GHZ FOR ION BEAM PROCESSING

335

53.2.4 Collisional off-resonance theory. A mathematical study of a colli­ sional ECR theory was made by Yusheng Rao et al [345] considering only classical electron-neutral (e-N) collision rates proportional to the gas pressure. It is shown that a marginally resonant RF power absorption occurs at 5-values shifted above B ecr onty when the gas pressure exceeds 10-1 Torr. In the ‘off-resonance’ sources however the pressure remains below 10-2 Torr yielding veN clearly below 109 s-1 . Assuming that vW /> ve^ and considering that the collective v0)p collision replace the classical veN collision a similar marginal res­ onance should occur. Let us take for instance a typical small overdense simple mirror ECRIS at 2.45 GHz (see section 1.3.7) with an effervescence T ~ 10-1 . If n ~ 5 x 1012 cm-3 one finds cop/lTi ~ 20 GHz > corf/ ^ tx ~ 2.45 GHz and v^ would reach ~ 2 x 109 s_1. In this case the above-quoted theory indicates a preferred RF power absorption as if p > 10_1 Torr were present in the source. 53.2.5 Assumptions and realities. In spite of all the previous more or less complicated assumptions and explanations, overdense 2.45 GHz and even ‘off-resonance’ ECRIS work and are more and more utilized for industrial applications, when single charged ions are desired. The reasons are simple: a microwave frequency of 2.45 GHz is frequently utilized, because industrial use of this frequency is permitted, higher frequency is not needed for singly charged ion sources and the low cost of the wave generator and of the magnetic field (B ~ 1000 G) are good industrial arguments. The longevity of ECRIS is also very much praised, but it turns out that the tuning of the ECRIS is more sophisticated than those of most ion sources. Thus they are harder to handle due to the greater number of parameters (microwave power, magnetic field strength and distribution, pressure). As seen previously in section 3.3, one finds for different values of parameters different plasma regimes which influence not only the degree of ionization in the source but also the uniformity, the quiescence, the reproducability, the ionic fragmentation and the ion energy. For these reasons, one desires facilitated tunings for given regimes. New methods were developed with specific 2.45 GHz equipment (wave couplers, launchers, impedance matchings etc). Eventually most of the sources reached good reliability in the overdense regime. Before going into detail, let me emphasize the outstanding role played by Japanese engineers in the development of these sources, and their leading position during the last 10 years. 5.3.3

Prototypes of modern ECRIS for industrial use

5.3.3.1 Sakudo’s ion sources. At the end of the 1970s, a slit-shaped 2.45 GHz microwave ion source adapted for a high-current ion implanter was developed by Sakudo et al at Hitachi Ltd [48]. In this successful ion source, a solenoid and ferromagnetic materials are effectively placed to form a magnetic field of

336

SIMPLE MIRROR AND BUCKET ECRIS

Microwave 2.45 GHz ^

Rectangular Waveguide

M a g n e t ic F l u x D e n s i t y (G ) 400

800

Magnet

Coils

ECR isma Extraction

System

Figure 5.3.2

A low-ion-energy ECR type microwave ion source (NTT Co).

more that 875 G over the entire discharge chamber. Thus the conditions are those described in section 5.3.2.2. However, as the inventor thinks that ECR is not involved in his source and as I very much respect his opinion, I do not include this source in the ECRIS category. In any case, Sakudo’s pioneering developments of ion implanters are well known over the world and his sources have been described in detail in different publications [48], [348]. 53.3.2 ECRIS prototypes at NTT Co. Another low-ion-energy ECRIS, shown in figure 5.3.2, has been developed by Matsuo et al and Ono et al [349], [351]. In this ion source, microwave power of 100-300 W is introduced into a discharge chamber having a cavity resonator structure through a rectangular waveguide. The ECR condition and cavity resonator structure allow a microwave discharge to be initiated at a relatively low gas pressure ( 10~5—10“3 Torr). A largediameter ion beam (10 cm in diameter) with an energy of 20-30 eV and a current density of 3-5 mA cm-2 was extracted from a single aperture. In order to transport such a low-energy ion beam, the magnetic field distribution as shown in figure 5.3.2 is important. Note that the ECR is clearly located close to the microwave window— and that the magnetic profile is not a tandem mirror but a single mirror. 5.3.33 ECRIS prototypes with special microwave windows [352], [353]. Torii et al at the LSI Laboratories of Nippon Telephone and Telegraph (NTT) have developed different ECR ion sources for a high-current oxygen implanter. The ion source, shown in figure 5.3.3(a), consists of a cylindrical plasma chamber and a 45 kV triode extraction system, with multiple 5 mm diameter apertures, surrounded by three solenoids. Quartz and quartz+alumina windows are utilized (figure 5.3.3(b)). In another source the 2.45 GHz microwaves enter the plasma

OVERDENSE ECRIS AT 2.45 GHZ FOR ION BEAM PROCESSING

337

chamber from a rectangular waveguide via a triple-layered window of quartz, alumina and boron nitride (figure 5.3.4(a)). Impedance matching between the waveguide and the plasma chamber is achieved by adjusting the dimensions of the elements of the window. The boron nitride, having a high thermal conductivity, also serves to dissipate the power deposited in the window as seen in ECRIS No 2. The optimum magnetic field at the window is 950 G. This high-current ECR ion source produces beams of oxygen ions with an 80% 0 + fraction. Advanced ECR sources with a high current density of more than 100mA cm-2 have been developed. One source provides high current density without the accompanying damage to the microwave transmitting window found with the earlier source. This damage, which occurs when high-speed backstream electrons attack the window, limits source lifetime. By adopting a multiple-microwave-inlet configuration for the introduction of microwaves into the plasma chamber, the ECR condition can be satisfied and high-density plasma can be generated without an attack by backstream electrons. The other is a very compact source producing a high-current beam at a very low power consumption (figure 5.3.4(a)). This is achieved by reducing the inner diameter of the plasma chamber to 5 cm, which is smaller than the cut-off dimensions for propagation of the 2.45 GHz microwave. A high plasma density of 1 x 1013 cm-3 has been obtained at a microwave power of 250 W (figure 5.3.4(b)). 5.33.4 Ishikawa’s miniaturized permanent magnet source [354], [356], [357]. Various applications require compact, microwave-plasma sources that are compatible with ultrahigh-vacuum technology and must be retrofitted into existing vacuum chambers such as molecular beam epitaxy (MBE) machines. Hence, small plasma sources have numerous potential applications. Among these are plasma-assisted MBE, oxygen sources for superconducting thin-film deposition and atomic sources for fundamental scientific plasma chemistry investigations. Small ring magnets, each magnetized along the longitudinal direction, are placed in a stack to form a cylinder enclosing the cylindrical discharge region. The magnets are orientated with opposing poles touching to form ECR regions inside the plasma. A small-size high-intensity microwave ion source using a permanent magnet as shown in figure 5.3.5 has been developed by Ishikawa et al at Kyoto University. It turns out to be a very successful device (1985) based on clear ideas and admirable miniaturized technology. In this ion source the magnetic field required for ECR is produced by the Co-Sm permanent magnet, so that a low-input-power small-size microwave ion source is obtained. The size is 50 mm in diameter and 65 mm in height. In addition, since a plasma density of the order of 1012 cm-3 is generated by an input microwave power of only a few tens of watts, a flexible coaxial line could be used for feeding the microwaves. Total extracted ion currents of more than 1 mA for Ar, N2, 0 2 and C 0 2 gases and Cs and Rb metals were obtained. This ion source is suitable for megaelectronvolt implanters but it is also convenient as an ion beam deposition source. Even

338

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200

UPPER COt- CURRENT I, (A) Figure 5.3.3 (a) A schematic cross-sectional view of a no-window-damage ECR source with high current density. (b ) The dependence of ion current on the different configurations of a microwave-transmitting dielectric as a function of coil currents. Microwave power, 480 W; O2 gas flow rate, 2 seem.

more important, large electron beams were extracted. Hence the Kyoto source can be utilized as an ECR plasma cathode. A discharge theory for this compact source was proposed by Sun [355], but further work is necessary.

5.3.4

Multipole or ECR bucket plasma sources

5.3.4.1 Generalities. These sources are useful when large singly charged ion beams with large extraction areas in weak B fields are desired, and when the gas pressure in the plasma must be kept low. The so-called bucket configuration in arc ion sources was obtained by eliminating the axial magnetic mirrors from the min-B configuration. It was proposed first by MacKinsey at LBL [358] and further developed by Green and others [359], [360] for fusion neutral

OVERDENSE ECRIS AT 2.45 GHZ FOR ION BEAM PROCESSING

339

M 1CROWAVES

(a)

(b)

Figure 5.3.4 (a) Compact ECRIS with triple-layered window; (b) comparative results of ECRIS 5.3.3 and 5.3.4. injectors. Multipole structures achieved decent confinement; however, their principal feature is good uniformity in large-size plasmas, and ECRIS builders did not forget this. The following ECRIS prototypes are based on this property. 5.3.4.2 Distributed ECR plasma sources (DECR) [361]-[364]. For beam applications such as etching and deposition, grids are a potential source of sputtered contaminants. They reduce the current density which can be extracted, and they tend to be easily damaged. Thus their elimination has been studied. The ECR plasma source combines an ECR plasma generation region— similar to that in the divergent magnetic field case, but without extraction grids— with a multipole magnetic confinement scheme, achieved with permanent magnets. This type of system is shown in figure 5.3.6. The potential advantage lies in the plasma generation and multipole regions which are quite distinct—the source plasma is not mapped into the multipole region by strong magnetic field lines. The multipole structure limits radial plasma loss to the chamber wall, while the interior region is magnetic field free. A small-area source can then be expanded into a larger-area multipole region, where the plasma can mix and become spatially more uniform. One disadvantage is that the plasma density in the multipole region may be substantially less than that in the source region, depending on the extraction area and relative sizes of the two volumes. Petit and Pelletier [342] have studied the plasma obtained in such a system, and the results obtained in etching silicon in SF6 (1987). ECR processing sources have been constructed using permanent magnets

340

SIMPLE MIRROR AND BUCKET ECRIS

MICROWAVE

Figure 5.3.5 A small-size and high-intensity microwave ion source. (Yoshikawa or Kyoto source) [354]. 1, sealed coaxial connector; 2, top flange; 3, antenna; 4, boron nitride; 5, heater; 6, middle flange; 7, gas inlet; 8, copper gaskets; 9, permanent magnet; 10, base flange; 11, plate with an extraction aperture; 12, Macor insulator; 13, extraction electrode; 14, coolant; 15, ferro- or non-ferromagnetic spacers.

only, without electromagnets. The permanent magnets are arranged in a multipole array and may be placed inside or outside the chamber. The resultant magnetic field both supplies the 875 G ECR resonance region and reduces radial plasma loss. The microwave power has been introduced through a tuned cavity in one case, and through an internal multipole antenna array in another. Permanent magnet multipole sources can be quite compact and have the potential to scale to large diameters as we will see now. The development of DECR excitation is based on two ideas: (i) the permanent magnet rows destined for multipolar magnetic field confinement are further used to provide the magnetic field intensity needed for ECR coupling; (ii) the microwave field required for ECR is provided by linear applicators (antennas) running along and close to the magnet rows. This scheme results in the generation of the plasma at the periphery of the reactor where the electrons (accelerated through ECR) remain trapped between the magnetic field cusps until they ionize the gas. The plasma thus produced then diffuses towards the central part of the chamber (magnetic field free regime) where a cold dc diffusion plasma is obtained free of high-energy electrons which remain trapped (in the cusps). At 2.45 GHz uniform argon plasmas are currently produced in cylindrical reactors, with ion densities ri[ < ncr (ncr ~ 7.5 x 1010 cm -3).

(b)

(C)

RF BIASING

MAGNETS SUBSTRATE-HOLDER

Figure 5.3.6 (a) A source consisting of an ECR plasma source region and a permanent magnet multipole (bucket) region [5]. (b ) DECR possible arrangements of the bucket zones and ECR zones, (c) A plane DECR reactor based on an array of parallel, linear antennas.

(a)

REGION

PLASMA

£

OVERDENSE ECRIS AT 2.45 GHZ FOR ION BEAM PROCESSING

342

SIMPLE MIRROR AND BUCKET ECRIS

A crucial advantage of DECR is that it allows fitting of the plasma source term to the reactor dimensions. However, well suited for the processing of small subsubstrate diameters, the cylindrical geometry is inadequate for plasma processing over large areas. It is then favourably replaced by a planar DECR configuration using a set of parallel linear antennas, but achieving large areas of uniform plasma requires that each antenna can generate a uniform plasma along it. According to Pelletier in the inital design of the DECR technique, microwaves propagate mainly in the region of ECR coupling, so that, in the presence of plasma, microwaves cannot propagate along the antennas without absorption. Damping of travelling waves along the antennas thus led to non-uniformity. A solution to produce uniform plasmas consists of sustaining a constantamplitude standing wave along the linear applicator. This can be obtained by the spatial separation of the propagation regime from the absorption region of ECR coupling. In a new uniform DECR design (UDECR), the antennas are set (see figure 53.6(b)) between the cusps, outside the ECR regions, but within the regions free from plasma, located between the reactor wall and specific field lines linking the successive magnet poles. Using UDECR, uniform plasmas with ion densities of the order of the critical densities can be obtained over very large rectangular areas. 5.3.4.3 Sakamoto's large-area source [364]. A large source was built by Sakamoto et al, who developed a circular device ( 0 = 30 cm, h = 9 cm). The magnets are set along four circles (figure 5.3.7(a)). The waves propagate towards the ECR along magnetic field lines where B > B ecr (Whistler mode without cut-off). They are launched from slots cut in the ‘H ’ wall of a rectangular waveguide. Thus even overdense plasma is achievable. Ion current densities of several milliamperes per square centimetre are obtained with P rf 500 W at 5 x 10“ 3 Torr. 5.3.4.4 ECR bucket ion sources (miscellaneous). For implantation it is desirable to use electrostatic grids which may improve uniformity of the extracted beam, allow some degree of downstream collimation and permit the use of just ions, instead of a space charge neutral plasma. The ion extraction voltage is in some cases applied to the entire discharge chamber, relative to an earthed grid. An additional advantage gained by using grids is that potential leakage of microwaves out of the source into the process chamber, which can occur with tenuous plasmas, or if the plasma extinguishes for some reason (e.g. magnet or gas failure), is eliminated. Figure 5.3.8 shows the ECR bucket ion source developed by Tsuboi et al [365]. The ion source discharge chamber is made of stainless steel with an inner diameter of 96 mm and a length of 185 mm. The coaxial antenna introduces microwave power of 2.45 GHz. A further two sets of hexapole permanent magnets made of Sm-Co form the multi-cusp magnetic field, where the ECR

OVERDENSE ECRIS AT 2.45 GHZ FOR ION BEAM PROCESSING Permanent Magnet

(a)

343

Cooling Water

(b)

Figure 5.3.7 (a) A schematic cross-sectional view of the circular plasma source 30 cm in diameter [363]. (b ) The arrangement of permanent magnets and microwave slot launcher. PM, permanent magnet; TWG, thin waveguide; MY, magnetic yoke; SL, slot launcher; VSW, vacuum seal window.

Figure 5.3.8 A compact ECR bucket source: 0 = 9.5 cm, / = 18.5 cm [365]. regions for 2.45 GHz are located (about 10 mm distance from the discharge chamber wall). The multi-cusp magnetic field can confine a plasma which is more stable and more uniform than can a divergent magnetic field, thus the plasma losses can be reduced. Using microwave coaxial antenna and permanent magnets, the ion source can be compact (flange mount type). Recently, the authors have developed a new version which has four sets of 12-pole permanent magnets, in order to spread the multi-cusp magnetic field. Another compact bucket ECRIS was developed at the University of Paris XI [366]. This 2.45 GHz ECRIS is obtained in a multi-cusp arrangement using a set of four parallelepiped-shaped Sm-Co magnets regularly spaced around a cylindrical ionization chamber 50 mm in diameter and 50 mm in height. The electromagnetic cavity is made of a shielded quarter-wavelength

344

SIMPLE MIRROR AND BUCKET ECRIS

Figure 5.3.9 A very compact bucket ECRIS [366]. Lecher line resonator coaxially coupled to the microwave generator through an excitation loop antenna and an SMA type connector. The extracted argon ion beam current density has been measured for different excitation modes fixed by the loop antenna orientation. A current density of 1 mA cm-2 has been reached with an incident microwave power of 110 W and a chamber pressure of 9 x 10-3 Torr. The small dimensions of this ion source and its performance allow its use not only in applications such as ion beam processing and cleaning or surface treatments in advanced microelectronics, but also as a neutralizer for ion deposition application (figure 5.3.9). Similar in principle to the two-stage min-Z? ECRIS, but at higher pressures, a large-size ECRIS, consisting of two chambers, was developed by Nihei et al [367] in 1990, with PRF up to 2.5 kW (figure 5.3.10). A high-density plasma is generated in the first chamber over which a magnetic field of the electron cyclotron resonance (ECR) condition or an even greater field is applied, and the plasma is made uniform at the second chamber, the peripheral region of which is surrounded by magnetic multipole line cusp fields. An uniform plasma over an area of 8-10 cm in diameter has been produced. Microwaves (2.45 GHz) are introduced into the plasma chamber through a rectangular tapered waveguide [213], a quartz window and a rectangular short waveguide with a cross-section of 1 cm x 8 cm. The densities and the temperatures of the source shown in figure 5.3.10(c) have been measured with a movable probe located at 2 cm above the extraction grid. Uniform plasmas over an area of 9 cm in diameter have been obtained under the condition where the intensity of the magnetic field is nearly zero (below about 10 G) at the probe. Many other compact ECRIS have been developed since 1985; most of them resemble the previous sources. Let us however also mention the cusped

OVERDENSE ECRIS AT 2.45 GHZ FOR ION BEAM PROCESSING

PRESSURE P (P a)

PRESSURE P (P a)

345

PRESSURE P (Pa)

Figure 5.3.10 (a) A schematic diagram of the two-stage microwave plasma source [367]. (b) The magnetic field intensity distribution along the chamber axis, (c) The dependence of the electron density • and the temperature O on gas pressure. The discharge gases are hydrogen, nitrogen and argon.

compact mirror ECRIS built by Delaunay (1988) in Grenoble where the magnetic structure is built with opposite SmCo5 magnets in which the magnetization M is perpendicular to the source axis (figure 5.3.11). A microwave antenna is made with a dense plasma in a quartz tube. This new microwave and gas injection makes ignition of the plasma easy and enables the production of ion beams at low extraction voltage (2 kV) but this structure may induce sharp changes of current (figure 5.3.11(b)) linked with different cavity modes. The cusps structure enables one to produce high current density (12 mA cm-2 at 2 kV of extraction voltage) with an argon pressure of about 10“ 3 Torr and a microwave power of 100 W [368].

SIMPLE MIRROR AND BUCKET ECRIS

346

Let us recall that an attempt at numerical modelling of compact ECRIS was made by Grotjohn [369].

0

J _______3 L_______ I_____L

1

2

3 (a)

U

5 (cm)

Gos pressure

(m bar)

(b)

(a) A schematic drawing of the ECR ion source and magnetic field profile in a cusp geometry [368]. (b ) Extracted ion current against argon gas pressure in the magnetic cusp structure.

Figure 5.3.11

5.4

5.4.1

INDUSTRIAL ECR PLASMA AND ION SOURCES RESEARCH AT MICHIGAN STATE UNIVERSITY

Internal cavity-matching devices [47], [370], [375]

In section 2.4 we mentioned the results obtained with movable antennas and sliding shorts applied to 2.45 GHz broad-beam large-area sources for processing, where the cavity applicators created a disc or bell jar discharge. In the lowpressure regime magnets were added to the microwave cavity applicator to allow more efficient microwave discharge coupling through ‘electron cyclotron resonance’. The use of permanent magnets together with this internal cavity matching resulted in a very electrically efficient, compact microwave plasma source. Using their many years of microwave discharge experience, Asmussen and co workers have developed a plasma source design methodology. This methodology has been used to design sources of many different sizes from

INDUSTRIAL ECR PLASMA

347

Figure 5.4.1 The historical development of the multipolar ECR plasma source at MSU. 2-3 cm diameter to very large 25 cm diameter discharges and has also been used to develop large, 33 cm diameter, 915 MHz excited plasma processing discharges. Many of these designs have been transferred to industry and now are commercially available plasma/ion sources. These plasma sources are often referred to as microwave plasma disc reactors (MPDR) and figure 5.4.1 displays their historical development. 5.4.2

The technological evolution of the MPDR concept

The addition of a ring of multipolar ECR magnets to the first MPDR I by Dahimene and Asmussen [372], [373] allowed simple, stable plasma production at low pressures. The early prototypes MPDR II and MPDR 9 created a 9.5 cm diameter discharge inside a 17.78 cm diameter cavity. Later this plasma source was further optimized by enlarging the discharge diameter to 13 cm (MPDR 13). The successful performance of these early designs led to the construction of both smaller-, i.e. MPDR 610, 3 cm and MPDR 5, 5 cm, and much larger-MPDR 320, 20 cm and MPDR 325, 25 cm, diameter discharges. The earliest applications of MPDR were to provide ions and radicals in very low-pressure environments of 10-4 Torr to several millitorr. Several differentsize microwave plasma sources, which include the MPDR 5, the MPDR II and

348

SIMPLE MIRROR AND BUCKET ECRIS

the MPDR 9, have been evaluated using broad beam double grids attached to the output plane for ion extraction and acceleration. However, due to its small size and many uses the MPDR 610 has particularly high performance. Therefore we describe it in detail here. 5.4.2.1 The MPDR 610 device. This is a compact coaxial ECR plasma source designed for MBE and other ultra-high-vacuum (UHV) applications. It has since been used for a variety of applications which include compound nitriding, supercomputing, thin-film deposition and precleaning subsubstrates using atomic hydrogen. Figure 5.4.2 displays the cross-sectional view of MPDR 610. The outside diameter of the source is slightly less than 5.75 cm, and thus can slip through most standard vacuum ports on existing MBE machines and a standard 4.5 in conflat flange provides the required vacuum seal. The MPDR 610 has a very small diameter, and thus employs a tunable coaxial cavity applicator and the excitation of the transverse electromagnetic coaxial cavity mode to create and maintain the discharge. As shown in figure 5.4.2 three ring magnets, each magnetized along the axial direction, are placed in a stack to form a cylinder enclosing the cylindrical discharge region. The three magnets are orientated with opposing poles touching to form ECR regions inside the plasma region. Plasma excitation takes place in a coaxial coupling section, which is terminated at one end with a sliding short and the other end by the centre conductor. Beyond this is a circular waveguide that has a diameter which is too small to support propagating electromagnetic modes at the 2.45 GHz excitation frequency. The TEM mode is excited by a separate,

Figure 5.4.2 A cross-section of the MPDR 610 (not to scale). 1, cooling air feed; 2, rigid coaxial cable with a type N microwave connector; 3, gas feed; 4, gas line; 5, ring-shaped permanent magnets; 6, quartz or alumina plasma chamber; 7, quartz or alumina chimney; 8, centre conductor; 9, loop antenna; 10, sliding short; 11, 4.5 in conflat flange; 12, discharge volume.

INDUSTRIAL ECR PLASMA

349

loop couple feedthrough in the sliding short. Variation of the axial position of the sliding short and the centre conductor control the size of the cavity and also provide the two independent adjustments required to match microwave power into the discharge. The reflected power can be minimized to be less than 5% of the incident power. A discharge can be easily ignited and sustained at submillitorr pressures for a variety of gases. Molecular, charged and atomic species diffuse out of the open end of the source, or an ion beam may be extracted by attaching biasing grids at the end of the discharge. For the evaluation of the plasma characteristics the source was operated without a screen or grid at the open end of the quartz tube. Langmuir probes and ion energy analysers have measured plasma density, electron temperature and ion energy distributions against position for the downstream output plasma region. The source produces downstream charge densities in the high 1010 to over 1011 cm-3 with input powers of 80-200 W. The ions have average energies of less than 50 eV and exhibit highly peaked energy distribution functions and the average ion energies are controllable using input power, pressure and substrate RF bias variations. Recent experimentally measured impressed electric field strengths reveal that the impressed maximum cavity electric field strengths are 20-40 kV m-1 and the plasma loaded cavity Q is 200-300. The typical coupling efficiencies are 85-90%. The discharge operates with absorbed densities of 3 6 W cm-3 , and the ion production energy costs are in excess of 6000 eV/ion. All plasma sources shown in figure 5.4.1, with the exception of the MPDR 610, use a cylindrical cavity applicator to couple microwave power into the discharge. Depending upon the cylindrical cavity diameter, the discharge can be excited with 2.45 GHz microwave energy in one of several different electromagnetic modes, if it is very large it may operate with two or more modes excited. 5A.2.2 The MPDR 325i device (figure 5.4.3). This reactor shown in figure 5.4.3 is also described here in detail because of its usefulness in etching large 6-8 in diameter surfaces. The MPDR 325i consists in a 30.5 cm i.d. cylindrical cavity applicator and a 25 cm diameter discharge. A disc-shaped quartz discharge chamber confines the working gas to the discharge region where the microwave fields produce an ECR plasma. The input gas is introduced into the discharge chamber through pinhole openings in an annular ring and the gas feed tube (not shown in figure 5.4.3) located at the bottom of the quartz chamber. Microwave power is coupled into the cavity through a coaxial input port via the side feed, adjustable, coaxial input probe. Twelve rare-earth magnets are equally spaced in a circle around and adjacent to the quartz discharge chamber. The magnets are arranged on a soft-iron keeper with alternate poles forming a 12-pole multipolar static magnetic field across a radial plane. Each magnet produces a pole face maximum field strength in excess of ~ 3 kG. The strength and position of these magnets produces a radial magnetic field surface of 875 G, approximately 1 cm inside the discharge zone

350

SIMPLE MIRROR AND BUCKET ECRIS

ECR Plasma Reactor Stepper Motor

Figure 5.4.3

Cross-sectional views of the MPDR 325i.

and, as shown in figure 5.4.3, this results in a three-dimensional ECR surface inside the quartz chamber. The cavity excitation region is enclosed by the cylindrical cavity walls, the sliding short and, during operation, the discharge that forms inside the quartz chamber. When using 2.45 GHz excitation, the cavity, depending on its length, can either be single-mode (T E m , TE 2 1 1 , TE3n , etc.) or multi-mode excited. An important feature of this cavity applicator is its ability to impress a high-strength, tangential electric field against the top of the quartz discharge chamber without reflecting power from the applicator. Thus, even for high-density discharges, microwave energy can be coupled into the discharge by an evanescent electric field. Another set of multipolar magnets is located downstream from the ECR microwave excitation region. The ions, electrons and radicals which are created inside the quartz discharge chamber diffuse downstream into a processing chamber where a cooled independently RF-biased substrate chuck is located. The downstream multipolar magnets reduce ion/electron diffusion and improve plasma uniformity near the substrate surface. An independently applied 13.56 MHz bias on the substrate provides an independent adjustment of the energy of the ion before they strike the substrate. A microwave discharge is created inside the quartz chamber by adjusting the sliding short length, and the coupling probe to allow the cavity applicator to resonate in a pre-selected EM mode. The stepper

ECR PLASMA CATHODE

MW

Gas 1

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0

i

351

PC: ECR-plasma-cathode M: permanent magnets WG: circular waveguide MW: microwave C: chamber EB: electron beam A: electrode IB: ion beam W: working space

Figure 5.5.1 A schematic view of Tamba’s experimental device with an ECR cathode [376]. motors attached to the sliding short and the adjustable probe are connected to a computer which controls EM mode selection by adjusting the sliding short and coupling probe to pre-determined programmed positions that select the resonant mode for discharge ignition, and then computer controlled impedance matching automatically adjusts the sliding short and the coupling probe length to tune the discharge to a matched operating condition.

5.5

5.5.1

ECR PLASMA CATHODE (ALSO CALLED MICROWAVE PLASMA CATHODE)

Tamba’s ion source with ECR plasma cathode

In 1965, when operating the ECRIS, we emphasized immediately the potential utilization of the ECR plasma as a powerful electron emitter (100 mA cm-2) (see section 5.1.1). Amazingly this discovery was not utilized until 1988 when Tamba et al [376] extracted an electron beam from an ECR plasma in order to replace the ordinary hot cathode of an ion source for reactive gases. One of their first devices is shown in figure 5.5.1. The 2.45 GHz microwave MW, which is circularly polarized, is transmitted from a magnetron. An axial magnetic field is externally applied in the EC R plasma-cathode PC by a permanent magnet M. The electron beam B, which is extracted from PC, is injected into the next chamber and produces a plasma in the space W. A voltage is applied between the two chambers so that positive ions in W are accelerated into the PC. The plasma in W can be produced under a condition with as low a pressure of gas as 3 x 10-5 Torr. Ions, which are accelerated into PC from W, are trapped by the magnetic field of M. Hence, ions collide with the wall of chamber which contains PC. As a result, new electrons are produced on the wall, and the plasma density in PC increases further. At the same time, the electrons, which are produced on

352

SIMPLE MIRROR AND BUCKET ECRIS

the wall by the counter-stream of ions suppress the space-charge of ions which makes the electron extraction easier. Ion beams IB are extracted from plasmas which are formed in the space W. Here V is the electron extraction voltage, V2 is the ion acceleration voltage and V3 is the extraction voltage. The thus obtained ion source characteristics were similar to those of hot-filament sources but with a damageless cathode. Electron currents, with low extraction voltage, up to 1 A could be obtained at gas pressures greater than 5 x 10“ 4 Torr. Nowadays different types of ECR plasma cathode are fitted to classical ion sources for ion processing and hot cathodes are now replaced by ECR plasma cathodes. 5.5.2

Electron beam characteristics of miniaturized ECR plasma cathodes

An ECR plasma cathode broadly similar to that of figure 5.5.2(a) has been experimentally investigated by Sun and^Zhao [377] to evaluate the extractable and useful electron currents versus (/?, PRF, Vextr) with three different magnetic field values regulated by means of different compositions of permanent magnets with ferromagnetic spacers. The structure of the cathode is shown in figure 5.5.2(a). Continuous microwave power at 2.45 GHz is fed through a coaxial line and supplied to an antenna via a rod which connects both the antenna and the sealed coaxial line connector. The helicoid antenna is made of stainless steel or molybdenum wire of 1.5 mm diameter. The discharge chamber is very small 16 mm in diameter and 6 mm in effective height. For wall protection a sleeve of 1 mm in thickness, 1 0 mm in height, has been inserted in the chamber, and as well a ferromagnetic cover with a 2 mm aperture was put on the surface of the base flange. The magnetic field needed for ECR, between the protrusion in the discharge chamber and the base flange, is produced by Co-Sm permanent magnets. The experiments show that the discharge characteristics inside the discharge chamber depend on the strength of magnetic field, gas pressure and incident microwave power. As the magnetic field agrees with ECR, i.e., 0.0875 T, for 2.45 GHz, the discharge can occur in the pressure range from 5 x 10- 4 to 2 x 10” 3 mbar and in the incident microwave power range from 20 to 120 W. The extraction characteristics of the electron current are shown in figures 5.5.2 (b) and (c). Magnetic fields above B ECr seem to improve slightly the performance; interesting experimental results are shown in figure 5.52(d). At a gas pressure of 6 x 10- 4 mbar, an incident microwave power PRF of 55 W and a magnetic field of 0.096 T, it was found that the extracted electron current rapidly increased when further raising the extraction voltage and reached 1.3 A at an extraction voltage of 340 V. Further improvements were made [378], [379]. 5.5.2.1 A Kaufman type source with ECR plasma cathode. Among the smallest and most effective ECR plasma sources we have already cited

ECR PLASMA CATHODE

SEALED COAXIAL CONNECTOR

MICROWAVE GAS INLET r a PERMANENT m MAGNET

MIDDLE FLANGE (a)

353

rm FERROMAGNETIC m MATERIAL

ANTENNA PERMANENT MAGNET

□

BASE FLANGE

NON-FERROMAGNETIC MATERIAL

PLATE WITH AN EXTRACTION APERTURE

extraction voltage ( V )

extraction voltage ( V )

gas pressure ( m b ar)

Figure 5.5.2 {a) The structure of the plasma cathode (Kyoto type) [377]. (b) The measured electron current as a function of the extraction voltage with variation in the magnetic field at an incident microwave power of 60 W and the gas pressure of 5.3 x 10~4 mbar: O, B = 0.008 T; • , B = 0.096 T; A, B = 0.12 T. (c) The extracted electron current as a function of the extraction voltage: (1) Load current of the extraction supply; (2) measured electron current [378]. (d) The measured electron current as a function of the gas pressure with variation in the magnetic field at the extraction voltage of 250 V and the incident microwave power of 60 W. The dotted lines indicate the measured electron current; A indicates the strength of magnetic field in the discharge chamber Bz = 0.120 T; •, Bz = 0.096 T; O, Bz = 0.080 T. (Thus, the cathode works around the ECR condition of Bz ~ 0.0875 T.)

354

SIMPLE MIRROR AND BUCKET ECRIS

Figure 5.5.3 {a) A schematic view of a Kaufman type ion source with plasma cathode. (b) The ion beam current as a function of the discharge current with variation in Ar gas flow rate. A broken line indicates the typical characteristics in a Kaufman type ion source operated with the conventional filament.

Ishikawa’s compact ECRIS [354] which can be utilized with electron extraction electrodes. The electron characteristics are broadly similar to those of figure 5.5.2. Using this plasma cathode, a Kaufman type ion source was developed by Matsubara et al [356] (figure 5.5.3). The main discharge chamber is the conventional axial field chamber with an anode diameter of 4 cm, and is electrically insulated from the cathode. A dc positive voltage is applied to the anode for electron extraction. The primary electrons emitted from the cathode are prevented from rapidly escaping to the anode by the magnetic field whose direction is approximately parallel to the cylinder axis. This type of ion source produces a high-density plasma at a low gas pressure (typically the 10-2 Torr range). An ion beam of 25 mm diameter is extracted through three grid optics. Figure 5.5.3(b) shows the ion beam current as a function of the discharge current. A broken line indicates the typical characteristics in a Kaufman type ion source operated with the conventional filament. Thus similar results are obtained when operating with O 2 gas. Ion beams of 40 mA at a discharge current of 0.88 A were obtained at steady state over 50 h showing that the ECR plasma cathode has not only a high electron emission but also a high endurance of reactive gases.

ECR PLASMA CATHODE

355

5.5.2.2 A bucket type ion source with ECR plasma cathodes. After the small Kaufman type source Matsubara eta l [357] developed a large bucket type source with an ion beam diameter of 115 mm utilizing three plasma cathodes arranged an equal distance from each other on a circle of 0 = 60 mm. The main discharge chamber 0 = 200 mm (see figure 5.5.4) is surrounded externally by 12 columns of Sm-Co magnets which form line cusp magnetic fields. This chamber wall serves as an anode, and is electrically insulated from the cathode. An ion beam of 115 mm diameter is extracted through three grid optics consisting of screen, accelerator and decelerator electrodes. The screen electrode has 861 apertures each measuring 2 mm in diameter. Typical characteristics are shown in figure 5.5.4(b) and (c). Figure 5.5.4(b) shows the measured results of the ion beam profile for the oxygen gas, at Vb = 1 kV and lb = 130 mA, which was measured at distance of 25 cm from the ion source by Faraday cups. The profile under the conventional filament type is also shown in the drawing for the sake of comparison. The two profiles are almost the same and a uniform profile was obtained over a large area. Thus, a broad-beam ion source without a filament, taking full advantage of the bucket type characteristics, can be realized by applying this type of plasma cathode. Another bucket type source has been described by Hakamata et al [380].

5.5.2.3 ER1S and MERIS with ECR cathodes. The IEF Laboratory of Paris XIII University has developed MP cathodes on two types of ion source [381], [382] schematically represented in figure 5.5.5: (i) an electrostatic reflex ion source (ERIS) and (ii) a magneto-electrostatic reflex ion source (MERIS). In both sources, the MP cathode has the form of a very compact capacitively loaded coaxial line fed by 2.45 GHz/50-125 W microwave power. A magnetic field B produced by small Sm-Co permanent magnets in a doughnut configuration was superimposed on the electromagnetic field. With Bres = 875 G close to the antenna edge, this field allows an upgraded ionization rate at rather low pressures (& 10“ 2 Torr). Different geometries of antennas were tested. Best results were obtained with a spear-head-shaped instead of a 16 mm diameter disc-shaped antenna. A gain of a factor of 2.5 was obtained when a dc negative voltage of 20-30 V was superimposed on the microwave power onto the antenna. This dc polarization could provide an ‘internal electronic tuning’ of the MP cathode which could advantageously replace the mechanical external tuning. A voltage discharge potential of 75-300 V is applied between the MP cathode chamber and either a rod anode or the cylindrical wall of the anodic chamber (MERIS).

356

SIMPLE MIRROR AND BUCKET ECRIS MICROWAVE (2.45 GHz)

GAS INLET\

CATHODE DISCHARGE PS.

in s u l a t o r

ANODE

(a)

CHAMBER PERM ANENT MAGNET

V b-r

ION EXTRACTION GRIDS

ION BEAM

CURRENT DENSITY ARBITRARY UNITS

RADIUS (cm) Oj ION BEAM CURRENT I ^130 mA ION ENERGV

1 keV

DISTANCE : 25 cm (FROM ION SOURCE) (b)

DISCHARGE CURRENT ^ (A) (C)

Figure 5.5.4 (a) A schematic view of a bucket type ion source with the MP cathode and the electrical connections. (b ) The 0 2 ion-beam profile measured at a distance of 25 cm from the ion source at Vb = 1.0 kV and Ib = 130 mA. (c) The ion beam current Ib against the discharge current Id at Vb = 1.0 kV and Vd — 200 and 150 V, with variation in 0 2 gas flow rate.

The oxygen ion beam intensity extracted by an accel/decel set of grids is represented in both cases, as a function of the discharge potential, in figure 5.5.5(c). The beam current density, in the range 2-5 mA cm-2 , has an homogeneity of ±5% over a 60 mm width of the 85 mm in diameter ion beam. The source produced as high as 90% atomic 0 + (or N+) ions. The anodic plasma potential being close to the rod anode potential (ERIS) or to the wall potential (MERIS), the ion bombardment and sputtering of chamber walls (ERIS) or of the MP cathode grid (ERIS and MERIS), is the principal

ECRIS FOR SPECIFIC WEAKLY CHARGED IONS cathodic cham ber

357

anodic chamber

W i

yj

I Aaticathode — * - | |

Pi

/d i

S

I

i l l i l l i l l

(d)

width (mm)

Figure 5.5.5 (a ), (b) Sketches of the ion sources with the microwave plasma cathode: (a) MERIS and (b ) ERIS (disc antenna and/or spear head antenna), (c) Ion beam current intensity against discharge voltage for ERIS (full lines) and MERIS (dotted lines), at respective oxygen pressures of 1.5 x 10~3 and 1.1 x 10-3 mbar, for two values of the microwave power, and at the extraction voltage of 1000 V. (d ) Ion beam profiles for ERIS and MERIS at a respective oxygen pressure of 1.5 x 10-3 and 1.1 x 10“3 mbar, at the discharge intensity of 1 A, and at the extraction voltage of 400 V.

source of contamination of the extracted ion beam (< 5%). When working with SF6 and CF4, one noticed that the presence of negative ions causes the operation to deteriorate.

5.6

5.6.1

ECRIS FOR SPECIFIC WEAKLY CHARGED IONS

Negative-ion ECRIS

Mori and Takagi [383], [384] have developed types of sputter source for positive and negative ions. The negative ions are produced at the surface of the metal which is located in xenon gas discharge in a cusp field, whereas the positive ions are generated by ionizing of sputtered neutral atoms in the ECR plasma. The RF power is introduced into the source through a special sputter target-waveguide

SIMPLE MIRROR AND BUCKET ECRIS

358

Waveguide to Coaxial Line Transformer

SmCo Magnet

Waveguide RF Choke Insulator

Extraction Electrode Electron suppression magnet(SmCo)

CM

Microwave * Converter (Sputter Target)

Figure 5.5.6 Negative-ion ECRIS (Blake IV) [384]. system (figure 5.5.6). Golovanivsky et al developed an H“ source called helios H- [385], the longitudinal B field of which is formed by SmCos disc magnets whose distance is smoothly regulated. The H " extraction is realized at 90° with respect to the B field, which enables the separation of H“ and electrons.

5.6.2

Polarized ion beam ECRIS— the general method [386]

5.6.2.1 Polarized atomic beam ECRIS. A typical atomic beam source employs four separate systems which have completely different physical functions but tightly intertwined engineering designs: (i)

Dissociators. Flowing H 2 or D 2 gas is dissociated by an R F discharge of 80-150 W. The resulting H or D atoms then emerge through a refrigerated nozzle into a series of differentially pumped vacuum chambers as a highly directed, near-supersonic jet beam directed down the axis of a series of sextupole magnets. Since the initial gas flow rate is high and since most of the emerging gas and all the defocused atoms must be pumped away to minimize intra-beam gas scattering, considerable recent effort has been expended to design large-capacity pumping systems.

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359

Figure 5.5.7 A polarized ion source with an optical pumped cell [389]. (7) ECR proton source, (2) superconducting solenoid, (3) optically pumped Rb cell, (4) deflection plates, (5) transition region, (6) ionizer cell, (7) ionizer solenoid, (5) quartz tube, (9) ECR cavity, (10) three grid extraction system, (77) boron-nitride end cups, (72) indium seals. (ii) A sextupole magnet system. Stern-Gerlach separation in the radially inhomogeneous, sextupole magnetic field focuses (defocuses) electronspin-up (spin-down) atoms. High-pole-tip-field, multi-element, permanent magnet sextupole systems are increasingly common. Individual sextupole elements have dimensions and axial placements matched to the velocity distribution of the atomic beam to focus the desired atoms selectively and optimally downstream. (iii) Radio frequency transition systems. Since nuclear rather than electron spin polarization is desired within the focused atomic beam, atomic transitions are implemented between selected hyperfine states. These require that the atomic beam pass through one or more carefully controlled axial regions of static and RF EM fields. Since the atomic beam has a significant velocity spread, the process of adiabatic fast passage is utilized to assure that the

360

SIMPLE MIRROR AND BUCKET ECRIS

transitions are affected for all available atoms in the beam. Recent designs have refined the hardware needed, especially for deuterium beams, so that a minimum number of separate transition units are needed. (iv) Ionizer systems. The oldest process produces polarized positive ions from polarized atoms in the focused H or D beam by ionizing collisions with fast electrons (H(pol) + e(fast) H+ (pol) + 2e). The electron bombardment ionizer (EB), which provides these electrons from a hot filament on the axis of a strong solenoidal magnetic field, is still used. However, recent sources more frequently employ an ECR plasma ionizer as proposed by Clegg and Schneider [386] (conversion of the polarized H+ or D+ beam produced to an H“ or D“ beam can subsequently be accomplished if needed using charge exchange in Cs or Na vapour; see section 5.1.8). 5.6.22 The ECR ionizer. The polarized atomic beam in these devices traverses the ECR plasma, which is confined axially by two sets of coils which create a tandem magnetic mirror field. Radial plasma confinement is provided by a weak multipolar (generally hexapolar) field created by a set of permanent magnets located symmetrically around the beam axis and at the centre of the axial mirror. This weak radial confinement is only required because, at the low operating pressures of ~ 10~6 mbar, the plasma density is insufficient to maintain a discharge simply with axial electron confinement. The 80-100 W of microwave power needed to maintain the plasma is fed in radially between the poles of the hexapole magnet. There is no unique choice of RF frequency. Although ready availability of inexpensive 2.45 GHz sources makes this an appealing choice, the corresponding magnetic field for ECR of 875 G means such systems are best suited only for deuterium operation. For hydrogen with its 507 G critical field, a larger magnetic field and thus a correspondingly higher RF frequency are needed to maintain full nuclear polarization of the atomic beam at the point of ionization. For this reason, several laboratories have selected variable-frequency RF sources which operate between 3 and 4 GHz. The polarization of ion beams obtained from ECR ionizers is slightly lower (~ 5%) than those obtained from EB ionizers. There are several likely reasons for this. Most probable is the larger radial extent of the ECR plasma. Background gas in the ionizer, from unpolarized hydrogen or deuterium atoms lost from the beam and recombined into molecules, can thus more easily re­ enter the plasma, become ionized and extracted and dilute the emerging beam polarization. Another contribution at radial positions off the beam axis comes from the known, non-axial components of the magnetic field which are created by both gradients in the axial field and radial mirror confining fields. However the ionization efficiency of ECR ionizers is somewhat higher than for EB ionizers, but, perhaps more important, for beam injection and acceleration in machines requiring bunching of the injected beam, is the ECR ionizer’s lower emerging beam energy spread [386].

ECRIS FOR SPECIFIC WEAKLY CHARGED IONS

361

In addition, it has been shown by Schmelzbach and Friedrich [387], [388] that the key to obtaining the largest beam polarization is opening up apertures at the ionizer exit to reduce the chance that un-ionized atomic beam impinges there. Once this is done, then an ~ 10 cm diameter quartz tube forming the actual ionization chamber vacuum wall can be placed between the hexapole and the ECR plasma without loss of the final beam polarization. The only pumping on the ionization region then is through the ends of this tube. This design provides significant technical advantages. The quartz is both transparent to RF and isolates internal high voltages used for beam extraction from the surroundings. Construction is thus much simpler, especially when only positive-ion beams are needed and when the only significantly high voltages required are inside this region. 5.6.2.3 Optically pumped polarized H~ sources [389]-[391]. Based on spin exchange polarization transfer in H-Rb collisions, this sophisticated technique using sapphire lasers for optical pumping of Rb vapour allows production of relatively large polarized H” beams. The characteristics depend on the performance of the primary ECR proton source, which must work with magnetic fields in excess of 10 kG (entailing the use of a 28 GHz, 1 kW power generator in order to maintain ECR conditions) (figure 5.5.7).

6 MIN- B ECRIS FOR HIGHLY CHARGED IONS

6.1

A BRIEF HISTORY OF THE DEVELOPMENT OF ECRIS FOR MULTIPLY CHARGED IONS

As already mentioned, it is always difficult for an author to write in an unbiased way about his own work. Therefore I decided to reproduce the history of ECRIS until 1986 as written by Jongen and Lyneis [14]. ‘The field of ECR ion sources has its roots in the plasma fusion developments in the late 1960s. The use of Electron Cyclotron Resonance Heating (ECRH) in plasma devices to produce high charge state ions was suggested in 1970 [326]. The first sources actually using the ECRH to produce multiply charged ions (MI) were reported in 1972 by Geller eta l [327] and in Germany by Wiesemann e ta l [392]. Geller’s MAFIOS source is illustrated in figure 5.1.10. Although these devices, which used solenoid magnetic mirror configurations, were capable of producing plasma densities of the order of 1 x 1012 cm-3 and keV electrons, typical operating pressures were 10-4 to 10-5 Torr, and the ion lifetimes were 10“4 s or less. This resulted in low charge state distributions (CSD) which, for example, peaked at N2+ for nitrogen and Ar2+ for argon. Similar sources were also developed later in Japan [393] and Russia [394].’ ‘A major step forward was made in 1974 when Geller transformed a large mirror device used for plasma research in Grenoble (CIRCE, 1973) [200], [395] into an extremely successful ion source, SUPERMAFIOS [12], [396], which is shown in figure 6.6.1 . Unlike the earlier ion sources using ECRH, SUPERMAFIOS used a hexapolar field. This produced a m in-# magnetic field configuration which stabilized the plasma against MHD instability. In addition, CIRCE was a two-stage device. A cold plasma was generated in a first stage, operating at a higher pressure of about 10-3 Torr. This cold plasma flowed along the magnetic field lines, feeding the main confinement stage, which operated at much lower pressure, about 10-6 Torr. These two features, plasma stabilization in a m in-5 field configuration and main stage operating at low neutral pressure, produced an enormous improvement in the lifetime of the ions 362

A BRIEF HISTORY OF THE DEVELOPMENT OF ECRIS

363

Microwaves 16 GHZ UHF cavity Gas injection Vacuum pumping

Vacuum pumping

Hot plasma

Hexapole field coils Ion extraction

Figure 6.1.1

The SUPERMAFIOS source: general set-up (1974) [12], [400].

in the source (~ 10~2 s) and thereby also in the CSD. Several variations of this ECR source were tested between 1974 and 1977: SUPERMAFIOS-A [397]— [399], TRIPLEMAFIOS [400], and SUPERMAFIOS-B [11], [405]. However, the basic features of the design remained unchanged and are still the basis for present source design.’ The transformation of CIRCE (a pulsed ECR mirror machine) with PRF ~ 25 kW, r ^ ^ O . l s and repetition rate less than 1 Hz) into SUPERMAFIOS was a difficult operation since in CIRCE the ECR surface intercepted the container walls. Therefore a closed ECR surface inside the chamber was only achieved after many cuts and trials. For this purpose, one utilized thin metallic sleeves covering the chamber walls to detect plasma impacts and then to modify the currents in the solenoidal and hexapolar coils. A closed ECR surface could only be achieved with currents exceeding the norms of the coils and roughly 3 MW of cw electrical power were necessary. Under these conditions, however, the SUPERMAFIOS could work in a continuous regime and the RF power could be reduced from 25 kW to less than 4 kW. However, the exorbitant power consumption incited the administration to cut the electricity in the building (1977)... but this negative decision became a positive incentive as it encouraged the author to utilize permanent magnets [401] (1978). ‘Thus the main drawback of SUPERMAFIOS was the 3-MW power consumed by the main stage. Different solutions were considered to reduce this power. The use of samarium cobalt (SmCo) permanent magnets was considered impractical because it was assumed that ECR sources should be as large as

364

MIN-B ECRIS FOR HIGHLY CHARGED IONS

Figure 6.1.2 MICROMAFIOS: the set-up of the first small ECRIS (1979) [405]. SUPERMAFIOS (diameter 30 cm, length 100 cm). Therefore, superconductivity was initially seen as the best way to solve this problem and large superconducting ECR sources were started in Louvain-la-Neuve by Jongen, in Karlsruhe by Bechtold, and in Jiilich by Beuscher [402]-[404].’ ‘In 1979, Geller transformed a reduced-scale permanent magnet model hexapole (studied by Pauthenet [405] and built in Louvain-la-Neuve) into a successful source of much smaller size (diameter 7 cm, length 30 cm) called MICROMAFIOS [401], [405]—[407], where in addition an iron plate reduced the power consumption of the 1st stage mirror field (figure 6.1.2). After development and simplification of the 1st stage it was renamed MINIMAFIOS [408], [409]. (A dozen MINIMAFIOS type sources have since been built.)’ ‘During the same period, small test sources using SmCo permanent magnet hexapoles were also built: PICOHISKA [410] in Karlsruhe and PRE-ISIS in Jiilich. A small fully superconducting source, ECREVETTE [411], was built in Louvain-la-Neuve and worked for a while. The first ECRIS linked to an accelerator was PICOHISKA (1981) at the Karlsruhe cyclotron.’ ‘In 1983, ECR source development began in the United States at Berkeley [412], [427] (with an octopole magnet) and Oak Ridge [413], followed by Michigan State University [414] and Argonne [415]. During 1984 and 1985, Geller demonstrated a new source, MINIMAFIOS-16 GHz, which, using higher microwave frequencies, could improve both the total extracted current and the charge state distribution of ECR sources [416], [417].’ Earlier (1982) a new type of 10 GHz ECRIS (called FERROMAFIOS) [439] was built in Grenoble, utilizing large quantities of iron for the magnetic

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365

configuration. This source was transformed into a very compact iron yoke ECRIS— with the help of Jacquot’s coaxial microwave injection (see section 2.4). Tested in 1984 and gradually optimized by Jacquot, who named this source CAPRICE, it became a very successful, high-performance source with modest electric power consumption (50 kW) [419]—[421]. More than a dozen CAPRICE type sources were built, and later 14 GHz CAPRICE sources with even higher performances were constructed in a small series [422]. In 1987, another type of ECRIS completely made of permanent magnets and iron parts called NEOMAFIOS was launched in Grenoble [428], [439] and gradually improved by Ludwig eta l [423]. Its electric power consumption could be reduced to less than 1 kW. An even smaller source called NANOGUN was developed later at Ganil by Sortais eta l [424]. Other different ECRIS were built all over the world (USA, Japan, Russia, Germany, Netherlands, Finland, India etc). Some of them exhibit original contributions but most of them derive from the above-cited prototypes which will be discussed in more detail in section 6.7. Recently, a dozen new ECRIS prototypes were developed in Japan. Those of the INS (Tokyo) have been described by Sekigushi et al; let us also mention the successful HYPER ECR at 14 GHz [425] and the contributions made by Nakagawa et al concerning the use of the ECR cathode and wall coating [426], [437], [438]. Incidentally, let us recall that, in 1975, the INTEREM device at Oak Ridge was another plasma fusion device converted into an ion source. It used a combination of solenoid and quadrupole coils to provide a min-R geometry. Although this device succeeded in producing small amounts of MI, it was so inefficient that the resulting currents were too small for practical use [429].

6.2

6.2.1

TH E STATUS O F UNDERSTANDING OF M IN - B ECRIS

G eneralities

Many review papers dealing with this topic have been published since 1975 ([11], [12], [14], [16], [109], [138]) and thus one can easily follow the evolution of the understanding. Let me emphasize the modern reviews by Kutner [399], Lyneis [430], Drentje [431], Melin [432] and Alton and Smithe [433] and the article by Sekiguchi [434] which present resumes of the most modern reasoning of the physics involved in the min-R ECRIS. Nevertheless, most of the old fundamental ideas have not changed at all. Let me quote them. The min-R provides a superior trap for ions and electrons. Since the ion confinement is considerably longer than in other magnetic structures, the conditions for MI production are radically improved. The min-R ECRIS provides electron heating through ECR processes which are not limited by electric arc potentials.

366

MIN-1? ECRIS FOR HIGHLY CHARGED IONS

The m in-# ECRIS yields relatively stable plasma where many instabilities are avoided. The two-stage plasma system generates ECR plasma streamers diffusing from a high-gas-pressure zone towards a low-gas pressure zone where hot electrons strip the ions, and where charge exchange is minimized. Thus hot cathodes are useless. All these properties are necessary for the MI production criteria (section 4.41) and early experiments showed that these properties were also sufficient. However, when the MI production in small ECRIS became routine (1980) accelerator people asked for higher ion charges, more ion current, better beam emittance etc. Though the low-cost m in-# ECRIS became a providential instrument for the accelerators, which allowed one to obtain immediate and substantial gain in particle energy, it was logically decided to improve the routine performance. A first impressive improvement is always obtained by reducing the neutral gas flow (i.e. the charge exchanges) in the system. But gas rarefaction decreases first-step ionizations which induces the creation of electrons, and so one reaches a threshold of electron starvation. Under these conditions, better electron confinement and/or artificial electron donors should allow supplementary improvements. Better confinement was obtained by systematically improving the axial and radial mirror ratios in the m in-# structure. However, in fact, three inexpensive a priori empirical findings, improved the performance remarkably. (i)

gas mixing, first systematically studied in Drentje’s group at Groningen [295], [445] and now utilized everywhere, but not yet completely understood; (ii) the wall coating, mainly observed and developed in Grenoble (1986) [439], Berkeley (1986) [440] and Riken (1992) [441] and (iii) the suppression of the first ECR stage obtained by utilizing independent electron injectors, for instance biased probes (Grenoble 1988), electron guns (LBL 1990) and ECR cathodes (Riken 1990). This chapter is an attempt to give an overview of the past and present m in-# ECRIS activity devoted to the production of highly charged ions: it therefore recalls experimental and theoretical efforts, technology, performances, plans and prospects as well. It gives the modern status of understanding of the ECRIS behaviour, both the current thinking on how they operate and the corresponding experimental evidence. Most of the explanations are based on arguments developed in the previous chapters and should not surprise the reader. However, as in the present section we can only summarize the arguments already considered, we suggest a second reading of those chapters. Nevertheless, the present situation, where plasma physics (section 1.3), atomic physics (section 1.4), particle dynamics (section 1.5) and surface physics (section 3.2) are simultaneously involved, makes data interpretation somewhat confusing. The statistical nature of plasmas and moreover the complexity of anisotropic

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367

hot-electron plasma (section 1.3) far from thermodynamical equilibrium, does not facilitate understanding. 6.2.2

A modern analysis of the plasma containment and electron heating

6.2.2.1 The mechanisms o f electron and ion confinement. The hot-electron population is created by interaction with RF waves in the ECR. The resonance yields electron anisotropy (v±/v/\\ > 1). In addition these electrons are nearly collisionless (see section 1.3 and 1.4). Hence these electrons are easily confined. They move back and forth along the magnetic field lines between mirrors making many bounces and so generate by space charge effects the confinement of cold ions (potential dip A0, section 1.6). Thus the system has the property of confining a neutral plasma. Its main ingredients are: (i) the min-B magnetic configuration, (ii) the heating of electrons by RF waves at the cyclotron frequency, i.e. at the magnetic field such that COce = ------ = (Orf me

(6.2.1)

(iii) the necessary sources of electrons, which allow the hot- and cold-electron density to build up in the trap, (iv) a small ambipolar field near the wall repels the cold collisional electrons which are easily expelled into the loss cone (see section 1.6). As compared to EBIS, the ECRIS do not have direct control of parameters such as electron energy and ion confinement; these are only indirectly controlled by external knobs, limited in number and not univocal, such as RF power, pressure, magnetic field and RF frequency. The price to pay for the multi-use of the same electrons for enhancing the ionization in ECRIS with respect to EBIS is the electron confinement, but its tremendous advantage is precisely the electron confinement enabling low-electron-power fluxes to accumulate and to work with reduced power injection (see section 4.5). 6.2.2.2 A simplified model o f ECR mechanisms (figure 6.2.1). Let us discard complicated EM wave propagation in underdense plasma. Then the ECR mechanism can be summarized briefly as follows: consider an empty box of undefined shape filled with microwave power (e.g. with a frequency co = 10 GHz and wavelength k = 3 cm). The box can be considered as a multi-mode cavity if its dimensions are large with respect to the wavelength. All the highperformance ECRIS for MI production utilize multi-mode cavity coupling (see section 2.4). On immersing the box in a min-B structure for which the magnetic field along the centre line is between Bmax = 1 T and Bmin = 0.2 T there must exist a magnetic surface with a spherical or egg-like shape where the field strength B ecr = 0-36 T (Bmax is the field on the closed magnetic surface— the walls are not intercepted— with the highest field strength and Bmin is the

368

MIN-2? ECRIS FOR HIGHLY CHARGED IONS B g auss ( H exa p o le a lo n e )

B gauss a xial

( S o le n o id s alone )

A B m ax

B m ax

360C Z

0 r a d iu s

B imax 3600 G = B e c r

Figure 6.2.1

Min-B ECRIS principal elements.

minimum field at the centre of the box). This so-called ECR surface ( B E c r ) gives a gyrofrequency of an electron that is 10 GHz, equal to the injector microwave frequency. In high-performance min-B ECRIS, mirror ratios of B m a x / B m in ~ 5 and Bmax/ B e c r ~ 3 are provided in order to confine the ECR heated plasma. Some kind of ECR necessarily occurs in such a multi-mode cavity because there is always a component of the electric field of the waves that is perpendicular to the magnetic field lines. The electrons thereby gain mainly perpendicular momentum 6.2.2.3 Electron energies acquired in the containment system. In section 2.3, we considered the case of one single-electron passage as well as the case when electrons in the magnetic well pass many times through the ECR surface where they can either be accelerated or decelerated according to their phase. So we know that the electrons undergo global ‘stochastic’ heating during the many passages. Hence, at least one given electron population can become hot and rapidly reach the kiloelectronvolt range whereas another population remains thermal. Thus it is clear that the electron velocity distribution is not a Maxwellian one. However, a precise description of all the possible mechanisms of the heating remains as yet impossible. 6.2.2.4 Ambipolar ES potentials in the containment system. These ES potentials are a by-product of the magnetic confinement of the electrons.

THE STATUS OF UNDERSTANDING OF MIN-B ECRIS

369

Figure 6.2.2 The potential profile along the axis of a min-2? ECRIS and transport line for ISOLMAFIOS. Atraps the cold ions and (j>reduces the cold electron losses. Actually the plasma potential along the axis of the ECRIS confinement region is observed to be a positive potential hill 0 with respect to the walls, the negative dip A 0 being presumably located at the centre, i.e. on the top of this hill. This (j) potential has to be compared with that of a sheath between a wall and a plasma (see section 1.3). The colder electrons of ECRIS leave the plasma faster than the ions due to collisional loss-cone diffusion. The potential 0 appears in order to accelerate the ions and to retard the electrons, so that the total current at the walls or near the extraction hole is zero. The retro-injection of decelerated ions into the ES trap of ISOLMAFIOS supports this image of the ES potential profiles (see section 6.5.2.1) (figure 6.2.2). A slow ion passes the positive potential hill (f) and is trapped in the negative dip A (p. The plasma potential

109 cm-3 s. Since the electron density in ECR plasmas is usually 10i2 cm "3 or less one requires ion lifetimes of more than 10” 3 s. ES potential traps created inside min-B electron confinement systems provide such ion lifetimes (see sections 4.3 and 4.9.10). 62.3.2 Computer codes [2751 [277], [278], [284], [292]-[294]. Computer codes based on long confinement concepts have been developed which incorporate the cross-sections for ionization, charge exchange and other atomic physics processes involved (section 4.8.4). These models usually require that the plasma density, neutral density, confinement time, and electron temperatures be specified. With a reasonable set of parameters these codes can reproduce measured charge state distributions. From these models it is clear that for high charge states the sources should run at low neutral pressures and high plasma densities, with sufficiently high electron temperatures and long ion confinement times in the ES potential dip A. However these arguments were already well known before the elaboration of the computer codes. The only new results stem from the possible ion cooling in light-gas mixture plasma which improves the ion confinement in the ES trap in steady state (section 4.8.5). 6.2.4

Auxiliary electron donors to avoid electron starvation

Electron starvation issues (see section 3.4) are probably important in min-R ECRIS and were emphasized as early as 1986 [439]. Supplying auxiliary electrons to the magnetic trap is then necessary to obtain an electron density large enough for efficient ionization of the very low-gas-pressure plasma of the ECRIS. Remarkable improvements were achieved using different methods, either from external sources or from internal sources. 6.2.4.1 External electron donors. (i) The first-stage ECR discharge is the most classical donor. In the early sources it was considered to be more important for the singly charged ion supply to the main stage than for electron supply; recently, the electron supply has been proven to be the essential role of the first stage [435], [437], [481] (figure 6.2.3). (ii) The ECR plasma cathode developed at Riken [437], [438] is actually a first stage with an electrode for electron extraction at low energy and injection into the main stage. (iii) A low-voltage electron gun was used on the AECR source [435] [436]; the effect on the performance was quite impressive, but the gun cathode has a limited lifetime. (In my opinion, it is a mistake to re-introduce hot-ephemeral cathodes into an ECRIS).

372

M IN -B ECRIS FOR HIGHLY CHARGED IONS

Charge state (Q)

Figure 6.2.3 The influence of first-stage bias on performance. A, electron supply; B, plasma supply; C, ion supply and Q, charge of nitrogen ions [481]. 6.2.4.2 Internal electron donors. (i) Multi-ionization of neutral atoms by electron impacts is of course, a permament source of new cold electrons; however it cannot sustain by itself the total electron density in very low-gas-pressure systems. (ii) Convenient coatings having a high yield for secondary electrons on the ECRIS walls, e.g. Th 0 2 [439], Si0 2 [440], or AI2 O 3 [441], prove to be very efficient: however under the impact of plasma particles these coatings need to be regenerated from time to time. (iii) A negatively biased disc or probe reduces the plasma electron losses and/or provides new electrons from secondary emission of impinging plasma particles [265]. Recent data show that the internal sources may have an interesting effect of lowering the plasma potential [434]. The permanent refuelling of rather cold electrons in the ECRIS by these electron donors compensates for the overall electron losses. 6.2.5

Empirical improvements in m in-B ECRIS

6.2.5.1 Light gas mixing effects and ‘Drentje’s ’ oxygen anomaly [295], [445], [446]. The discovery of the ‘gas mixing’ phenomenon in a min-B ECRIS by Drentje et al [445] in 1983 resulted in immediate application by many users, for obvious reasons: more current for high-charge-state ions, usually at a lower RF power level. The beneficial effect is that the intensity for a given ionic type (e.g. argon) increases substantially when a lighter gas (e.g. helium or oxygen) is mixed into the plasma in large amounts (for example 90% oxygen, 10% argon). It appears however that not all light gases are suitable, i.e. hydrogen is usually a ‘bad’ mixing gas. Thus, a necessary but not sufficient condition for a gas to behave as a good mixer is that its atomic number is smaller than that of the ionic species to be used, A mix < Abeam (figure 6.2.4).

THE STATUS OF UNDERSTANDING OF MIN-B ECRIS

| Mixing e ffe c ts [

373

M m 1 6 ,6 G H z X e n o n : lo g I + vs (q) © X e 50%

20 50%

P= 0/5KW

© X e 20%

20 8 0 %

P ^ K W

© Xe

20 95%

P=2/7KW

5%

Figure 6.2.4 Oxygen-xenon mixing effects [439].

Many authors attempted to explain the observations, usually in a qualitative manner. A somewhat quantitative explanation was given in [439], based on the arguments of averaged ionic lifetimes being inversely proportional to the average charge state in the plasma. By adding a lighter component (hence with lower charges), the average ion charge is reduced, and therefore the average ambipolar losses are reduced and the average lifetime increased, due to a better confinement. This results in a shift in the CSD towards higher charges for the heavier ion species. Later Delaunay (1992) showed that the ionization term may also increase through gas mixing [285]. Note also a possible decrease of resonant charge exchange (figure 1.4.15). Measurements of the energy spread of beams extracted from a pure plasma as compared with those of a ‘mixed’ plasma by Meyer [448] gave rise to a different explanation formulated by Antaya [283]. In Spitzer collisions of ions with different masses, there will be a net transfer of kinetic energy from the heavier to the lighter component. Since inside the plasma many of these collisions occur, the result is that the heavier components are ‘cooled’ by the lighter species. Because of the reduced kinetic energy, the heavier component will be better confined, hence it will be exposed for longer to electron bombardment, giving a CSD peaked to higher charges. This argument is now strengthened by Shirkov’s theory (see section 4.8.5.1) To decide whether the beneficial effect of gas mixing is due to a charge effect or to a mass effect, Drentje performed a series of precise measurements with a gas mixture consisting of three stable

374

MIN-B ECRIS FOR HIGHLY CHARGED IONS

oxygen isotopes (masses A = 18, 17 and 16). Here, the atomic properties of the components are exactly the same, so there will be no difference in terms of ionization rates and average charge state. The results (reported at the Oak Ridge ECR workshop (1990)) were at first glance puzzling for the experts. The CSD for the isotopes were systematically different for the various isotopes in the sense that the heavier the isotope, the more the CSD was peaked to higher charges; this effect was called the ‘oxygen anomaly’. These observations would favour the explanation based on ‘ion cooling’. Here, the lighter isotope, in spite of its slightly lower mass, could still act like a coolant because of the great number of collisions. Drentje’s observations were confirmed in a different ECRIS: measurements were made, where a ‘regular’ mixing gas such as helium was added to the isotopic mixture too. When the amount of helium was increased, the observed isotopic anomaly disappeared. In fact, the output of the lower-mass isotopes increased. Again in terms of the qualitative model, in this situation all three oxygen components are effectively cooled by the helium ions. 6.2.5.2 Wall coating effects. In 1986, Ludwig observed that the performance of FERROMAFIOS improved outstandingly when Th 0 2 was utilized in the source. Not only was lower RF power needed but also highly charged ions with unusually high currents were obtained [439]. At the same time after the operation of ECRIS at LBL with silicon, Lyneis demonstrated that the performance of the source for high charge states had significantly improved. This effect was due to a wall coating with SiC>2 delivering secondary electrons to the second-stage plasma [440]. As seen in section 3.2.4 it is clear that the wall conditions are an important parameter and many chemical wall coatings may be useful electron donors. The secondary electrons can either return towards the central ECR plasma or neutralize ions near the walls and subsequently reduce the ambipolar electron drain [439]. In both cases they improve the electron density inside the ECR plasma. Due to a plausible change of the electron velocity distribution, the possibility of suppression of micro-instabilities has also been envisaged. Other popular coatings were obtained with AI2 O 3 [441], SiH 4 , Mb, W, Mg 0 2 etc. Figure 6.2.5 shows the wall coating effect in the 10 GHz Riken ECRIS [475]. 6.2.5.3 Briand’s biased probes. A very simple reliable and reproducible electron donor was invented by Briand. He found that an improved ion charge performance can be obtained by simply using a negatively (~ —300 V) biased disc or cylinder located in the space of the first stage. This probe reflects electrons back to the second stage and attracts ions, which produce secondary electrons, which are accelerated into the second-stage plasma [265]. At Riken a similar biased probe was positioned inside the first stage to push electrons to the second stage, so allowing a reduction of the pressure in the second stage by a factor of two. Nowadays in many ECRIS one just replaces the first ECR stage by a biased probe [442]—[444], [470], [487] (figure 6.7.1(B)). Let us emphasize

THE STATUS OF UNDERSTANDING OF MIN-J3 ECRIS

375

Charge State

Figure 6.2.5 Characteristics with AI2 O3 wall coating • and without O [438].

0

500

1000

1500 2000

2500

300 0

Bias vottage (Vott)

Figure 6.2.6 The effect of the bias probe voltage on beam intensities [487]. that optimum bias voltage acts not only on the secondary emission but also on the energy of the injected secondary electrons. Figure 6.2.6 shows the bias potential effect in the superconducting MSU ECRIS [487]. Figure 6.2.7 shows the electron donors effects in the Riken ECRIS. 6.2.5.4 Comments on the so-called ‘empirical’ improvements. In the process of voluntarily reducing the charge exchange losses through neutral atom rarefaction, one also reduces the ionization collisions in the residual gas and subsequently the liberation of free electrons issuing from ionizations (note that a strong reduction of 1+ ions also hinders further step by step ionizations from occurring). Thus, the concept of electron starvation of the plasma becomes very plausible. Under these conditions biased probes, wall coatings and electron guns are not empirical methods; on the contrary these empirical solutions are the most rational and direct remedies against electron starvation. Though gas mixing also acts against electron starvation [432], ion cooling has probably an even more beneficial effect [277], [283].

376

MIN-B ECRIS FOR HIGHLY CHARGED IONS

Charge State

Figure 6.2.7 Effects of first stage bias, wall coating and both on the Riken ECRIS, obtained by Nakagawa. Argon beams: O—no bias, A—biased electrode, □ —AI2 O3 coating + biased electrode [475]. 62.5.5 The two-frequency heating. According to Lyneis and Xie [449] the LBL advanced electron cyclotron resonance (AECR) ion source, which is a single-stage source designed to operate at 14 GHz alone (single-frequency heating), is enhanced by heating the plasma simultaneously with microwaves of 10 and 14 GHz (two-ffequency heating). Production of high-charge-state ions has been increased by a factor of two to five or higher for the very heavy ions, as compared to the case of single-frequency heating. Plasma stability is improved and the ion charge state distribution shifts to higher charge state, which indicates an increase in the n er,- product of the ECR plasma. With twofrequency heating, the source can produce more than 109 pps of fully stripped argon and exceptionally high-charge-state ion beams of bismuth and uranium have also been produced by the source. A method using several frequencies surely increases the stochasticity (see section 2.3.6). It also makes the heating more distributed (several ECR surfaces). Under these conditions one can think that the local gradients of temperature and density are weakened, which in turn hinders the onset of some drift instabilities (see section 1.3.7) and improves the performance (table 6.2.1) (figure 6.2.8).

6.3

6.3.1

THE MAGNETIC STRUCTURE IN MODERN M IN-B ECRIS

Generalities

Wolf from GSI recently reviewed many technical aspects, comparative results and designs. In his book [6] one can find much practical advice and numerous data related to topics which are not always mentioned in this book.

THE MAGNETIC STRUCTURE IN MODERN MIN-R ECRIS

Plasma Chamber

377

Extraction

Figure 6.2.8 A schematic view of two-frequency ECR heating in the LBL ECRIS. Variations between the sources arise from the types of material used to construct the structure comprising solenoids S and hexapoles H (made of copper wire c, superconductors sc, permanent magnets p and iron yokes i). All the modern sources illustrated in this chapter can be designated as follows: (i) (ii) (iii) (iv)

S.sc + H.sc; S.c + H.p; S.c + H.p + i; S.p + H.p.

Group (iii) is presently very popular because it allows compact sources with a smaller power consumption than (ii). Type (i) is the most promising in spite of its larger size and higher cost because it can reach the highest values of co and Bmax whereas (iv) is limited to 0.8 T by the properties of currently available (SmCo 2 or NdFeB) rare-earth magnets. However, type (iv) gives respectable performance with very small power consumption, thus facilitating installation on high-voltage platforms. Note that NdFeB magnets operate at temperatures T < 60 °C. Therefore very efficient cooling systems are required.

6.3.2

The axial field

When the axial magnetic field is generated by sets of solenoid coils one generally uses iron yokes to reduce power consumption of the coils. In addition, without an iron yoke, ferromagnetic materials in the vicinity of the ion source may also influence the extracted ion beam by steering effects. The power consumption of the coils for a typical field of Bmax ^ 1 T is between 100 kW (for type (ii)) and 30 kW (for type (iii)). In figure 6.7.2 we show the CAPRICE ECR with iron yoke and axial magnetic

378

MIN-J3 ECRIS FOR HIGHLY CHARGED IONS

Table 6.2.1 Results of AECR source with two-frequency heating and comparison with the best results with single-frequency heating. All ion beams are extracted at 10 kV extraction voltage and through an 8 mm aperture. Currents are measured with the Faraday cup biased at 150 V to suppress the secondary electrons [449]. Ar (e/zA) Q

SF

TF5

13 14 16 17 18

53 24 2.5

59 33 4.0 ^ 0 .1 6 c ^ 0.005c

25 26 28 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 46

86 Kr (e/z A) SF

5.5 3.0 0.6

TF~

136Xe (e/z A) SF

TF

Bi (e/z A) SF

TF

238U (e/z A) SF

TF

8.3 6.0 1.0 5.0 1.5 0.5 0.15

d

6.0 2.5 1.5 0.5 0.2 0.05

d

d d d

8.4 6.0 3.0 2.2 1.3 0.5 0.25

12.1 10.2 d 6.5 5.0 3.2 d 1.8 1.1 d d 0.24 0.08

d

d

3.6 3.8 3.0 2.4 1.6 1.2 0.7

11 12 d 10 8.7 7.1 5.4 3.7 d 1.5 1.0 0.5

a Best results with single-frequency (14 GHz) heating. b Preliminary results with two-frequency (14 + 10 GHz) heating. c Measured with small slits (6 mm). Normal slit opening is 20 mm for argon ions. d Mixed ion species.

field coils. A similar design is shown in figure 6.7.3 representing the ECR4 model. Sources with iron yokes tend to have higher mirror ratios due to the sharp maxima generated by the ferromagnetic material. With NdFeB magnets, it is possible to generate the necessary axial mirror fields. This reduces the power consumption even more. The disadvantage of permanent magnets is the ‘frozen’ field structure which does not allow further tuning of the plasma by local changes of magnetic field strength (type (iv)).

THE MAGNETIC STRUCTURE IN MODERN MIN-B ECRIS

379

Figure 6.3.1 Loss surfaces for octopoles, hexapoles and quadrupoles and corresponding radial fields Br. • are the extraction holes.

Figure 6.3.2 The open hexapole structure. 6.3.3

The radial field

For the stable confinement of the plasma magnetic multipoles are used. The higher the order of the multipole the larger the loss area at both ends and thus the area usable for ion extraction. A quadrupole with a superimposed mirror field has just a thin loss line at the ends making ion extraction difficult. A hexapole leaves a triangle and an octupole a square as shown in figure 6.3.1. The order of the multipole is generally limited by the field strength necessary for a closed ECR resonance zone. The hexapole configuration is preferred in most modern min-B ECRIS. Nowadays most of the multipoles are made of NdFeB permanent magnets with a surface field strength of more than 0.8 T. There are two designs for the multipole, a closed structure, which allows the full volume to be filled with magnet material, resulting in higher fields, and an open structure shown in figure 6.3.2, which allows radial access. Figure 6.3.3 shows a cross-sectional view of the magnet orientation for a hexapole using the full volume. The first theoretical studies of the magnetic structures of an ECRIS were

380

MIN-B ECRIS FOR HIGHLY CHARGED IONS

performed analytically by Pauthenet in 1978 [128] and reconsidered by Sortais [129]. Halbach’s structures are now frequently utilized in sources [127]. In order to visualize the complex B field in the ECRIS a spatial computer code was studied recently by Biri and Vamosi [450]. At present, numerical codes are utilized for the elaboration of min-2? structures. Let us mention among them the Poisson group of codes [433]. Finally, let us recall that in modern superconducting ECRIS both the mirror coils and the hexapole coils are made of superconductors immersed in high-tech cryostats. In this case, mechanical anchoring and quenching issues give the upper limits. Generally, the current in the hexapole bars is the most limited.

6.4

HIGHLY CHARGED METAL IONS PRODUCTION IN M IN-B ECRIS

The efficient confinement of energetic electrons in min-B ECRIS allows a specific evaporation method for all refractory materials: the insertion technique (see section 6.4.3). Otherwise, for the production of ions from non-volatile materials the following classical methods can be applied: gaseous compounds techniques; oven techniques and wall recycling techniques. In an effort to explore new evaporation methods, arc sputtering and laser ablation techniques are presently being developed in Argonne National Laboratory [451] and Lanzeou [452].

METAL IONS PRODUCTION IN MIN -B ECRIS

381

Table 6.4.1 High vapour pressure metalloorganic compounds [161].

6.4.1

Needed element

Compound

Boiling point (°C)

Cr Fe Ni Ga Ge Sn Pb Bi

Cr(CO)5 Fe(CO)5 Ni(CO)4 Ga(CH3)3 Ge(CH3)3 Sn(CH3)4 Pb(CH3)4 Bi(CH3)3

420 105 43 56 43 78 110 110

Gaseous com pounds

The compound gas can serve as a mixing gas if it contains a light element. H2S and S 0 2 for example have been used for sulfur [439], SiFL* for silicon [453] and UF6 for uranium [454] (but there are better methods). A list of metallo-organic volatile compounds is given in table 6.4.1 [455]. As specified in [6 ] special care has to be taken using aggressive compounds to prevent damage of the /x-wave window, the O-rings and the other parts of the source. Sometimes an admixture of an additional element which binds the corrosive element in the source will overcome these problems. This was demonstrated in the case of a potassium beam from KC1 by addition of calcium where the calcium binds the chlorine and just a small amount of free chlorine was found in the spectra [456]. 6.4.2

Oven techniques

Low- and high-temperature ovens [14], [456], [457] are utilized. Depending on the design of an ECR ion source an oven can be mounted to feed the second stage radially or has to be positioned axially in front of the first stage if there is one. In the first case the oven design does not cause any problems since there is enough space available with open hexapole structures and the oven can be positioned in a way which does not need special care to keep the boiling liquid in it (figures 6.4.1 and 6.4.2). Axial ovens have to be of compact design due to the limited space available on the injector side of the ion source. For ECR4 at Ganil a micro-oven just 6 mm in diameter has been developed for lead and other materials (figure 6.4.3(a)) which can reach temperatures up to 1500 °C [458]. The centre pipe has a bore of just 1.5 mm and holds the liquid by capillary forces if the material combination is selected properly. A larger oven has been developed in Grenoble with an outer diameter of 15 mm and an inner bore of 6 mm for a crucible with 3.4 x 20 mm 2 usable space for the material to be evaporated [459]. If the ovens are designed

382

M IN -B ECRIS FOR HIGHLY CHARGED IONS Hexapole

Figure 6.4.1

A hexapole with a vertical oven.

" C u r r e n t in

' Cool ed c o p p e r end d a m p - T a n t a l u m cr uci bl e

- Charge

- C u r r e n t ou t

Figure 6.4.2

A miniaturized vertical oven.

in a way such that they can be moved in and out through a vacuum lock the vacuum in the second stage stays undisturbed on necessary refilling of the oven and long-term operation over weeks is possible. An oven similar to the Grenoble design which can be introduced into the ion source through an air lock is shown in figure 6.4.3(b). Other oven developments have been made at MSU and Argonne. The temperature control is performed with a thermocouple and a feed-back circuit which has a good response time since the mass of the oven can be small due to the low material consumption of approximately 1 mg h_1. For high temperatures 1500 °C) the control has to be performed optically on axis through the extraction hole or in radial designs through a window opposite the high-temperature oven. Table 6.4.2 summarizes the ion yield of different charge states for various elements using oven techniques [6 ]. The usual oven designs give a temperature range up to 1000 °C or 1500 °C. Higher temperatures need good heat-shielding arrangements of ovens heated by dc flow or by electron bombardment of high-temperature metal or graphite crucibles. Thus, for the production of ions from refractory materials oven

METAL IONS PRODUCTION IN M IN -B ECRIS

1 2 3

1

2

Power supply R e f l e c t o r tube Insulator

3

4

5

4 H e a ti n g system 5 Insulator 6 E v a p o r a t o r tube

0 1 6 mm

014mm4

6

1

Ta-cylinder

2

Crucible

5 Insulator

3

BN-heater

6 El ec. c o n n e c t i o n

Figure 6.4.3

383

026mm

W-wire

Movable coaxial ovens [6], [458].

techniques are not convenient but otherwise they are the most efficient and popular methods and they yield the highest possible charge states of metal ions as compared with other techniques (figure 6.4.4). 6.4.3

The insertion technique [460]-[464]

This technique has been mainly developed since 1981 by the Grenoble team with the MINIMAFIOS and CAPRICE sources (Jacquot alone studied some 30 different elements) and eventually with the NEOMAFIOS by Ludwig et al [423] and a RIKEN team [462]; completely stripped A l13+ ions were produced as early as 1983 [463]. 6.4.3.1 The basic principle. The ECR yields energetic plasma electrons and, hence, metal vaporization becomes available through electron bombardment. Thus, at steady state, the available heating power can be a fraction of the input RF power absorbed in the ECRIS (operating with a support gas). For vaporization one has to move the sample into a plasma zone where the density and energy of the electrons is adequate. For low-temperature vaporization

384

M IN -B ECRIS FOR HIGHLY CHARGED IONS

in

5

I I II I I I

x> cu

II

3

II I I I II

II in in