Research and application of pulsed plasma accelerators: monograph 9786010431904

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AL-FARABI KAZAKH NATIONAL UNIVERSITY

A. M. Zhukeshov

RESEARCH AND APPLICATION OF PULSED PLASMA ACCELERATORS Monograph

Almaty «Kazakh University» 2018

UDC 536 BBK 22.3 Z 62 Recommended for publication by the Academic Council (Protocol №4 dated by 27.11.2017) and the decision of the Editorial-Publishing Council of the al-Faraby Kazakh National University (Protocol №3 dated by 07.12.2017) Reviewer: Higher doc. Phys. and Math. Sci., prof. K.А. Zhaksybekova Higher doc. Phys. and Math. Sci., academician of NANS B.М. Ibraev Higher doc. Phys. and Math. Sci., Senior Researcher V.Ya. Nikulin

Z 62

Zhukeshov A.M. Research and application of pulsed plasma accelerators: monograph / A. M. Zhukeshov. – Almaty: Kazakh University, 2018. – 130 p. ISBN 978-601-04-3190-4

The monograph is devoted to experimental investigation of physical processes of formation and acceleration of the plasma flow in high-power pulsed discharge occurring in the powerful coaxial accelerator, development of plasma diagnostics methods for pulsed plasma, the study of the interactions of the accelerated plasma fluxes with material surfaces, as well as the theoretical substantiation of the observed physical phenomena.

UDC 536 BBK 22.3 ISBN 978-601-04-3190-4

© Zhukeshov A.M., 2018 © Al-Farabi KazNU, 2018

INTRODUCTION 

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evelopment of plasma sources moving at speeds 10-103 km/h, which corresponds to the kinetic energy of ions from 10 to 104-105 eV, is of great interest for various problems of science and technology. A special class of such devices are pulsed plasma accelerators, which are based on the conversion of electromagnetic energy storage in the energy of the moving plasma flow The first ICS was developed in the 1950s and currently find application as plasma sources for fusion research in technology for cleaning surfaces, applying metal films, of hardening, as well as in research on ionospheric aerodynamics, and experimental astrophysics (simulation of space phenomena) in space as electric propulsion. A promising application is the creation of nanomaterials by using ISP. Progress in the development of the IPU largely depends on the development of main ideas about ongoing physical processes. This task became extremely difficult, despite the relative ease of the accelerator structures. One of the first theoretical models proposed for calculation of integral characteristics of the IPU, is the electrodynamic model of L. A. Artsimovich. In this model the plasma is considered as a moving element of an electric circuit. With its help, accurately calculated the parameters of the discharge circuit. However, the electrodynamic model does not give an adequate description of the main physical processes occurring in the ISP. Significant progress in developing the fundamental understanding of the physical processes in pulsed accelerators achieved by modeling the continuous environment that are based on the equations of magnetic hydrodynamics (A.I. Morozov, K.V. Brushlinskii, D., Potter, etc.). The use of MHD models allowed us to calculate the structure of plasma formation: the density distribution, velocity, temperature and magnetic field along the direction of motion. It was found that the nature of the plasma flow is determined by the parameter exchange, which is expressed by the ratio of the discharge current to the flow of the working substance. The significant influence of Hall effect on the plasma flow along the electrodes, which manifests itself in the slip of streamlines along the anode of the accelerator, 3

which leads to the so-called "crisis of power". The current crisis significantly limits the maximum achievable flow rate. Experimental investigations of plasma accelerators has allowed to establish that for gas densities of more than 1016 cm-3 in accordance with an MHD model in the accelerator is formed of the thin current layer, through which flows the entire discharge current (a model of the "snow plow"). Current layer has a clear ionization front, which may fluctuate as a result of development of instabilities. However, the lower initial gas density and pulse overlap the current layer in the coaxial accelerator becomes transparent and remains current layer in the plasma with density equal to the initial density of the gas. In these conditions, the flow structure changes significantly, and almost it violates conditions of applicability of the MHD approximation. Thus, if for large densities of the MHD approximation is in a good agreement with the experimental facts, for plasma low-density physically complete model has not yet been created. At low densities the time of ion-electron collisions is of the order of the time of flight and there are a number of phenomena that do not fit into the framework of hydrodynamic approximations. One of the most important and interesting experimental facts is the discovery of the mode of the particle (the socalled "fast mode") in the plasma accelerators with pulsed gas inlet (D. Marshall, A A. Kalmykov). Under certain conditions (the presence of a density gradient along the electrodes, etc.) in a pulsed plasma accelerators of the observed acceleration of ions up to tens and hundreds keV. This effect is associated with the turbulent heating of plasma and acceleration of ions on small-scale instabilities excited by the discharge current. Since the mechanism of acceleration are fundamental physical effects, in principle, it can be implemented in any plasma accelerator. For example, the method of acceleration of elementary particles by using plasma in the so-called Wake electric field (which is created by the laser beam in the plasma) was proposed in 1979 by G.D. Dawson, University of California, Los Angeles, and the first experiment was set up in 1993, H Joshi. Currently actively attempts of creation of compact particle accelerators at GeV in the capillary plasma channels. All this suggests that the ability of plasma accelerators have not yet been exhausted. In later studies it was shown that in high-current plasma systems can be observed, the structures that play a role in the acceleration. The 4

analysis of the works on the electrical discharges shows that the observed plasma structure, which manifests itself in the form of striations, threads, hot spots, strips, or channels, correlation with fluctuations of the signals on the waveform of the current and the applied voltage, the generation of electromagnetic radiation and streams of fast ions and electrons. Thus, physical processes in plasma accelerators is incredibly diverse, and depend substantially on the initial gas density and its distribution. Insufficiently investigated the processes of formation and plasma acceleration at low density from 1016 cm-3 and below, where a possible realization of the maximum energy flow settings. Not quite clear what the role of such effects as "anomalous conduction" and "fast mode" in the overall picture of the formation of the plasma flow, and whether they occur in the absence of a density gradient along the electrodes, which is characteristic of the mode of operation of the IPU with a solid fill. In addition, requires a detailed analysis and synthesis of the mechanism of plasma acceleration in a coaxial pulsed accelerators. Today there was a misconception that this setup is already understood. It is related to utilitarian notions of the processes taking place in the ISP, and the lack of adequate theory that can describe the whole range of observed regularities. Insufficiently studied direction in the development of ICS is the study of regions of compression flow, as this effect can be used to solve a number of physical and technological problems, which require high power density. Another actual problem of plasma physics is the study of stability of materials of the first wall, divertor and other components of fusion reactor to the effects of hot plasma. To date, promising materials for the construction of ITER are tungsten, graphite and alloys based on vanadium. To simulate the plasma disruptions on the wall, you must have the plasma sources that provide streams with a high power density. For this purpose the most suitable pulsed plasma accelerators generating plasma with ion energy up to several keV. In this direction, carried out an extensive range of studies, including the study of surface erosion under the impact of IPP of different energy density and composition. In recent years, actively developing a new direction in applied plasma research associated with the surface modification of materials 5

by powerful pulsed plasma flows. Fundamental interest in this area due to the possibility of implementing a non-equilibrium thermodynamic conditions in subsurface area of the material in the interaction of high-power plasma stream with the surface. From a practical point of view, the use of pulsed discharges can provide greater process performance, compared to inpatient discharges. Thus, the solution outlined above, actual tasks of plasma physics and the implementation of potential possibilities of pulsed plasma accelerators required to carry out the complex studies aimed at experimental study of characteristics of plasma flow in IPU, peculiarities of its formation in the channel of the accelerator and to study the patterns of plasma flow interaction with material surfaces. In light of these problems it is necessary to study the formation of plasma flows in a pulsed accelerator with coaxial electrode geometry, the mechanism of plasma acceleration at different initial density of the working gas, plasma diagnostics and the study of patterns of plasma flow interaction with material surfaces. The solution must proceed by stages, so the main problem is divided into tasks, each of which is itself complex and has a solution. First, it is necessary to develop the experimental setup of the pulsed plasma accelerators for the study of the formation of plasma flows in a wide range of densities of the working gas in the discharge chamber and the input power. On the basis of electrodynamic model is required to assess the maximum flow settings. Secondly, it is necessary to develop diagnostic methods and devices are applicable to measure integral and local characteristics of pulsed plasma flow, generated in the channel of the Communist party for a short time of the order of microseconds. Further, the aim is to determine the basic physical characteristics of the accelerator and plasma stream: bit current, voltage, volt-ampere characteristic, the conductivity of the plasma, the duration of the stage of formation of the plasma flow velocity, energy density and capacity, to investigate the features of formation of current layers in the coaxial accelerator channel and to determine the magnitude of the azimuthal magnetic field to evaluate the thickness of the current layer and its velocity. It is also necessary to investigate the influence of the pressure in the working chamber of ISP on the structure formed over the cut electrode plasma flow, investigate physical mechanisms for the acceleration of the flow at high and low 6

densities of the gas, to determine the basic plasma parameters – concentration and temperature using probe diagnostics and other methods. A particularly important problem is to study the conditions of formation of the plasma focus in the accelerator during its operation with a continuous filling and distribution of the energy density of plasma flow and study characteristics of plasma flow interaction with the surface of solid materials and the erosion of FR materials when exposed to plasma of various energy and chemical composition. Finally, it is necessary to explore the possibility of using of pulsed plasma streams for modification and strengthening of surface materials when using the plasma flows as a working fluid. In General, the above tasks have been studied in leading foreign laboratories of plasma physics and in the laboratory of plasma accelerators IETP (KazNU al-Farabi) for the last 10-20 years. The object of the research of authors are of the pulsed plasma streams, generated by electrical discharge in the accelerator with coaxial electrode geometry. Subject of research – physical processes occurring in the accelerator, the parameters of pulse plasma flows, and changes on the surface of materials exposed to these flows. We used mostly classical experimental and diagnostic techniques, such as electric and magnetic probes, calorimeter, spectroscopy. Studies were conducted with the use of modern digital and analog instrumentation and analytical equipment. The authenticity of the information provided a good comparability of the experimental results with those of other authors and theoretical calculations. In the laboratory of plasma accelerators, with the direct participation of the author created by setting the "CPU-30" experimental setup "Coaxial plasma accelerator KPU-5", the design of which allows to form the plasma flows in various modes of operation depending on the operating gas pressure and energy drive. The presence of a complex plasma systems with energy from 10 kJ to 200 kJ provides a current in the plasma from 50 kA to 0.5 MA with a current density above 103 A/cm2, which allows to study the occurring at such extreme conditions, the fundamental properties of plasma, the patterns of physical processes in high-speed plasma flows and their effect on various materials. Briefly list those results that were first obtained by the authors on these settings: 7

 The discharge current of the CPU when its operation with a solid content remains high (over 100 kA) and almost unchanged in the pressure range from 5·10-2 to 5 Torr, indicating the formation in the channel of a plasma accelerator with a high degree of ionization, irrespective of the initial gas density in the interelectrode gap. It is shown that the current in the channel of the accelerator is almost completely transferred electrons, the average electron temperature is 4 eV.  There is a threshold value of initial gas density (about 1016 cm3 ) within which is changing the structure of the discharge. Higher edge density in the accelerator channel is formed by a plasma flow consisting of layers with radial-axial direction of the streamlines, moving with low speed (2-3) cm/µs. At the same time, below the boundary density is formed a flow with a diffuse current distribution, whose rate is several times higher.  At densities below the boundary in temporary expansions of current, voltage and derivative of the magnetic field appear fast oscillations associated with the presence of instability or, more likely, with the structuring of the plasma. This is evidenced by such facts as the presence of abnormal resistance at the initial moment of discharge, the constancy of the speed along the electrodes, the presence of areas of erosion at the ends of the electrodes, as well as photographs of the plasma in the similar design and electrical parameters of the accelerators.  Effective acceleration of the plasma flow in a coaxial system is achieved by equality of length of the Central electrode and the distance traversed by a stream in a quarter period of the discharge current, when the amplitude of the magnetic field maximum. In the accelerator KPU30 this condition is implemented when the initial pressure is below 0.1 Torr, when the distance ion-electron collisions becomes of the order of the length of the electrode.  With an initial density below the boundary a substantial portion of the discharge current is taken out of the cut electrodes and forms a region of compression where the compression plasma flow to the axis of the system. (8-10) cm from the end of the outer electrode of the accelerator forms a focus at the point which realizes the electron temperature is 6 eV and the energy of 48 J/cm2. With increasing initial pressure the point of focus shifts towards the Central electrode. 8

 Directed velocity of the plasma flow in the area of free flight when continuous mode is (3-6) cm/µs, depending on voltage, and depends weakly on pressure. At the same time, the average flow velocity of the plasma in the interelectrode space remains essentially unchanged or decreases. The lack of adequate electrodynamic model of the dependence of the velocity of plasma clots, as from the distance traveled and the pressure suggests that the role of the magnetic force of the ampere in the acceleration of the plasma is negligible, and it is necessary to consider other possible mechanisms of plasma acceleration in coaxial.  An analysis of a set of experimental facts, and the calculations suggest that the main role in accelerating the plasma flow plays inside electric field, which occurs when the structuring of the plasma. The mechanism of this acceleration is associated with the emergence of inside electric field, whose magnitude is of the order of 106 V/cm, in which the acceleration of ions. The obtained results are of great importance for understanding the physical processes taking place in pulsed plasma accelerators. The results can be used to develop an effective accelerator of plasma with high kinetic energy flow, to determine the parameters of pulsed plasma microsecond duration when creating theoretical models of processes in high-current discharge of z-pinch and plasma focus. The obtained results are also important in researches on the TCB program with magnetic and inertial confinement of plasma for creation of new technologies modification of materials.

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I. POWERFUL PULSED DISCHARGES IN  MODERN SCIENCE   

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he emergence of pulsed plasma accelerators is closely linked to the development of impulse bit in the 50-60-ies of the last century, when it was formulated the idea of magnetic confinement of the plasma and full-scale research began in the USSR, the USA and other countries [1]. While these studies do not resolve the problem of controlled synthesis, the main idea of the high-current pulsed discharge and diagnostic methods have been developed then. To pulsed high-current systems include all himself gas discharges: Z and Θ are used to live, as well as the so-called fountain used to live. We will mention briefly some of the classic experimental results of Zpinches that are experiencing the basic features inherent in all pulse systems. In [2] investigated high-current discharge in a cylindrical chamber filled with hydrogen, helium or deuterium. The initial value of the current in these experiments was up to 2 MA, at a pressure (10-2-10-1) Torr. Used different diagnostic techniques: the oscillography of the currents and voltages in the discharge chamber, spectral measurements, high-speed filming, the piezoelectric measurement. In initial experiments common features of operation of pulse highcurrent discharges were set. On all experimental curves some characteristics were shown: on current curves during the first halfcycle fractures and gaps were watched; duration of the first half-cycle was always more subsequent; with increase in tension of feature became more and more clear and moved to early phases of process. The main information on optical data for these discharges was obtained using high-speed filming of process. Temporal scanning of the image of the shining plasma was carried out by means of the rotating mirror and the system of lenses. Results of researches showed that in initial stage of process the plasma glow almost completely fills the bit camera, and then it is tightened in rather narrow plasma cord which is torn off from walls. The moment of the first feature matched, within the accuracy of the described experiments, formation of the 10

plasma cord tightened to an axis. At later stages of process the cord got out of the steady original shape, and, at last, broke up. Application of electronic methods of registration gave radial distribution of a glow in time (exposure in the tenth shares of microsecond). In operation [3] measurements are executed in a monochromatic light of the Hβ line, radiation registered by means of the photoelectronic multiplier. The pulsating discharge nature is here too confirmed. In operation [4] using a cell of the Kerr pictures of process at 10-20 times were received by higher temporal resolution. The general sequence of events completely is reproduced and in this case, besides, more detail details escaping when filming are found. First of all, until the first feature, on a surface of a cord perturbations with obviously expressed spatial periodicity are found. Besides, the statement about coincidence of the moment of the first feature to the maximum compression of a cord to an axis also is the confidant. Next, let's consider the experimental results in units of PF. This type of discharge is the basis of operation of modern ICS. A feature of this type of discharges is the presence of a Central electrode surrounded by the camera. In contrast to conventional Z-pinch, in this case, the collapse of the axis occurs simultaneously: the phase of the squeezed state moves along the axis, as the following parts of plasma involved in the compression process. All the above-mentioned diagnostic methods are applicable here, but the short duration of the existence of plasma focus and its small size has led to the development of additional specialized methods [5-7]. Thus, in analyzing these line splitting of specially selected admixtures, managed to get a reliable estimate Bφ in the accelerator channel. Was developed by the spatial analyzers of the charged products of nuclear reactions occurring in the plasma at the time of the collapse. Developed a device that amplifies the intensity of x-ray radiation and enables to obtain a few consecutive shots of plasma focus in the light of his own x-ray radiation with exposure of the order of 10 NS. High-speed photography of plasma focus has shown that the light gathers to the front axis at a speed of 20 cm/µs. Compression is replaced by a short-term extension followed by a new contraction and disappearance of the glow. New flash slowly expanding glow occurs near the axis of the system after 100-200 NS. During the pause, when visible luminescence disappears, plasma focus (PF) becomes a source 11

of neutron radiation of 1011 neutrons per discharge. The final interpretation of this phenomenon remains open. The technical development of devices type PF steel plasma accelerators. This is the device for generation of plasma flows with velocities of 10-100 km/s or more, which corresponds to the kinetic energy of ions from ~10 eV up to 105 eV. The lower limit to plasma accelerators are combined with the generators of low-temperature plasma – plasmatrons, upper – with the collective accelerators of charged particles. As a rule, plasma accelerators are accelerators fully ionized plasma, therefore, the processes of ionization and excitation, and thermal processes play in them, in contrast to the plasmatron subsidiary role. In contrast to conventional accelerators of charged particles in the plasma accelerator channel are simultaneously particles with charges of both signs – positive ions and electrons, then there is no violation of quasi-neutrality. This removes the constraint associated with spacecharge and allows to obtain plasma fluxes with an effective ion current of the order of a million amperes at energies ~ 100 eV. When ion currents of ~1000 And already achieved the energy of the particles in Kev. Since the plasma is quasi-neutral, plasma accelerator of ions and electrons come out with almost equal to the aimed speed, so that the energy flow is in the ions (due to their large mass). Therefore, the plasma accelerators referred to the class of electrical systems that accelerate ions in the presence of electrons for compensating space charge of the ions. We will consider the existing ideas of acceleration mechanisms in plasma accelerators. In the analysis of worker process in such accelerator plasma can be considered and as continuous medium and as set of particles (ions and electrons). Within the first approach an acceleration of plasma is caused by overfall complete (the ionic and electronic) pressure and actions of the Ampere force arising in case of interaction of the currents leaking in plasma with a magnetic field. Within the second approach an acceleration of ions can result: 1) actions of the electric field existing in plasma volume; 2) collisions of a directional flow of electrons with ions ("electronic wind"); 3) collisions of ions with ions thanks to which energy of chaotic movement of ions passes into directional. The greatest value for plasma accelerators has an electrical acceleration of ions. Plasma 12

accelerators share on thermal and electromagnetic depending on whether differential pressure or Ampere force prevails in the course of an acceleration. Electromagnetic plasma accelerators are subdivided on character of an application of energy to plasma into three classes: 1) radiation accelerators in which acceleration of a plasma flow happens at the expense of pressure of the electromagnetic wave falling on a plasma bunch; 2) induction accelerators – impulse systems in which the outside accruing magnetic field induces current in the plasma ring created one way or another; 3) electrode plasma accelerators in which there is a direct contact of the accelerated plasma with the electrodes connected to a voltage source. In case of force interaction of this current to outside or own magnetic field there is a plasma acceleration. L.A. Artsimovich and his staff have carried out theoretical and experimental investigation of plasma acceleration between two parallel plate electrodes – rail [8]. This type of discharge device called a ”railgun”. A working body was the plasma formed at electrical explosion of thin metal wires. The electric circuit consisted of a capacitor Bank connected through the ball gap to a massive copper electrodes – rails. Further with this type of accelerator started to work as the feeding gas and the erosion of the electrodes and dielectric. Along with plate rails are used electrodes of different geometry: cylindrical rods, the coax system. Discharge device with a coaxial arrangement of the electrodes got the name cannon Marshall [9]. Earlier work on plasma accelerators are mainly associated with the establishment of the basic regularities of acceleration of plasma clot and measurement of discharges. In [10, 11] studied neutron and x-ray radiation produced at the end of the internal electrode in a pulsed coaxial plasma accelerator. The obtained neutron yield per pulse at a voltage of 25 kV. Studied soft x-ray emission from plasma focus in the form of several bursts well correlated with the bursts in the waveform of the voltage. These bursts can be associated with the unstable nature of the flow of plasma through the area of focus. In addition, out of the focus area was observed hard x-rays with an energy of the order of hundreds of Kev. In [12] was studied the work of a coaxial plasma injector with the preliminary ionization of the gas. Ablative pulsed plasma accelerators (AIP) are a well-known kind of pulse plasma accelerators [13, 14]. In these devices the plasma is 13

formed by pulsed evaporation of the insulator separating the discharge gap. This method of feeding the working substance to the discharge gap, allows to harmonize the flow of matter and parameters of the accelerator. This gives you the opportunity to put into practice a sufficiently high conversion efficiency of energy provided from the power source into kinetic energy of the plasma. The AIP produce plasma flows with duration from a few microseconds to milliseconds with a minimum diameter of ~ 1 cm, the particle flux of 1016 cm–2s-1 and velocities up to 105 m/s. Choice of the geometric parameters of the API and the parameters of the electric circuit can be implemented as gasdynamic and electrodynamic (ED) the acceleration of the plasma. In the first case, the acceleration of the plasma in the accelerator channel is due to its gas-dynamic expansion. In this mode, the magnetic pressure on the plasma less than gas-kinetic. In the mode of electrodynamic plasma acceleration, the magnetic pressure exceeds the gas-kinetic, and acceleration of a plasma occurs mainly due to the ponderomotive force [JH]. Coaxial plasma accelerator KPU-1 with continuous electrodes [15-17] was the first object is a thorough physical studies of plasma accelerators of this type are conducted in I. Kurchatov’s IAE a from

the beginning of 1960, the Duration of the working pulse  раб =(110) 10-6 s, on the one hand, do not create difficulties with heating the coax and did not require a great deal of energy (in this case, a capacitor Bank), and with another – chosen time was almost two orders of magnitude greater span of time of 3·10-6 s. this selection process can be considered quasi-stationary. The discharge rate was (20-100) kA. Research and development of pulsed plasma accelerators of different types and their application in technology as sources of hot plasma and space electric propulsion systems is discussed in [18-26]. Progress in the development of ISP is largely determined by the development of the fundamental concepts of ongoing processes. This task became extremely difficult, despite the relative simplicity of design of the accelerator devices. The specific feature of ISP is that the development of the process of forming them is in the nature of successive stages. For plasma itself consists of several typical zones: the plasma jumper from venting holes in the initial stages of discharge, the current layer during the filling of the plasma of the interelectrode 14

gap, the current front on the border of the gas distribution on the cut electrodes, PF [27]. It is shown experimentally that in IPU under certain conditions, the observed acceleration of ions up to tens or even hundreds of Kev [28, 29]. This mode is characterized by a peculiar structure of the plasma flow. Typically implemented two modes of plasma acceleration: fast and slow speed, which differ in tens times. The speed of quick clot is far beyond the estimates based on the magnetohydrodynamic approximation and exceeds the speed that can acquire particles in direct acceleration by the applied voltage. This indicates the existence of a mechanism of acceleration based on the turbulent heating and acceleration of ions on small-scale instabilities excited by the discharge current. The most significant difference in the mode of operation of the accelerator makes the distribution of gas density along the length of the accelerator. The "slow" regime corresponds to a more uniform pressure distribution along the length and a relatively high initial gas density. Fast mode corresponds to a significant density gradient with a decrease toward the exit of the accelerator and a relatively low initial density of the gas. In "slow" mode, the entire discharge current is concentrated within a small size of the current layer, which is opaque to gas. Is gas making the current layer. In "fast" mode, the current layer is not formed. The discharge current is concentrated in the whole volume of the accelerator. In front of the current layer remains magnetized plasma. In the plasma behind the current front develop vibrations in which ions gain significant energy. The main acceleration fast plasma clots occurs when the output current of the front border of the gas distribution due to the expansion of a magnetized plasma to vacuum. There are modes of operation of the ISP, accompanied by the appearance of plasma focus for a slice of the electrodes [30]. If a coaxial accelerator with a positive polarity of the electrode is "plasma piston", when you exit the current layer in the cut electrode, he collapses to the axis, near which there is a focus. Part of the magnetic energy stored in the moving current sheet and in the external circuit, quickly transformed in the plasma energy for the time during which the plasma layer collapses to the axis. Compression and plasma heating due to both magnetic forces and forces of inertia. Under these 15

conditions the experimentally obtained plasma with density 1019 cm-3, temperatures (0,1-1) Kev and a lifetime of 0.1 µs. The plasma focus ~1011is a source of neutrons per pulse, and a powerful x-ray and microwave radiation. Another variant of the focus plasma is observed when the coaxial accelerator with a negative polarity of the Central electrode operates in "fast" mode. After passing the discharge current through a maximum in the interelectrode gap formed closed loops of current, magnetic field which is under the action of ampere force on the cut electrodes are self-focusing of the flow to the axis. Arise in this case near the end of the cathode PF is quasi- stationary in nature: the duration of its existence – the order of the lifetime of current loops far exceeds the flight time of the ion. Plasma clots generated by the IPU in all modes have three characteristic areas: area of ionized gas, the area of impurities and a region with a predominance of neutral gas. First, almost luminous region, consists of a clean, nearly fully ionized gas. In the area of luminescence of impurities moving with less speed, found ions and atoms of the materials of the insulator and electrodes. The particle density in this region is several times smaller in the third (intense luminous zone) there is a significant amount of neutral gas. Over the past few years have provided new data on plasma diagnostics in IPU. In [31] fabricated a high-frequency magnetic probes to study the dynamics of the acceleration of the current layer in the axial part of the parallel accelerator of dense plasma bunch with low energy. The device used in the environment of nitrogen gas. The response time of the probes was of the order of 1 NS, the size of the probes well suited for the study of the small volume of plasma without perturbations. The probe has detected the magnetic field associated with a pulsed plasma. The magnetic probes were calibrated using a simple and reliable technique calibration factor calibration was (0.34 ± 0.03) T/B. Studies using these probes showed that the current layer parabolic shape is accelerated along the electrodes, reaching a speed of about 6.1 cm/µs. The average layer thickness in the axial acceleration phase was found equal to ~3 cm, the loss Factor of the flux density and loss of mass is estimated by the authors, 32% and 40% respectively. Thus, an approach using high-frequency magnetic probe in the study of the current dynamics of the current layer in the 16

described device highly effective in obtaining accurate and spot measurements. The formation and distribution of thin current sheets in the ISP with rectangular geometry were also observed by the authors [32], using high-speed cameras, equipped with linear filters with narrow slits. The purpose of these studies was to determine whether there are any asymmetry or instability in current sheets, which may be undesirable for the operation of the pulse generators of the plasma. These photos were taken of light emitted from the current layer (plasma clot) within the formation, propagation and extinction layers. We studied the effect of kinds of gas used, pressure, voltage on the capacitors and the polarity of the electrode on the layer structure. The most notable feature of these registered images current layers formed a sharp boundary (edge) at small angles relative to the normal to the electrodes. The reasons for the formation of Kant, according to the authors, can be electrode erosion, magnetic field asymmetry, or the Hall effect. In [33] presented the dimensionless parameters of the accelerator, which had a "leak mass" after the current layer. It is established that full impulse and momentum current are experimentally measured, are in direct dependence on the mass and velocity of the accelerating current layer. Found in the parameter values also depend on the instability of accelerator operation and the initial pressure. A characteristic that parameter values that increase with pressure for hydrogen and helium, constant for neon and decreases for argon. These trends indicate that the leakage process, which differs for the different layers has a great influence on the operation of such device as a plasma accelerator. In [34] investigated the accelerator with parallel plates, which blocked the movement of breeding thin current sheets in the transition electrode, an insulator, and the expiration of a period of sustained discharges. Photographing with the help of Kerr cells, magnetic and electric studies of voltage measurements showed that these sustained discharges accelerate the gas through itself while the gas is in the chamber, after which increased erosion of the insulator and the discharge you receive an electrode material. To supply fresh gas stable discharge area with the minimum of delay, we used the technique of introducing a gas blow out of the pipe. Found that even with this procedure for flow control requires time on the order of hundreds of microseconds required for electrodynamic stabilization. This "quasi steady" flow regime, 17

characterized as the current, and gas stabilization, provided a significant acceleration of the flow from the inlet. The experimental cards of magnetic fields for the current layer on a section with rarefied area of the accelerator which had variable length and amplitude are received in operation [35]. The rectangular form of the front of a flow specifies that on an initial section distribution of the discrete current layer is followed by transition to the quasistabilized form of a large number of a diffusion flow of conductivity. This steady stage which is usually reached after several tens microseconds after discharge brings, in essence, to invariable electrode voltage and a persistence of the current characteristics and provides a flow of the accelerated gas. The effect of stabilizing and physical details of transition of formation of the current layers to a constant stage in discharge are in more detail studied in case of a onedimensional configuration with parallel plates where magnetic methods of a research, photography using a cell of the Kerr and strain measurement on electrodes are applicable. Thus, it is supposed that the model of "the plasma piston" describing the characteristic of process of an acceleration of any IPU – in essence, start transient phenomenon of an acceleration of the set current for such electrode geometry. We will specify also some other the operations concerning operation of the accelerators [36-39] similar to already described. In [40] described compact plasma accelerator. The current characteristics of the discharge device have been registered by magnetic probes and potential analyzer. It is established that the character of the discharge current depending on the discharge voltage is nonlinear. The device can generate ions with energy of ~80 eV and a current density of 7 A/cm2, is comparable by parameters with accelerators of higher power. It is noted that the device works best at very low bit currents, which ensures dense clumps. The concept of a compact plasma accelerator could potentially be used as a source of low-energy ions for use in the processing of materials. In [41] studied the phenomenon of ablation near the surface of the material in the discharge plasma in correlation with the type of ionization in accelerated plasma. Identified two characteristics of the ablative regime, namely the regime with the velocity in the Knudsen layer is smaller than the ion acoustic speed and mode at a speed close to the sound. The existence of these two ablation regimes, determined 18

by the current density in the region of acceleration. Studied nonequilibrium ionization region in the presence of strong electromagnetic fields. In the subsonic mode, the thickness of the region of ionization proportional to the ionization rate and inversely proportional to the magnetic field. The conditions for equilibrium of ionization in the accelerating plasma. It is shown that in this device occur and the equilibrium and nonequilibrium regimes of ionization. The concept of a second generation of accelerators plasma of hall type (ATON-thruster), which has a record of operational parameters of the characteristics described in [42]. A method is proposed to analyze the parameters of operation of the accelerator based on the characteristics of its performance. The results of measurements of plasma parameters in the accelerator channel used in a jet engine. Features of a research and use of magneto-hydrodynamic accelerators of plasma are considered also in works [43-46]. Power characteristics of the plasma streams made on the quasistationary accelerator of KSPU-50 plasma, the Kharkiv physics and technology institute which is in institute of a plasma physics (Ukraine) are provided in these works. Features of plasma interaction with the surfaces of tungsten depending on plasma loadings and high temperature are studied. On the same installation the large number of experiments on plasma processing of other constructional materials is made [47-56]. Thus, as a result of numerous experimental studies, it was found that plasma clots generated in IPU, have a complex structure and inhomogeneous in density, temperature and other parameters. These studies were primarily due to the possibility of using the ISP as the external injection system for filling and heating of plasma in magnetic traps. Later significantly increased the interest in the prospects of the use of IPU to study the interaction of high temperature plasma flows with surface materials. In this direction, plasma accelerators at the present time are used for the creation of the atomic-clean surfaces, spray materials, the hardening of surface layers of metals, coating the surface, for thin films, ion doping, and annealing. Such research is actively carried out on different types of accelerators generating plasma in a wide range of power densities, concentrations and temperatures [57-76]. Work in this direction are also carried out on pulsed plasma accelerator IETP KazNU al-Farabi. 19

In the basis of the described plasma technologies are plasma generators, that is, systems in which ionization of the working substance and the imparting of energy to the generated plasma. The plasma generators according to their design features and the nature of the processes, you can more be divided into 4 types (classification by A.I. Morozov [83]). From the point of view of working principle, the plasma generators can be divided in stationary and pulsed. Stationary plasma accelerators are limited by small discharge currents, since an increase of current to hundreds of amps, it becomes an actual problem of erosion of the electrodes and their cooling. IPU is the generators of plasmoids (pulse gun), or streams with relatively large particle energies from tens of eV to hundreds of Kev and above. The advantages of these accelerators is the high power density afforded by short-term exposure to a pulsed discharge. Heat input to the discharge pulse cannons can range from hundreds of joules to hundreds of kilojoules, but it is not necessary to cool the conductive parts of the installation. The most complex node is a valve that needs during the time of the order of microseconds to form between the electrodes of the gas layer, through which flows the current, to ionize it and accelerate under the action of Ampere force. This shows that the work of the accelerator strongly depends on the performance of the valve and the control injection. Because of the large discharge current (~105) and small mass of accelerated gas (~10-6 kg) these accelerators has many features, as mentioned above. The work of the IPU can be done in two modes: with valve for gas injection and continuous gas filling the interelectrode space (the socalled "continuous mode"). In this mode, the valve is not used. The advantage of continuous mode is that there is no inhomogeneous distribution of the gas along the length of the accelerator, so the discharge behavior more predictable and it is possible to study in detail. In addition, by adjusting the pressure, it is possible to obtain various modes of acceleration. It is essential that at low densities of gas can get quite high speed clusters [84], to implement various acceleration mechanisms of the plasma – electromagnetic and purely electric. Therefore, the study of plasma accelerators in a continuous mode has great scientific potential. The analysis of literary sources shows that the work on the systematic study of pulsed plasma accelerators, both in pulsed and in 20

continuous mode as well as comparison of experimental data with theoretical results obtained on the same device, no. To understand the processes occurring in the organization, great importance is assessing orders of magnitude of such basic parameters as discharge current, speed and energy of the bunch. To make a quantitative assessment of these values by using calculations based on theoretical models. It is then possible to compare with the experimental results and analysis of the processes. We will briefly review existing theoretical models of the description of work of IPU. Electrodynamic model is the most simple and suitable for calculations of energy parameters of the ISP. For the ISP with a coaxial electrode geometry of the magnetic field H is concentrated in the space between the electrodes and is determined according to the law H

I , 2 r

(1.1)

where I – the current flowing in a contour, r – radius. Let the field in conductors be absent. The magnetic field energy of WM in interelectrode space is WM  



H 2 I 2  2 d  2 2 ( 2 ) 2





R2

dz

0



R1

dr  I 2 R L I  ln 2  1 r R1 4 2

2

The running inductance of the coaxial accelerator is defined by a formula

L1 

 I 2  R2 , ln 2 R1

(1.2)

where R2 – the inner radius of the outer electrode, R1 is the outer radius of the inner electrode, ℓ- is the length of the electrode system, μ=4π·107 GN/m – magnetic constant. Let be С0, L0, R0 the capacity of the capacitor Bank, the inductance ~ of the supply cables and tires and their resistance, L – inductance of ~ the electrodes, R – the resistance of the current jumper. Considering 21

.

the energy loss due to ionization, radiation, ohmic heating of the plasma, etc., we will consider the movement of the plasmoid along the z-axis coax. In reality, you should consider the system consisting of constant components and variable components. Equivalent Electromechanical circuit of this system shown in figure 1.1.

Figure 1.1 – Equivalent circuit of IPU

Idealsauna description of plasma acceleration in such a system is given by a system of equations Artsimovich

d 2 I 2 dL m0 2  ; dt 2 dz dz  ; dt dV I   C0 ; dt dLI  R0 I  V  0; dt L  L0  bz. In General, even the simplest system of equations Artsimovich, due to its nonlinearity, can be solved only by numerical methods. To solve the system it is convenient to bring to dimensionless form. We introduce the dimensionless quantities 22



t , L0C0

y

b V I  z,   ,    L0 V0 C0V00   ,  C  y  b 0   L0

(1.3)

where  , y , y ,  ,   – dimensionless value of time, path, speed, voltage and current, respectively. In these variables the equations Artsimovich when will take the form of R0 = 0

dy   q  2 ; d

(1.4)

dy  y ; d

(1.5)

d    ; d

(1.6)

d 1  y      0 , d

(1.7)

where equation (1.4) is the equation of motion, (1.5) is the speed equation, (1.6) is the equation of current, (1.7) is the equation of the voltage. Consider

b2C02V02 q 2m0 L0

(1.8)

-force, or energy parameter, introduced by L.A. Artsimovich. Its physical meaning – ratio of the characteristic values of the magnetic pressure over the characteristic magnitude of the force of inertia of the

23

accelerated plasma clot. The initial conditions will take the form if τ=0, y  0,

y   0,    0,

 1 .

(1.9)

For calculations it is necessary to estimate the value of the parameter q in (1.8), i.e., at typical parameters of the accelerator C0  100 мкФ, L0 ~ 107 Гн, b  1  107 Гн / м,

V0  3  104 В,

.

m0  107 кг, q  1

The q-value for the real accelerators varies depending on its parameters over a wide range and takes a value in the range of 0.1 100. This system is numerically solved on a computer, where we investigate the effect of parameter q on the characteristics of the accelerated plasma. Numerical results showed that the increase of the parameter q leads to rapid change in the amplitude of the current, the discharge decreases and approaches aperiodic, the half life increases. The increase of the parameter q leads to a sharp increase in speed, and the speed for a short period of time reaches its maximum value. The set of equations (1.4-1.7) is of interest in two relations. First, this system in pure form shows features of transformation of electromagnetic energy of a contour into a kinetic energy of plasma in high-current the accelerator. These features are: a) intensive decrease of amplitude of current and tension even in the absence of an energy dissipation that will be explained by transfer of electromagnetic energy in mechanical at acceleration of plasma under the influence of forces of magnetic pressure; b) at the same time the period of fluctuation of current due to change of inductance of system changes; c) acceleration lasts a short time term about several microseconds, speeds of sizes about 105 m/s; d) on dynamics of process in ideal consideration the main impact is exerted by the size of parameter q which increase leads to increase in the most accessible speeds of plasma on escaping of the accelerator. Increase in parameter q is equivalent to increase in the distributed inductance of unit of the 24

accelerator, capacity of C0 condensers, tension on its facings to V0, decrease of the accelerated mass of m0 and stray inductance of a contour of L0. Secondly, this system can be considered as the limit of features that can be extracted from a pulsed accelerator, both from the point of view of maximum speed and from the point of view of the coefficient of conversion of electrical energy into kinetic energy of the plasma. This system does not account for any losses or phenomena, complicating the picture of the movement under the action of magnetic pressure. In practice, the related phenomena can play a significant role and drastically change the overall movement pattern. It can be nearelectrode phenomena, particularly the distribution of gas along the length of the channel and some others. Let's consider further methods of the theoretical analysis of processes in the pulsed plasma accelerators based on the analysis of magneto-hydrodynamic currents. Now the research of currents of plasma is concentrated on two main questions. First, there are results of a series of calculations twodimensional the Moscow City Duma currents, belonging mainly to distribution of electric current in the channel [85]. The last essentially defines quality of the plasma accelerator: current of the radial direction in an azimuthal magnetic field accelerates plasma along an axis of the channel, and current of the axial direction, especially current whirlwinds, fall into to the undesirable phenomena. Calculations of stationary currents of plasma in the simplest problem definition showed that distribution of current in the channel is defined first of all by value of the dimensionless parameter β0 = 8πр0/Н2о – the relations of the reference gas and magnetic inlet pressure to the canal. At small values β0 current is close to radial, and at β0 ˃ 1 sliding of current along electrodes and current whirlwinds is observed. The tendency to formation of whirlwinds of electric current at great values β0 is noticed also in early theoretical works [86-87]. Secondly, it discusses issues arising in the analysis of the calculations and their comparison with experiment. They are connected so that the experiment can provide complete information about the details of the flow throughout the battery, and the calculations, although allow in principle to obtain values for any 25

involved in the model of values, based sometimes on inadequate baseline information – parameters, initial or boundary conditions. This raises the issue of comparability of calculations and measurements. An example of this is the above – mentioned effect of the parameter β0 in the properties of the calculated currents. Its value is not directly follows from the experiments, as information about the pressure P0 at the entrance to the channel is not always available. To easily measurable values include the full discharge current J and voltage V in the channel. For an unambiguous mathematical formulation of the problem of course need to know a third value – for example, pressure, density and temperature at the inlet of the channel or the mass flow. The relationship between these quantities, including J and V, and the method of their calculation or estimate according to the known from the experiment the values of the three variables and therefore calculate β0 can be obtained by using approximate theoretical models. Two well-known approximate approach to the solution of the steady MHD equations without taking into account the dissipative factors – viscosity, thermal conductivity and electrical resistance (infinite conductivity), in cases where two-dimensional effects are not strong, are: 1) quasi-one-dimensional (hydraulic) approximation involves averaging all of the characteristics of flow over the cross section of the channel at each axial coordinate z ; it is widely used in a gas dynamics, its MHD- a version is explained, for example, in works [87,88], and article [86] contains its generalization on the current of plasma in narrow tubes along twodimensional trajectories; 2) the approximation of "the smoothly varying kalan" assumes that the section of the channel sluggishly changes along an axis z; it is offered in A.I. Morozov and L.S. Solovyov's works of the 60th years which entered reviews. Both approaches are realized in approximate solution of various tasks about a current of plasma in channels and, in particular, approximate connection between the sizes characterizing a current is established with their help. Calculations of the MHD-flows by the establishment. Numerical studies of fundamental properties of the plasma flow in the plasma accelerator channel is conducted in the simplest formulation of the problem equations of magnetic gas dynamics:

26

In the proposal of the axial symmetry

These equations are integrated numerically in the region of cylindrical coordinates (z, r) corresponding to the shape of a channel. Feed type nozzle is formed by two coaxial electrodes. At the entrance to the channel over the assumed designline

therefore at z = 0 distributions of three sizes are set, for example: 1) density ρ or a mass flux ρυz, 2) temperatures of T or pressure р, 3) a magnetic field of N = 2J/cr, where J – the total digit current between electrodes. Besides, some information on speed υr, for example, the direction is set here: υr/υz. On escaping of the channel a current superalarm (υ˃Cm), and conditions on the right border of area are not required. It should be emphasized that the considered model in its simplest version is used to determine basic properties of currents without taking into account dissipative processes and, strictly speaking, only in the main core flow, ie, less fine when the electrode layers, the processes that are the subject of special studies [87, 89]. 27

2. INSTALLATIONS FOR PRODUCING A  PULSED PLASMA   

F

or production and investigation of pulsed plasma flows and processing materials in the IETP was designed and developed by two of the accelerator with coaxial geometry: CPU-30 and CPU-5 at working voltage 30 kV and 5, respectively. With comparable dimensions of the electrode system, they differ primarily in the parameters of the drive and its own inductance.

2.1. Powerful coaxial accelerator "CPU-30" The installation of the CPU 30 consists of a discharge chamber, inside which the coaxial electrodes, capacitor, vacuum arrester, grounding system and protection and control panel located in a separate room, vacuum system, diagnostic equipment and electric utilities. Schematic diagram of the IPU ispresentedin figure 2.1. The principle of operation is based on the acceleration of plasma clot formed in the interelectrode space in an electric discharge, its own magnetic field. For this purpose the electrodes is applied a high voltage, as in the working chamber is created, an initial pressure sufficient for breakdown of the discharge gap. Thus, the task of control consists of the execution of the Paschen conditions for plasma gas, in which ionization of the working substance and the formation of the plasma. When the pulse overlap of the working gas need to arrange a time getting gas in the interelectrode space at the time of the supply voltage. This applies to a special signal generator. When working with a solid fill in the pre-chamber is filled a gas to a pressure at which breakdown occurs. Electrode system coaxial geometry is made of copper cylinders with flanges separated by an insulator made of Plexiglas. Holes for gas inlet located on the inner electrode. The diameter of the outer electrode is 90 mm, bore – 26 mm, length of outer and inner electrodes, respectively, 450 mm and 400 mm. the Diagram of the electrode part shown in figure 2.2.

28

2

3

12

1

10

11 4

13

9 7

5

8

6

1 – working chamber, 2 – cylinder with a plasma-forming gas, 3 – manometer, 4 – electrodynamic (ED) valve, 5 – vacuum spark gap, 6 – battery high voltage capacitors, 7 – coaxial electrodes, 8 – pumping system, 9-sample holder with integrated system of calorimeters – 10, 11 – plasma clot, the 12 – valve to run gas with solid content of gas, 13 – additional section with I / o's for plasma diagnostics. Figure 2.1 – schematic diagram of the accelerator KPU-30

Cumulative IPU system is a capacitor Bank with total capacity of 69 ICF, consisting of 23 high-voltage switching low-inductance capacitors IR-50-3 (voltage up to 50 kV, 3 µf capacity). Operating voltage range ISP from 10 to 30 kV. The spark gap consists of two massive circular steel disks separated by an insulator made of Plexiglas. To create a vacuum is a separate roughing pump. The breakdown of the vacuum gap is in the ignition initiating spark discharge, which on the perimeter of the disk has three igniting electrode. Voltage for firing is supplied from high-voltage capacitors charged to 5 kV. Funded system and arrestor shown in figure 2.3.

29

40 см 10 см

45 см

Figure 2.2 – Scheme of the electrode system of the accelerator KPU-30

The vacuum chamber of the accelerator is made in the form of a pipe with a diameter of 160 mm and a length of 105 cm stainless steel with a wall thickness of 2 mm. At the ends of the pipes installed flanges ДУ160 through which power supply and diagnostics. The control panel located in a separate room from the current highvoltage part of the installation, provides the necessary preliminary operations and starts the installation in the specified mode, and control over the installation during the whole experiment. The management of the unit ensures safe charging-discharge capacitors and ignition. Ignition is required for switching a high voltage to electrodes installed in a given time. In addition, it provides galvanic separation of high voltage parts from the controls and starts the diagnostic equipment. Developing the possibility of automatic control of the installation using the computer. During the experiment, the door of the room with the installation is automatically locked, and monitoring the operation of the installation by means of an electronic camera on a monitor 30

screen located in the console room. The control panel is shown in figure 2.4.

Figure 2.3 – the Discharger and the storage capacitors of the CPU-30

Figure 2.4 – the control Panel CP-30

Figure 2.5 – General view of the CPU-30

Work experimental setup occurs in the following sequence: from the control panel on the charger serves the control signals for which the capacitor is charged to a specified ISP voltage. Then using the sync generator, the operator from the control panel launches the schema of the ignition arresters and measuring equipment, then the discharger circuit of the electrodes and then starts measuring apparatus. General view of the assembled accelerator KPU-30 shown in figure 2.5.

31

2.2. An experimental plasma accelerator "CPU-5" Stand "CPU-5" was created for research and educational process in the laboratory IPU IETP. This is a full installation that can be performed all work associated with the plasma diagnostics and materials processing. The power unit and the gun is compactly arranged in the area of 5 sq. m. The basis of the power source of the accelerator KPU-5 is the power unit of the quantum generator GOS-1001. General view of the block shown in figure 2.6. This unit has a compact casing (28), which houses two sections 24 of the capacitor to 5 kV (29), and a control unit (30). Control the unit is controlled from the control panel on the front panel of the device. There is placed kilovoltmeter and a pulse counter. For safe operation, the device can be operated via remote control length 5 m. the Bank of capacitors is divided into 4 channels, which is useful for consistent capacity. For the organization of a controlled ignition discharge device designed on the basis of the ignitron and control circuit for firing the ignitron. The ignitron is installed in the compartment instead of the thermostat 34, which is not used. To improve the reliability diagram of the ignition for the CPU-30 has been upgraded by removing the discharge lamp as its service life is limited. The bulb used is a semiconductor thyristors. Re-designed diagram of the ignition semiconductor elements is shown in figure 2.7. In this arrangement the transformer TR1 delivers a voltage firing of ignitrons. IRT-6 size 1400 V. Through the thyristor T 250 provided by the ignition current of 200 A at the discharge of the capacitor C. When the inclusion of the ignitrons. high voltage 5 kV is applied to the electrode of the accelerator and pulse discharge occurs. The basis for the design of the accelerator is a vacuum chamber with inserts for optical observations. Vacuum flanges are made of stainless steel with a thickness of 10 mm and are welded to the ends of the chamber. Removable cover made from organic glass with a thickness of 60 mm with a lining of vacuum rubber and has 4 holes for mounting bolts.

32

Figure 2.6 – the Power block of the accelerator KPU-5

Figure 2.7 – diagram of the ignition of the ignitron to install 5 kV

The camera is designed in such a way that it is possible to establish the main diagnostic devices both outside and inside. Outdoor systems is a Rogowski loop, diamagnetic coils for measurement of the flow velocity. The camera has four parallel slits for spectroscopic methods, and flow rate measuring method of signal detection with a photomultiplier. In addition, installed 8 bushings for electrical probes, 33

2 diametrically opposite openings at different distances along the length of the camera setup for the optical diagnostics. The electrode system consists of copper cylinders with a diameter of 9 mm (outer) and 4mm (inner) with a thickness of 3 mm. Collected in the discharge chamber of the stand shown in the photograph (figure 2.8).

Figure 2.8 – Bit camera stand of the Communist party-5

In General, the presence of complex plasma systems with energy from 10 kJ 0.2 MJ provides a current in the plasma from 5 kA to 0.5 MA with a current density above 103 A/cm2, which allows to study the occurring at such extreme conditions, the fundamental properties of plasma, the patterns of physical processes in high-speed plasma flows and their effect on various materials.

34

3. METHODS OF DIAGNOSTICS OF PULSED  PLASMA   

T

he magnitude of the discharge current and voltage are some of the most important parameters not only ISP, but all highcurrent plasma systems [90, Pp. 16-18]. As in pulse accelerators have to deal with quickly changing currents of large magnitude, the problem of measuring current it is convenient to solve using the associated rapidly changing magnetic field. For calculations of some plasma parameters, in addition to measuring current, it is necessary to know the voltage of the plasma gap. In recent years we have developed many new methods of measuring plasma parameters without disturbance. However, such methods are suitable for measuring magnetic fields in complex systems containing both a magnetic field and the plasma apparently does not exist yet. However, on the deflection of fast charged particles injected into the plasma, can, in principle, determine the internal magnetic field, and attempt to use this effect have been undertaken, but interpretation of the deflection of the beam is almost a hopeless task except in the case of the simple stationary systems. Therefore, when measuring the magnetic field distribution has to enterthe sensor directly into the plasma, which can lead to significant errors due to perturbations of its probe. The need for the measurement of magnetic fields due to the fact that the spatial position of the plasma relative to its holding system of forces (usually magnetic fields) is crucial in various cases of practical use of ionized substances. Issues of confinement and magnetohydrodynamic stability are directly linked with the relative position of the plasma and magnetic field. So, given normal ratios of balance of pulses it is often possible for the magnetic field distribution to determine the spatial position of the plasma, the density of its thermal energy and the stability of the configuration.This requires, however, that the plasma in the studied system is strongly influenced by a magnetic field. It is clear that the magnetic sensing would be useless in determining the spatial distribution of several thousands of 35

ions and electrons in the external magnetic field of several thousand oersteds. Another limiting case is when the magnetic field is entirely due to plasma currents (for example, samostalna discharges and plasma accelerators) – ideal for use in a direct magnetic sensing [90, Pp. 60-61]. Unfortunately, the high sensitivity to the magnetic field is not the only quality required of the probe. Extensive and very interesting class of systems, typical representatives of which are the thermonuclear reactor with magnetic plasma compression, designed to produce a plasma with such high temperature and density at which the probes will be destroyed. Thus, the use of magnetic probes is limited to experiments with plasma, has a reasonable energy density and has a noticeable impact on the containment field.

3.1 The measurement of discharge current and voltage For measuring currents using the method of oscillographic register using a Rogowski loop [90]. The Rogowski belt is a long solenoid, wound in a toroid (figure 3.1). The toroidal coil (solenoid) is shorted to the small resistance R. the voltage Drop across the resistance is measured using a measuring device.

R C Figure 3.1 – Rogowski Belt with passive integrating chain

The equation for determining the current zone Rogowski has the form I

VN R

36

where V- is the measured voltage, N- is the number of turns, R- is the load resistance. Thus, the output voltage is proportional to the measured current and the Rogowski belt works as a current transformer. The pulsed plasma accelerator operates at high voltages up to 30 kV. For high voltage measurements made combination resistive and capacitive voltage divider. The choice of this type of divider is based on the fact that it can be used to measure a wide frequency interval of voltages. When using it must be running condition R1 C2  R2 C1

To provide a division ratio of 1:10000 was chosen resistor values, R1= 510 kOhms, R2 = 50 Ohms, and capacitors C1 = 1100 pF, C2= 11 UF. The voltage pulses from the divider is transmitted through a shielded coaxial cables with matched wave impedance of the oscilloscope S8-14 or UT3200. For protection from electromagnetic interference oscilloscopes were in the room control panel installation. There have been several zones: outside to measure the discharge current and the internal for the direct detection current in the plasma flow. External Rogowski belt was made as a solenoid with a diameter of 4 mm and a length of 60 cm, folded in the form of a toroid, the number of coils 2450. The solenoid shorted by a small resistance of 0.5 Ohms. If the outer zone covers N current tires from their full number M, the calculation formula for current will be

I

2450Vосц M  . N 0,5

(3.1)

Taking into account the ratio of the number of wires 16/7 multiplication factor will be 11200. To study currents inside the accelerator was applied the Rogowski belt with the number of coils 528 and a length of 30 cm. the experimental setup is shown in figure 3.2. This belt is also used to measure current density in the plasma by changing the cross section of the torus. Belt were installed at different distance from the end of 37

the outer electrode inside of the liner accelerator. To study the structure of the flow zone was set at a different distance from the end face of the outer electrode: 2-80 cm 2 and 5 cm. Calculation formula for the current of the plasma passing through the zone is given as

I внутр.  N U по осц / R , where N – number of rounds of a belt (528); R – load resistance, equal 1 Ohm. Thus, the measured current passing through the cross section of the ring. In the case of the outer circuit, this current corresponds to the discharge current of the capacitors, and in the case of inner – current in the plasma. The signal was applied without amplification to the input of the oscilloscope via a coaxial cable of 50 Ohms.

Figure 3.2 – Scheme of the experiment on the study of the structure of the plasma flow

3.2 Measuring directional velocity of the plasma Pulsed plasma accelerators of the most important parameter is the speed of the plasma flow as it affects the energy flow. At the same time, the flow rate in the plasma accelerator does not smoothly increase from zero to a maximum value, since there is a voltage 38

breakdown of the gas, below which the plasma is generally not formed. Therefore, the speed of plasma need to be measured in a certain interval, a constituent of ISP values from units to several tens of kilometers per second [91]. The directed velocity of the plasma flow of the CPU was measured in two ways: with the use of electrical probes and magnetic probes, Rogowski belts. The speed recorded by the position of the current maxima on the oscilloscope screen. According to a time shift between the peaks of the signals determines the rate of flow of the plasma. The probe measurements of the plasma velocity was calculated with the formula



 t,

where  -is the distance between the two probes, t is the time interval on the oscilloscope screen. Errors in this measurement method is connected not with the precision reference on the oscilloscope screen and with the correct identification of a signal in the background noise or random processes. For example, there may be superposition of two peaks in the presence of oscillations in plasma or blurred width of the peak. To solve this problem the measurements were carried out according to the method of successive approximation, when at first we have chosen those conditions of the experiment, which was observed "clean" signal, and then when you change the plasma parameters were monitored change speed values in the expected limits. In some experiments, the determination of the velocity of plasma flow was carried out by two photomultiplier tube, located opposite the diagnostic cracks along the length of the chamber. Signals from the PMT were also recorded using a dual channel storage oscilloscope.

3.3 Energy parameters of a pulsed plasma In the study of the parameters of pulsed plasma flows is particularly important information about the magnitude and the distribution of heat flow in plasma. For this purpose, the chamber includes heat (calorimeters), which are made of suitable material (Cu, Ni, Mo) in the form of small cylinders or discs (figure 3.3), each of them attach a separate thermocouple. Depending on the expected flux 39

density of that energy is foil or solid sheet material. The thickness of the heat sink is determined by the amount of energy absorbed. Often in high-temperature flows using heat of stainless steel. Coming from plasma, the amount of heat ΔQ increases the temperature of the calorimeter and partly lost by conduction and radiation. If the temperature of the receiving surface increases slightly, and the fixing of the traverse is thin enough, the first moments of time losses can be neglected and write the approximate equality for the heat balance in the simplest form:

Q = McT.

(3.2)

Here M-is the mass of the heat receiver, c- is its specific heat capacity and ΔT- is the observed temperature rise. Rough estimates of energy flow based on the formula (3.2) and the measured value ΔT, can be somewhat clarified if one knows the absorption rate of the energy receiving surface of the calorimeter chosen design. Of course, that the heating of the heat is caused not only by contact with the surface of the plasma, as well as expose it to radiation and a fast neutral particles resulting from recharge. The possibility of determining the contribution of each of these processes without detailed consideration of each of them depends on the nature of the object.

Figure 3.3 – Calorimeters with thermocouples

In General, the coefficient of reflection from the surface of the calorimeter, the amount of heat is determined by the formula 40

 Q   c V 1  

.

Here is the ρ-density, c – heat capacity and V – the volume of the heat sink, γ – is the reflection coefficient of the plasma on the surface of the heat sink. Considering that the proportion of digestible energy sink Qand does not depend on registering the temperature of the heat sink located in different places, to determine the distribution of heat on a wall in relative units. To determine the absolute values of the energy carried by plasma on the surface area of the wall of the vacuum chamber, it is necessary to grasp either the entire incoming energy, or to know the reflection coefficient γ. The easiest task is solved by means of the calorimeter with a developed surface. This calorimeter is manufactured in the form of a deep cylinder, usually made with walls perpendicular to its bottom. Deep cylindrical bowl provides almost 100% capture of incident energy, regardless of whether it comes in the form of radiation of particle streams or in plasma clots. Multiple reflection from the walls leads to a more complete absorption of energy by the calorimeter. Developed taking into account the above experimental device is a system consisting of four calorimeters, located at the same distance from each other in the same plane (around the circle, 1200) and in the center. Thus, using this system, one can determine the distribution of the energy density of the plasma stream in the cross section, and when moving along the axis of the working chamber – the volume distribution of the accelerator. Used in this work, the calorimeters are cylindrical copper cups, to the end of which is soldered a thermocouple. As the pulse flow is directed perpendicular to the square of the calorimeter, particles of plasma with a high probability will be inside the glass and give the walls their energy. Temperature measurement is a thermocouple sensor connected to the input of the microvoltmeter. The energy transferred to the calorimeter by the plasma flow (in joules) per area of the bottom of the glass calorimeter is given by the formula

Q 

cmk U , S 41

(3.3)

where ΔU – change of the indication of the digital voltmeter; c – specific heat of copper; S-sectional area; m – mass of a calorimeter; k – thermocouple constant. The evaluation of the linearity of the scale and uniformity of readings of the calorimeters. Calibration was carried out for the three calorimeters (then one of them placed in the center). For this purpose, the holder with the calorimeters and the nearby thermometer illuminated by the radiation of the incandescent lamp with a reflector with a power of 500 watts. In this case, for all calorimeters falls almost identical radiation flux. For measurements used the same company APPA multimeters with a sensitivity of 1 mV.

Figure 3.4 – Experimental calorimeter

The peculiarity of these devices is that there is a possibility to measure both voltage and temperature with precision to 0.10 C. the Device determines the voltage with an accuracy of 0.02%. The measurements showed that for all calorimeters is observed almost linear dependence of stress on temperature in the range of 0-500 C. the Data presented in figure 3.5. The graph shows that the calorimeter No. 1 (upper line) at high temperatures gives an overestimation of about 10%. The testimony of two other practically identical (difference of not more than 2 %). 42

However, these differences are associated with different weights of calorimeters and do not affect the absolute readings, as in the formula (3.3) is substituted for the mass of each calorimeter individually. The mass of the calorimeter is measured on an analytical balance with high accuracy, other parameters can also be determined with accuracy not worse 5% As for the absolute value k, from a series of measurements (with thermal baths), its value amounted to (39±2) µv/0C. Since the product кΔU same temperature, the formula for determining the energy density is simplified. Thus, in the linear region 0-50 j/cm2 measurement error of the energy density of the device, will not exceed 10 %. N1 N2 N3

3,5 3,0

U,mV

2,5 2,0 1,5 1,0 0,5 0,0

20

30

40

50

60

0

T, C Figure 3.5 – Gradirovsky schedule for calorimeters 1, 2 and 3

In conclusion, we note that the absolute accuracy of the measurement devices high-speed plasma flows is not determined by technical reasons, and the method of measurement. Here the most vulnerable point is the interaction of the plasma with the surface of the calorimeter, when the plasma creates a shielding effect and some of the energy may not get inside the calorimeter. In some works it is 43

noted that to eliminate this effect should use cone calorimeters, which dissipate flow and prevent the formation of the layer, however, the effectiveness of this method has not been investigated.

3.4 Probe methods of investigation of pulsed plasma For studies used a miniature magnetic probe. Made the magnetic probe consisted of 5 turns of wire with diameter 0.12 mm, wound on a frame with a diameter of 1.5 mm. Coil mounted on the end tightly twisted wire, which was placed in a quartz tube with a diameter of 4 mm and a length of 60 cm, the Probe was mounted on a special holder which was placed between the coaxial electrodes, as shown in figure 3.6.

1 – the radial current, 2 probe, a 3.4 – external and inner coaxial electrode Figure 3.6 – Scheme of location of the magnetic probe in the interelectrode space

The ends of a winding were intertwined and removed outside; on escaping of a protecting tube they united to a 50-omny coaxial cable on which the signal was given to a measuring oscillograph. Ekvivalentnaya Square of the coil of the probe nS is equal to 0,26 cm2, and the inductance of L is 1,0 мкГн.At the same time L/R0 time constant about 2 nanoseconds, that is is very short for the considered experiment. As time during which changes of a magnetic field were considered was about 1 microsec, the passive integrating line-up with

44

RC = 50 Ohms 0,5 мкФ = 2,5 microsec was used.From here sensitivity of the probe V nS   200 мкВ / Гс B RC

This sensitivity provided the capability of connecting directly to an oscilloscope without the use of additional amplifiers with an acceptable signal/noise. Other probes with a large area (diameter 0.5 cm) was made to analyze the deviation of the plasma from the axial direction for the cut electrodes. It was made ring in which the diameter was located four identical magnetic coils with the windings 12, and used two dualchannel oscilloscope to monitor the deviation of the plasma flow from the system axis. The temperature of the plasma in pulsed plasma accelerators is not very high (~104 K), so that the electric and magnetic probes here can be successfully used. In respect of the electric probes are the most appropriate a single cylindrical probe and probe multigrid [90, Pp. 9497]. In the first case, the WAH probe is removed as an average of multiple measurements relating to one and the same phase discharge at different voltage on the probe. According to the obtained probe characteristics can define the parameters of both electronic and ionic components of the plasma. Difficulties of implementation of this method can be associated with a significant scatter of data, as the plasma stream generated by the accelerator may not be uniform along the length of the accelerator. Another predictable difficulty could be the melting of the probe after several measurements, because the energy density of more than 40 j/cm2 is critical for the surface of most construction materials. In addition, as shown in [92], a satisfactory mathematical model of the probe in a moving plasma can be obtained if the mean free path of particles exceeds the size of the probe. Otherwise, it is necessary to consider diffusion processes, and the possibility of shock waves. The calculations in this case is much more complicated. Less viable option for a moving plasma is the use of two-electrode probe consisting of a manifold and placed in front of them mesh. The role of this grid is to cut off the plasma electrons. To do this, it serves 45

a large negative potential. Electrons are repelled by the field mesh and the ions from the plasma pass through the cells to the manifold. The collector serves a positive potential, the inhibitory ions. By changing this potential, it is possible to obtain the delay curve of ion current. Manifold reach only those ions whose energy exceeds the retarding potential difference between the plasma and collector. Thus, in the case of a directional flow of ions curve delay represents the integral energy spectrum, from which graphical differentiation to obtain a differential spectrum. The value of total ion current on the probe we can estimate the ion density in the plasma. Changing the polarity of the potentials on the grid and the collector, you can select and perform the electronic component of plasma. Although two-electrode probe and allows to separately delay curves of the electrons and ions, it has the following disadvantages: high potential on the grid leads to a strong perturbation of the plasma.Though the two-electrode probe also allows to receive separately curve delays of electrons and ions, it has the following shortcomings: high potential on a grid leads to the strong indignation of plasma; insufficiently external and secondary emission from electrodes is suppressed. Therefore apply three more widely – and four-electrode probes, and sometimes and probes with a large number of electrodes. As already noted above, in the case of fast-moving plasma flows problem diagnosis become more challenging as the number of parameters is added to the directed velocity of plasma particles. Despite this, the parameters of such a plasma can be measured using existing theory probe diagnostics. Let us consider the use of this theory for experimental determination of the electron temperature and concentration. As you know, for diagnostics of plasma parameters can be used in particular single and double probes of cylindrical shape. These probes are placed directly in the plasma region, which is necessary to measure the concentration and temperature. This assumes that the distribution of electrons and ions energy is the Maxwell.Preliminary studies of current voltage characteristics of double probes conducted in [93], have shown that the current waveforms are difficult to analyze due to the high noise level. Thus, to measure parameters of the pulse plasma, it is expedient to use a single probe that creates less noise (the measurement scheme is presented in figure 3.7). The basic idea of probe measurements is that 46

the particle flux to the probe is determined by the presence of the shielding layer, the thickness of which is determined by the potential probe. The particles on the boundary layer of fall of the surrounding the probe region of the plasma, and this allows us to determine the temperature. For measurements in a moving plasma to use electric probes may be the case if the directional velocity of the electrons is much less heat to have time to form a shielding layer. Formed in pulsed plasma accelerators of the flows are directed velocities of about 105 m/s, which corresponds to electron temperature of about 0.1 eV.The electron temperature of the plasma is usually much above this value.

1 – single Langmuir probe 2 oscilloscope, 3 – power supply circuit of probe measurements Figure 3.7 – schematic diagram of measurement of parameters of plasma using a single Langmuir sandy

Therefore, at such flow rates the electron temperature in the plasma is not directional velocity, and heat and probe the theory, in principle, applicable. The ions, then they directed speed is above the thermal speed, and the use of classical probe theory can lead to large errors. Thus, for a plasma generated in a pulsed accelerator, the probe characteristic is in principle possible to determine only the electronic temperature and concentration. The temperature of the ions can be found by other methods, for example by broadening of spectral lines. In the studies I-V characteristics of the probe were determined as follows. With an oscilloscope determined the current through the 47

probe at certain points in time. Then built a series of current-voltage characteristics for a given time and determined the temperature and concentration of electrons.

3.5 Optical methods of investigation of pulsed plasma Radiation emitted by plasma sources, carries information about the chemical composition, temperature and physical processes occurring in them. This information is encoded in a relatively easily measured parameters of radiation power in some parts of the spectrum, the width and shape of the observed spectral lines [90, Pp. 165-166]. For the pulsed plasma flows is of particular interest to study specific features of formation of flux, its structure and composition. Conducting spectrometric studies of the pulsed plasma is associated with some difficulties, as they are very laborious and require large numbers of similar operations. However, this method is most informative for studies of plasma. Work on optical observations carried out with the spectrograph "STE 1" and the monochromator "MUM". As a Registrar radiation used digital camera for General spectrum analysis, film and a photomultiplier for quantitative measurements. Spectrograph "STE-1" has been calibrated in wavelength and intensity on the reference source (of mercury), with the famous lines: green line and yellow 5460,73 Å doublet 5769,60 5790,66 Å and Å. Calibration of the intensity was carried out with the filament lamp of SIRS.

48

4. THE FORMATION OF PLASMA FLOWS IN  ACCELERATOR CPU    4.1. Pulse voltage and current at different pressure The bulk of the work was completed on installation of the CPU30 with a cold long copper electrodes. Before each discharge chamber to the suction pressure of 0.133 PA (10-3 Torr). After that, depending on the task, the chamber pressure rose to values in the range of 0.05-5 Torr. This method allows you to set the same initial pressure before each shot. To register the current used oscilloscope UT3200. A series of oscillograms taken at a pressure of 5, 0.1, and 0.05 Torr and a voltage of 24 and 12 kV are shown in figure 4.1

Figure 4.1 – Waveform current at 5 Torr, 24 and 12 kV.

As can be seen from the drawings, the discharge accelerator is a damped aperiodic signal. The number of half-periods is almost independent of the initial pressure in the chamber. This suggests that the discharge period is determined by the inductance of the coaxial electrodes. The current period weakly increases of 1-2 µs, the amplitude of the current falls exponentially with a decrement of ~105. The amplitude of the current is determined by multiplying the voltage in volts at 11200 according to the formula (3.1) and in the range of 300-450 kA.

49

The presence of rapidly damped oscillations in the beginning of the sweep can be explained by reflection of the signal from the cable ends, which is typical for such measurements. Next, figure 4.4 shows the waveforms of voltage and current at various pressures. Draws attention to the following features of these curves. First, the line voltage is very indented. The curves of the current in the primary at time you can also notice the presence of fast oscillations, but since the Rogowski belt has a high self inductance, brokenness manifests itself not so much. In addition, it is seen that the current at the beginning of the discharge grows very quickly, reaching a value of 500 kA (figure 4.3, lower graph) over the time of 3 µs. In this case, the rate of rise of current will be 1.7 1011 A/C. Secondly, the tension in the first quarter of the discharge becomes more attached, and then falls. This behavior is connected, apparently, with the anomalous resistance of plasma during the initial moment of the discharge. In this case, the total resistance of the plasma dominates its ohmic resistance. As a result, the voltage at the discharge gap increases. In more detail, this effect is considered below in the analysis of experimental results.

a – 0.1 Torr, b – 0.05 Torr Figure 4.2 – Waveform voltage at 15 kV

Let us consider the dependence of the shape of the discharge current of the initial pressure in the chamber of the accelerator KPU30 at a constant voltage. Figure 4.3 shows the waveform of current at 20 kV, obtained at three different pressures of 5 Torr (a), 0.1 Torr (b) and 0.05 Torr (C, d). 50

As can be seen, at all pressures in the beginning of the interference signal is present in the form of a RF oscillation, which quickly fades. At the same time at 0.1 Torr and below the high frequency oscillations are also present in the signal of the discharge current.

а

б

в

г

a – 0.1 Torr, (b), g – 0.05 Torr. Figure 4.3 – Waveform current at 20 kV

4.2. The current-voltage characteristic of the accelerator The main characteristic of the accelerator is its current-voltage characteristic. To build a WAH dependence of discharge current on the voltage. Experimental data on the accelerator KPU-30 when using the continuous operation mode is shown in figure 4.4. As can be seen, the current-voltage characteristics of discharge in current range 150500 kA are virtually linear at all pressures. 51

Figure 4.4 – current-voltage characteristic accelerator KPU-30 at three different pressures

Next were obtained dependence of discharge current on the pressure. The result is presented in figure 4.5. Data current obtained at a constant voltage of 20 kV. The curve has a gently sloping maximum at about 0.2 Torr.

400

I, kA

350

300

250

0,01

0,1

1

10

P, Torr

Figure 4.5 – Dependence of the discharge current of the initial pressure

52

4.3. The flow rate at different pressures The flow velocity in the chamber is an important parameter showing the efficiency of acceleration. Waveform data from the magnetic probes, which were determined by the speed shown in figure 4.6. The results of experimental measurements are shown in table 4.1 and figure 4.7.

0.1 Torr Figure 4.6 – Waveform data, which were determined by the flow rate Table 4.1 Results of experimental measurements of the flow velocity zones Rogowski at base 17 cm Uзар., кВ 12 14 16 18 20 22 24 26

V· 106, см/с 0,1 Торр

0,05 Торр 1,8 ± 0,5 1,7 2,1 3,1 3,4 4,2 4,8 5,0

3,4 3,4 4,8 5,6

53

5 Тор

3,2

In accordance with figure 4.7, the dependence of speed on voltage is nonlinear. Maximum flow rate at a voltage of 26 kV was (5,6±0,3) cm/µs. In addition, there is a noticeable difference of the flow velocity from the pressure.

Figure 4.7 – the Dependence of flow rate on the voltage at different pressures

The determination of the velocity of plasma flow and energy of the particles for accelerator KPU-5 was conducted using two photomultiplier tube, located opposite the diagnostic cracks along the length of the chamber. Signals from the photomultiplier were recorded using a dual channel storage oscilloscope S8-14. The value of the velocity was (4,6±0,1) cm/µs at an accelerating voltage of 3 kV. As can be seen, the experimental value of flow rate for the accelerator is lower than for the CPU, and this is connected, primarily, with the magnitude of discharge current.

4.4. Dynamics of thin current sheets and magnetic fields The distribution of magnetic field was shot using magnetic probes and Rogowski belts (with the nozzle). Waveform data from the magnetic probes, taken at a distance of 26 cm from the end of the outer electrode shown in figure 4.8. 54

When the pressure probe detects the high frequency oscillations of the derivative of the magnetic field, get rid of them by connecting the integrating chain. To start investigated the frequency spectrum of these oscillations. Fourier images of the signal from the magnetic sensor 5 turns are parallel to the coaxial axis at 26 cm from the end of the outer electrode, when the conversion frequency of 1,250 MHz is shown in figure 4.9. A pressure of 0.05 Torr, a voltage of 15 kV.

0.05 Torr

1 Тоrr

Figure 4.8 – Waveform derivative of the magnetic field

Figure 4.9 – frequency images of the signal from the magnetic probe at 0.05 Torr

55

As can be seen, the oscillations represent a broadband signal in the range of 2-3 MHz. Further, figure 4.10 shows the evolution of the signal from the probe using different values of the constant of integration of the probe.

Thor 0.05 to 0.25 µs

0.05 Torr of 2.74 µs

1 Torr of 2.74 µs Figure 4.10 – Waveforms of the magnetic field at different pressures

Next, we consider a series of oscillograms of the magnetic field along the coaxial axis is shown in figure 4.11. With the help of magnetic probes were obtained by waveform Bφ(t) for different positions of the probe in the middle between the cylindrical electrodes at distances from 1 to 40 cm from the beginning of the outer electrode. Discharges made under the same conditions: the voltage on the 56

capacitors of 20 kV and a pressure of 0.1 and 1 Torr. The results showed good reproducibility of signal from digit to digit. From the waveforms it can be seen that the magnetic field moves forward along the z axis. The average speed of the front signal was 2.5 cm/ľs, which is slightly lower than the earlier measurements. The slew rate of the front is about 1 µs, so the thickness of the current layer, which forms the discharge current is 2-3 cm. More accurate data on the measurement of the instantaneous and the average velocity of the magnetic field in the accelerator channel is shown in tables 4.2 – 4.4.

1cm from the end

10 cm

25 cm

40 cm

Figure 4.11 – the Waveform of the magnetic field at 0.1 Torr

Next, figure 4.12 presents a series of oscillograms of the magnetic field at 1 Torr. 57

Table 4.2 Speed magnetic field at 0.1 Torr, measured in the middle of the coax Δz, см 40-34 34-25 25-22 22-19 19-16 16-13 13-10 10-7 7-4

zср, см 37 29,5 23,5 20,5 17,5 14,5 11,5 8,5 5,5

Δt, мкс 4-1,5 5,5-4 6,5-5,5 7,5-6,5 8,5-7,5 9-8,5 10,5-9 13-10,5 11,5-13

υср, см/ мкс 2,4 6,0 3,0 3,0 3,0 2,0 2,0 1,2 2,0

1 cm

10 сm

25 сm

40 сm

υ, см/ мкс 6,7 4,0 4,5 4,2 4,1 4,0 4,1 3,8 3,7

Figure 4.12 the Waveform of the magnetic field at 1 Torr

58

The average front velocity of the signal was 2.3 cm/µs, which is almost the same speed at a pressure of 0.1 Torr. The slew rate of the front is about 2 µs, therefore, the thickness of the current layer, which forms the discharge current, is 4-5 cm, the speed of the current layer is only weakly dependent on pressure. Table 4.3 the Speed of the magnetic field at 1 Torr, measured in the middle of the coax Δz, см 40-34 34-28 28-25 25-22 22-19 19-16 16-13 13-10 10-7 7-4

zср, см 37 31 26,5 23,5 20,5 17,5 14,5 11,5 8,5 5,5

Δt, мкс 2 2,5 1,5 2,5 0,5 2 1 1,5 3,5 4

υ, см/мкс 3,0 2,4 2,0 1,2 6,0 1,5 3,0 2,0 0,9 0,8

Table 4.4 Speed magnetic field at 1 Torr, measured at the outer electrode Δz, см 43-40 40-37 37-34 34-31 31-28 28-25 25-22 22-19 19-16 16-13 13-10 10-7 7-4

zср, см 41,5 38,5 35,5 32,5 29.5 26,5 23,5 20,5 17,5 14,5 11,5 8,5 5,5

Δt, мкс 6.0-5,0 7,0-6,0 8,0-7,0 9,5-8 11,5-9,5 12-11,5 13,5-12 15-13,5 19-15 20,5-19 21,5-20,5 25-21,5 26-25

59

υcp, см/мкс 3,0 3,0 3,0 2,0 1,5 6 2 2 1,0 2,0 3,0 0,9 3

υ, см/мкс 1.4 1.7 1.9 2.0 2.0 1.9 2.0 2.0 2.0 1.8 1.8 1.7 1.7

Further, in figure 4.13 and 4.14 shows a graph of the amplitude of the magnetic field in the interelectrode space and the average velocity of the plasma.

Figure 4.13 – Dependence of the magnetic field on the distance in the interelectrode space at pressures of 0.1 and 1 Torr

Figure 4.14 – Dependence of the average speed of the magnetic field on the distance at different pressures

60

A clear picture of the process of formation of the plasma allows the study of current distribution in the accelerator channel. This field measurement was carried out every 3 cm along the length of the electrodes, under the assumption of axial symmetry of the discharge. To recalculate the voltage probe in the magnetic field values were used, the ratio НkG=0,038UmV. Further, in the figures 4.15-4.16 shows the current distribution in the interelectrode space of the CPU. In accordance with figures 4.15 and 4.16, in the solid fill pattern density distribution of plasma in a coaxial electrode system is changed when reaching the boundary values of the gas density of order 1016 cm-3, which corresponds to 0.1 Torr, passing from the compact to the diffuse character. Higher edge density in the accelerator channel formed plasma flow with predominantly radial direction of streamlines, moving, as was shown above, with a constant speed of about 3 cm/µs. At the same time, below this density is formed by the flow with a diffuse current distribution, whose rate is several times higher. The word diffuse here means that the amplitude of the magnetic field varies continuously in space, i.e. it is diffuse, in analogy with the diffusion of particles in gases. However, if a physical cause of diffusion in gases is the collision of the molecules during their motion in the plasma to such a picture leads, conversely, the absence of particle collisions at distances of the order of system size. Here we have an analogy with the diffusion field. It is clear that the similar behavior of the plasma significantly affects the flow pattern and its velocity.

Figure 4.15 – map of the current distribution in the interelectrode space of the CPU 30 at a pressure of 1 Torr

61

Figure 4.16 – map of the current distribution in the interelectrode space of the CPU 30 at a pressure of 0.1 Torr

4.5. The formation of the currents of the removal and erosion of the electrodes Above was investigated area inside the coax, but no less important is the compression zone, located by slice electrodes. In the presence of currents of the removal in this zone is possible to focus the lines of force of the current. Consider first the data on electric probes is shown in figure 4.17. Two probes were located at a distance of 10 cm along the axis of the system. The discharge voltage constant and equal to 18 kV. In accordance with figure 4.17, the signals are identical for both probes, regardless of the pressure. Moreover, it is impossible to determine the speed, as the time difference is less than 1 µs. This situation can be, if the probes are in the zone of turbulent or diffusive motion, i.e. the motion of the plasma in directions perpendicular and parallel to the axis are equally probable. More understandable information about the structure of the currents in the area directly adjacent to the end face of the outer electrode, given current measurements of the removal using a miniature Rogowski belts. These results are shown in the following figures. In the figure 4.18. shows a diagram, which made the measurement. Rogowski loop located on the three lines on the edge, in the center and in the middle of the axial axis. Distance from the end face of the Central electrode was changed through one centimeter. Thus, getting the series of waveforms, which counted the current density and built lines of equal current.

62

а

б

в

г

а – 0,05 Тоrr, б – 0,1 Тоrr, в – 1 Тоrr, г – 5 Тоrr Figure 4.17 – Signals from the electrical probes at 18 kV

----- – the line along which measurements were conducted Figure 4.18 diagram of the measurements for the cut electrodes

The following shows waveforms of current at the system axis, at a distance of 1 cm from the end face of the inner electrode, but at two 63

different pressures. It is seen that at 0.1 Torr current signal appears after a period after the beginning of the discharge current (figure 4.19.), and at 1 Torr, almost immediately, but opposite amplitude.

5 kA/cm2, 0.1 Torr

2.5 kA/cm2 1 Torr

Figure 4.19 – strong current at 0.1 and 1 Torr at the end of the internal electrode

Further, in figure 4.20, when the tip moves from the axis to the edge of the coax signal changes the polarity. Since the cross section of the probe is sufficiently small, this suggests that the current (more precisely, the axial component of the current) changes its direction. That is, the current lines go from the end of the center electrode and come to the edge of the outer electrode, making a semicircle. Picture of the formation of currents of removal will become clearer if we turn to the photographs of the electrode system of the accelerator, shown in figure 4.21. In figure 4.21 a, the area of the lateral part of the Central electrode (cylinder surface) contains small traces of erosion. At the same time, areas at the ends of the Central electrode (the beginning and the end) melted, indicating the presence of large electronic currents to these areas. Several other pattern of erosion was observed on the same accelerator, the Communist party, studied at IAE them. I. V. Kurchatov [83, Pp. 412-413], are shown for comparison in figure 4.21 b. Unlike our case, there are different types of erosion with the formation of etching figures, bands, etc. were subjected to mainly a lateral surface of the electrode, while the outer end is also melted.

64

а

b

с A – around the outer electrode, B – is in the middle between the outer and inner electrode, С – on coaxial axis Figure 4.20 – current Signals at different distances from the axis of the system

a

b

A – electrode system CPU IETP, B – the Central electrode of the Communist party IAE them. I. V. Kurchatov Figure 4.21 – Erosion electrode of the Communist party

65

These facts indicate that during the discharge to the surface (or surfaces) of the Central electrode flowing large electron currents that cause the melting. In this case, the plasma must have a significant erosive component. The proof of this fact is figure 4.22 shows a photograph of a plate of aluminum, exposed at a distance of about 10 cm from the end of the electrode. In this plate several shots were fired at a pressure of 0.05 Torr. As can be seen, the surface of the plate covered with a thin layer of copper.

Figure 4.22 – The photo of the plate from aluminum put opposite to the central electrode

On the basis of set of the experimental datas the scheme of currents of carrying out in the accelerator KPU-30 shown in the figure 4.23 is constructed.

Figure 4.23 – diagram of the formation of currents of the removal

66

In the diagram in the upper part shows the line current (electrons and ions) at a pressure of 0.1 Torr, and at the bottom at a pressure of 1 Torr. Since ions are heavy particles, their motion occurs along the electrode, practically in a straight line. However, due to the presence of currents of electrons ions are forced to shrink to the axis of the system, as there is a high density of negative charge. Because of this some distance from the end of the Central electrode should be the focus.

4.6. The study of field compression and plasma focus Thin enough focusing effect can be seen only with special measurements. It is obvious that the focus area should be the maximum value of energy density flux, as there will be the greatest current density. On the location of focus has a significant impact, the pressure in the working chamber, as shown above. In this regard, has done a careful measurement of the area of compression flow and the position of the focusing point of the thread. The scope of compression have been investigated in a series of experiments using steel grids, which are placed in a plasma conduit of the accelerator at different distances from the edge of the electrodes (figure 4.24). Data are given for three pressure values of 0.1, 0.5 and 0.05 Torr. The charge voltage was 20 kV. Experiments have shown that the cross section of the plasma flow with a distance increasing in diameter from 5 to 8 cm (figure 4.25). Within these limits there is a formation of uniformly irradiated spots on the surface of the exposed grids. In this regard, it can be assumed that the formation of the plasma focus (PF) in the accelerator KPU-30 occurs within a certain distance from the Central electrode. Next, we explore the density of energy flow at the point of focus. First, the energy density was measured for accelerator KPU-30 depending on the distance from the end face of the outer electrode, fixing the position of the calorimeter at intervals of 2.5 cm using a positioning device. For each position of the calorimeter was carried out by three shots. The discharge was performed at a voltage of 20 kV on the electrodes of the accelerator KPU-30. A voltage value high enough to capture the minimum value of the energy density flux in the range of 5-45 j/cm2, which can be realized at a pressure of 0.2 Torr. Selection pressure due to the fact that at 0.2 Torr is observed in the 67

transition phase from the compact to the diffuse flux, which is of interest as the most common mode of operation of the accelerator. The purpose of these measurements was to find out what is the energy distribution of the plasma stream in the cross section of the chamber and along the length of the accelerator. The results of the measurements are presented in table 4.7.

2 сm

4 сm

8 сm

12 сm

Figure 4.24 – Section of the plasma stream, depending on the distance to cutoff the external electrode P=0.1 Torr

68

Figure 4.25 – variation in the diameter of the plasma flow with a distance

Table 4.7 Results of calorimetric measurements Uзаряд, кВ

P, Торр

L, см

20

0.2

2.5

20

0.2

5

20

0.2

7.5

20

0.2

10

20

0.2

12.5

20

0.2

15

N1 32.1 34.48 37.5 31.2 32.4 34.7 21.8 27.1 27.9 23.9 21.9 23.6 14.9 15.9 18.9 14.7 8.5

69

Q, Дж/см2 N2 23.8 26.0 26.8 22.2 25.8 23.5 22.8 23.7 24.0 21.5 20.8 19.1 15.1 19.6 18 12.5 7.6

N3 42.2 42.5 42.7 40.6 38.4 36.9 29.3 34.8 34.8 28.2 29.2 29.7 22.1 21.2 21.9 16.5 9.4

Noteworthy is the fact that the testimony of the third calorimeter is always larger than the first, and the first is greater than the second. Such a systematic difference between the readings caused by the different sensitivity of the calorimeters, which is determined by its mass. Since the calorimeters accurately centered (i.e., they are located at the same distance from the system axis), the axial symmetry of the plasma is maintained. Figure 4.26 shows the dependence of the energy density from distances of 2-16 cm from the end of the outer electrode constructed according to the readings of the calorimeters in one shot (discharge) in the accelerator. It is seen that a nonlinearity of the power density values along the length of the coax, but there is a General downward trend. At the same time, if we take the average value of the readings of each calorimeter by three shots at fixed discharge parameters (figure 4.27), the nonlinearity appears much weaker. This suggests that every single shot readings of the calorimeters may vary slightly. The reason for this, in our opinion, the local inhomogeneity of plasma flow on the cross section due to the presence of instability. In addition, some influence may provide the holder of the calorimeter, covering the flow cross section. If we take the average value of three measurements from three calorimeters, we get a smoothly falling curve. This dependence is shown in figure 4.28. So, the energy density of the plasma flow falls down from 35 to 12 j/cm2 as the distance from the cut edge of the outer electrode almost evenly. Hence, the plasma density also decreases, which indicates expansion of the flow as the distance from the electrodes. Thus, these measurements confirm the results of the above grid measurements of the flow. Thus, the energy density on the periphery, at a distance of about 3 cm from the axis of the system tends to a uniform decrease along the length of the accelerator. From General considerations it is clear that the energy should decrease as the distance from the end of the electrode and, indeed, at a distance of more than 14 cm readings of the calorimeters are relatively small and almost equal.

70

Figure 4.26 – Dependence of energy density on distance for a single testimony for three calorimeters

Figure 4.27 – Dependence of energy density on distance in three dimensions for each of the calorimeter

71

Figure 4.28 – Averaged over three calorimeters dependence of the density energy from a distance

Above were the results of the study of the distribution of energy density in the three calorimeters. Also of interest is information on the axial part of the system. So you installed an optional fourth calorimeter in the Central part of the holder. Under this system, it is possible to follow the process of compression plasma flow, as discussed in paragraph 4.5, which describes experiments with a Rogowski belt. Let us consider the dependence of the energy density along the chamber depending on the charging voltage. The schedule of dependence for Central calorimeter is shown in figure 4.29. In General, at any available point along the camera, the dependence of the energy of the voltage are directly proportional. Small deviations are observed at high voltages. To study the density distribution of the plasma flow on the axis of the accelerator and the calorimeter was mounted at a different distance from the end face of the outer electrode. The graph of the calorimeter, located in the center, as shown in figure 4.30. The measurements were carried out at various voltages from 10 to 26 kV. As the graph shows, on the dependence of the energy density of the distance there is a gentle maximum in the region of 8-10 cm the origin of the maximum is connected, apparently, with the formation of the plasma focus, as mentioned above. 72

Figure 4.29 – Dependence of the energy density from the tension at different distances

Figure 4.30 – Change in the energy density along the chamber depending on voltage

73

Figure 4.31 shows the dependence of energy density on distance for the system of the four calorimeters. It is seen that the peripheral calorimeters, arranged in a circle through 1200, show a decrease in the value of the energy density from distance. At the same time, indications of the Central calorimeter, located on the axis of the coax, in the region of 8-10 cm have a significant maximum. Such behavior of the values of the energy density confirms obtained using magnetic probes, the fact of the compression plasma flow to the axis of the system. In addition, obtained new non-trivial result, namely, a significant increase of energy density on axis at a distance of 8-12 see This result confirms the assumption made above about the formation of the plasma focus, when the expense of the removal of lines for current slice electrodes are focusing the ions, and in this place should notice an increase in energy density. Obviously, compression of the plasma in the radial direction of the energy reaching the calorimeter, located in the periphery (that is, not in the center), decreases and the system axis increases, as observed in the experiment.

Figure 4.31 – the Dependence of energy density on distance for the system of four calorimeters

74

4.7. The plasma flow pattern for the cut electrodes In order to clarify the features of formation of plasma flow in the chamber behind the cut electrodes, i.e. in the plasma conduit, depending on the initial pressure, a series of experiments with a Rogowski belt, which is located inside the chamber. First, we determined the current flow through the internal zone of 9 cm in diameter, depending on the voltage of the discharge at initial pressures of 0.05, 0.1, 0.5 and 5 Torr. The discharges are produced at voltages of 12 and 20 kV. Typical waveforms of the signals shown in figure 4.32. If we consider the pressure dependence on all the oscillograms obtained at 0.1 Torr and below, there are negative and positive peaks, separated in time. In the analysis of these waveforms noteworthy following. The time shift between these peaks decreases with increasing distance from 12-15 µs 20 cm to 1-2 µs for 50 see Also, the shift between the peaks decreases with increasing pressure. In General, when you remove from the edge of the electrode peaks become narrower. The amplitude peaks at the distance from the cutoff electrode behaves. Namely, it is maximal at a distance of 40 cm from the plasma electrode. Data on the amplitude are given in table 4.8 and figure 4.33. About such behavior signals Express the following considerations. The Rogowski belt, and located perpendicular to theflow, needs to fix the axial component of the current passing through its cross section. As we know, plasma is quasi-neutral in General, so with the passage of plasma flow through a section of belt of negative and positive current components in the sum give zero, and we should not recordany signal. However, we observe two peaks of opposite polarity. If we assume that the positive peaks in the waveform are associated with ion current, a negative e, then each half-cycle of discharge current is generated a plasma flow consisting of a bundle of a single charge. Then, these clots are separated in space. We can assume that the origin of these peaks is due to the removal of the currents that flow back and forth. In this case, the peaks on the waveform correspond to different polarity at the electrodes, i.e. in each half-cycle of discharge current flows in one direction. However, in this case, we actually break quasineutrality because the ions can't move back. 75

Table 4.8 Results of measurement of current in the plasma from a distance Component Put., v Neg., v Neg., v

3 cm 0,2 5,0 4

20 cm 3,0 8,5 8,2

30 cm 3,2 7,0 5,8

40 cm 13,0 30,0 4

50 cm 12,5 24,0 10

Pressure 0,05 Torr 0,05 Torr 0,1 Torr

20 сm 0,05 Torr Figure 4.32 – the dependence of the current in the plasma pressure at the distance of 20 cm from the plasma electrode 40 35

I+ I-

30

I-, I+ V

25 20 15 10 5 0

10

20

30

40

50

60

L, cm

Figure 4.33 – Dependence of the amplitude peaks from a distance

76

In figure 4.33, the amplitude of the current at a distance of 50 cm increases. Assuming bunches with different charges that may be associated with a decrease in the dispersion of speeds at inhibition of clot, as the area under the curve of the current remains constant. Assuming currents of the removal of it can be explained by the geometry of the current lines, i.e. focusing the beam at a distance of 40-50 cm at a pressure of 0.05 Torr. However, in this case, should be the focus and at a distance of 10 cm for the beam generated at 0.1 Torr, which is not observed. In this regard, was conducted more thorough experiments with the Rogowski belt is 9 cm in diameter, installed every 5 cm of This zone, the diameter of which is equal to the diameter of the outer electrode, disposed of from 5 to 75 cm from the end of the electrode. All the shots were performed at a fixed voltage on the capacitor battery is 20 kV and the two pressures of 0.05 and 0.1 Torr. In this way were obtained a series of waveforms, and figure 4.34 shows a typical pattern

0,05 Тоrr

0,1 Тorr

Figure 4.34 – Waveform current at a distance of 5 and 40cm from the end of the outer electrode

The results of measuring the amplitude of the first peak distances are shown in table 4.9.

77

Table 4.9 results of the measurements of current from a distance Distance Pressure 0,1 Тоrr 0,05 Тоrr 0,04 Тоrr

5сm

15 сm

20 сm

30 сm

40 cm

50 сm

60 сm

50 v 45 v

58 v 57 v

40 v 58 v

19 v 35 v

9v 30 v

3v 25 v 26 v

3v 19 v 14 v

As the number of turns of the belt is equal to 528, and the belt area of 64 cm2, for calculating the current density multiply the readings on the oscilloscope by 8.25. A graph of current density against distance is shown in figure 4.35.

Figure 4.35 –dependence of the current density on the axial axis of the accelerator

Thus, according to the amplitude of the current is indeed maximum at some distance from the end face of the outer electrode. Moreover, with increasing pressure, the maximum point is moved closer to the electrode. The results of the experiments indicate that we are dealing with bias currents that are focused on the axis of the system depending on the pressure at different distance. 78

4.8. The energy density at different pressures To determine the conditions for maximum energy starred dependence of the calorimeter from the pressure in the working chamber of the accelerator. This dependence is presented in figure 4.36. The calorimeter was installed at a distance of   10 cm from the edge of the electrodes. The graph shows that the maximum energy deposition in the CPU is implemented with the pressure of the working gas P = 1,5 · 10–2 Torr. The maximum energy release amounted to Q = 48 j/cm2.

Figure 4.36 – Dependence of energy release from the pressure at a constant voltage

To determine the conditions for maximum energy of the accelerator KPU-5 starred dependence of the calorimeter from the pressure. The dependence is shown in figure 4.37. The calorimeter was installed at a distance of 14 cm from the plasma electrode. Removed the dependency of energy density on the distance from the end electrodes and the voltage. A graph of the energy density Q from the voltage obtained for the CPU-30 in the solid content with operating pressures of 0.04, 0.1, and 0.5 Torr is presented in figure 4.53. As can be seen, the maximum value of the energy density at a pressure of 0.04 Torr is 45 j/cm2 , while at 0.5 Torr, this value is three times less. 79

Figure 4.37 – Dependence of the energy density of the operating pressure

Mode with pulse overlap, a similar graph was constructed for different gases: N, Ar, He (figure 4.38). As can be seen, in this mode, the energy density is determined by the atomic mass of the accelerated gas. The maximum value of energy density for argon is about 90 j/cm2, which is almost two times higher compared to the previous regime. This difference is due to the fact that the mode with a pulse overlap of the heavy ions are accelerated in a vacuum, so their kinetic energy is higher

Figure 4.38 – Dependence of Q on the voltage in the mode with solid fill

80

Figure 4.39 – Dependence of the density of energy flow from pressure mode with pulse overlap

4.9. Plasma diagnostics with electric probe Next, we consider data for the determination of plasma parameters the probe method. As electric single Langmuir probe was used a cylindrical electrode made of steel with a length of 19 mm and a diameter of 1.8 mm. by Changing the potential difference between the probe and the grounded outer casing and ISP and determining a probe current, which is obtained as the waveform (figure 4.40 a, b, C). The chamber pressure was 0.05 Torr.

а) 0 V

б)+50 V

в) -50 V

The coefficient of variation 10 V/div Figure 4.40 – Waveform data from Langmuir probe for the delivery of capacity

81

From the waveforms were obtained voltage-current characteristic (figure 4.41). Of WAH, using the ratio dV kT  e  Te d ln I e

,

you can calculate the electron temperature. According to the dependence of the logarithm of the current from a potential probe for electron temperature was obtained the value Т = (50 10) eV. The average thermal velocity for electrons at this temperature is 2·106 m/s, which is two orders of magnitude above directed. Using the found value of saturation current, it is easy to calculate the concentration of the charged particles I se , ne  0,52  S  e   e where Ise is the electronic saturation current, S a is the area of the probe, e is electron charge, ve is the average thermal velocity of electrons. Estimates show that the electron concentration is 1,5·1012см-3. The concentration value is in accordance with the data of other authors obtained on other installations with a low initial pressure in the chamber.

Figure 4.41 – Voltage characteristic of a single Langmuir probe

82

4.10. Spectroscopy of plasma flow Previous investigations on plasma diagnostics probe methods and zones Rogowski gave some information about the features of formation of plasma in the accelerator channel, but for a full explanation of pattern formation of plasma requires additional research using other methods, in particular optical. Experiments were performed on a pulsed plasma accelerator CPU mode with continuous filling of the working gas. The discharges are produced at a fixed voltage of 20 kV and a constant pressure of 0.08 Torr. For the comparative analysis used discharges in air and argon. To receive argon plasma at first the installation was evacuated to 0.01 Torr and then was filled with argon to 1 Torr and the pressure was lowered to 0.08 Torr. The spectra during the discharge in the environment, the residual air and argon. Photographing all of the spectra were performed with a fixed camera position and exposure. The obtained pictures are shown in figure 4.42. Visual analysis of these spectra allows to conclude that the position of several bright stripes in the different sites (vertical lines) remains unchanged. If in the spectrum of air contains a small number of distinguishable lines, the range of argon contains a large variety of closely spaced lines. The presence of the ever-present lines in both spectra are due, most likely, the radiation of impurities in the plasma, as their intensity does not depend on the pressure of residual air. Impurities can occur as a result of erosion of the electrodes, interelectrode insulator or the chamber wall. As shown by our study [94], mainly impurity is copper and carbon as a product of erosion of the electrode and insert plexiglass accelerator. It should be noted that the captured spectra contain also solid continuum. The emergence of a continuous spectrum caused, most likely, characteristic radiation of electrons generated at the ends of the electrodes.

83

а

б

в

Figure 4.42 – Spectra, taken at a pressure of 0.08 Torr. a – mercury, b –air plasma, in argon plasma

Integrated picture of the plasma in the shooting process shown in Fig. 4.43. The picture was taken by the end of the accelerator while the shutter is open in a dark room. It is seen that the glow plasma fills the entire space of the discharge chamber (diameter 16 cm), to see if there is any localization in the form of cords and other instabilities characteristic of plasma is not possible. At the same time, irradiation of nets set across the plasma flow showed that the diameter of the fused under the action of the flow region does not exceed 10 cm, However, these measurements were conducted at a distance of not more than 20 cm from the end electrodes. As is known, the compressed plasma flow, formed in the area of focus of the installation, eventually expanding. In addition, the glow discharge pulse is reflected from the walls of the chamber, we observe the effect uniform filling. 84

Figure 4.43 – Photo of pulsed discharge in coaxial accelerator.

Thus, studies have shown that formed in the chamber plasma radiates good, which testifies to a sufficiently high temperature of the flow. Spectral observations allow to conclude that in the plasma contains certain amount of impurities, the amount of which may increase when the pressure decreases and depends on the gas type.

5. THE ACCELERATION OF THE PLASMA IN  PULSE SYSTEMS    5.1. Calculation of plasma parameters on the basis of electrodynamic model For the ISP with a coaxial electrode geometry of the magnetic field H is mainly concentrated in the space between the electrodes and is determined according to the law, H

I 2 r

where I – is the current flowing in the circuit, r -is the radius. Let the field inside the conductors is missing. The magnetic energy WM in the interelectrode space is W

M

 



H 2 I 2  2 d  2 2 (2 ) 2





R

dz

0

2



R1

dr  I 2 R2 L I ln   1 r R1 4 2

2

. Inductance per unit length of the coaxial accelerator is determined by the formula  I 2  R2 , (5.1) L1  ln 2 R1 where R2 – the inner radius of the outer electrode, R1 -is the outer radius of the inner electrode, ℓ- is the length of the electrode system, μ=4π·107 GN/m – magnetic constant. Then, per unit length of the accelerator has a distributed inductance b

 2

ln

R2 Гн .  2,18  10 7 R1 м

86

(5.2)

We rewrite the equations of plasma acceleration in a simple, idealized system in which neglect energy dissipation in current jumper, leaving only ohmic heating m0

d 2 z I 2 dL ,  dt 2 2 dz

dz , dt I   C0

(5.3) dV . dt

The equation of motion we write in compact form by entering current

m0

d 2z b 2  I . dt 2 2

(5.4)

The equation of current of a non-member with energy dissipation d 2 ( L0  bz ) I dI 1  R0  0. 2 dt dt C0 I

(5.5)

The initial conditions for this system dz  0; dt

z  0;

I  0;

V  V0 .

If L0 >> bz, equation (5.5) can be studied analytically. Have

L0

dI 1 d 2I  R0  I 0. 2 dt dt C0

Compose the characteristic equation

L0r 2  R0r  87

1 0, C0

(5.6)

which has two roots

r1, 2  

R0  2 L0

R02 1 .  2 4 L0 C 0 L0

(5.7)

Usually the ohmic resistance of the plasma is small, that is,

R02 1 .  2 4 L0 C0 L0

(5.8)

We introduce the natural frequency of the circuit

0 

1 L0 C 0

and a damping ratio of

 

R0 . 2L0

Then the solution for the current write in the form

I  Ae  (  i  0 ) t  Be  (  i  0 ) t . Taking into account the initial conditions we get the following solution

I  C0V0 0 e t sin  0t , V  V0 e t cos  0t .

(5.9)

If there is no ohmic heating, the current will oscillate with a constant frequency

I  C0V00 sin0t . 88

However, we are interested in the amplitude and the initial values for the estimates of the current and speed of the jumper. If R 0  Imax  C0V00 . Calculate the discharge current for the accelerator while the above parameters and voltage of 20 kV

I max  20  103

7  10 4  1МА. 2  10 7

Let in accordance with the above calculations

b  2,18 10 7 Гн / м

. Then the magnetic force

Fм 

If ,

2,18107 12 10  1104 Н . 2

S  1см2 then the strength of the magnetic pressure plasma Р м  1  10 8

Н  1000 атм . м2

Next, we calculate the velocity of the current layer in the initial time, when t is small. You can use the decomposition in a number

 3 t3  I  C0V00 sin 0t  C0V00  0t  0   C0V002t . 3!   Substituting this in the equation of motion are m0

Интегрируемпри t  0 ,

d 2z b 2 2 4 2 .  C0V0 0 t dt2 2

dz  z  0 получим dt

89

dz bC 02V02 04 t 3 ,  dt m0 6 z

(5.10)

dz  (t / 4 ) . dt

To calculate the speed at a known discharge circuit parameters need to know the mass of the accelerated bunch. With solid filling, obviously, the mass of the clot will continue to grow as the movement of a clot along the axial axis, if the thickness of the skin layer is sufficiently small. Thus, the calculation according to the formula (5.10) can hold only for a compact mode of the bunch, but for the diffuse mode, the concept of mass loses its meaning. However, at constant mass, in principle, possible to calculate, which is shown in figure 5.1. Figure 5.2 shows a graph obtained by measuring the flow rate inside the coax method of magnetic probes. As can be seen, the theoretical curve and the experimental dependence are somewhat different. At the beginning of the discharge, or rather in the first quarter of the period to 3.5 µs, the speed should increase as Amirova force is proportional to the square of the current. Unfortunately, at this stage there is no experimental data to compare with. Further, in the third quarter, and that period of 7-10 µs, we see the growth rate that corresponds to the theory. Of course, without regard to the forces of braking and energy dissipation theoretical curve is suitable only for the calculation on initial stage of the movement, and this is the first quarter of the period. Further, the experimental graphs show the speed limit. At a pressure of 0.1 Torr restriction comes at the end of the first half cycle, and at 1 Torr – at the end of the second period. The speed limitation is due to the release of a clot on the end of the electrode. In fact, at 0.1 Torr the speed reaches a maximum value at 10 µs. If the average flow rate to take 3.5-4 cm/µs, during this time the clot will move the distance equal to the length of the Central electrode. For pressure of 1 Torr, this corresponds to 2 cm/µs and 20 µs. Thus, at the end of the electrode, the clot is braked and then accelerated. But the more important conclusion is that in the diffuse mode, the clot reaches a maximum speed at the end of the electrode, and in compact mode on the middle. In the first case, the 90

clot comes out of the coax at a negative polarity of the Central electrode, in the second case, at zero polarity. This may have some influence on the erosion of electrodes, because it turns out that at low pressure of 0.1 Torr, the Central electrode should emit current. As to the nature of the issue, it is likely that secondary electron emission.

1200

1000

V, (m/s)*100

800

600

400

200

0 1

2

3

t, (s)*10

4

5

-6

Figure 5.1 – Dependence of speed from time to time calculated according to the formula (5.10)

91

3,5 3,0

v, cm/s

2,5 2,0 1,5 1,0

0,1 Torr 1 Torr

0,5 0,0 0

2

4

6

8

10

12

14

16

18

20

22

24

t, s

Figure 5.2 – the Dependence of speed on time, obtained experimentally

Make an assessment of the energy of the ions, since we already know the flow rate. For accelerator KPU will accept the maximum velocity of ions is equal to 100 km/s. based On the speed, calculate the kinetic energy of the ions according to known formula Е 

1 m 2 . 2

Taking for nitrogen ions mass equal to 14.e.m. get 14 ·1,6 10-27 kg = 22,4 ·10-27 kg. Then for the energy of the ions of the CPU will get a value of 700 eV. Carry out the same calculations for the accelerator KPU-5, taking the value of velocity 50 km/s. When using the above mass of the ion energy for the CPU-5 will be four times less and is 150 eV.

92

Further, it is possible to estimate the kinetic energy of the flow, if you know the mass of the accelerated gas. Calculate the mass of the accelerated gas for ISP. The gas pressure in the working chamber of the accelerator is determined by the ratio P = nkT. The concentration of gas at a pressure of 0.1 Torr is 3·1015 сm-3 The amount accelerated gas take is equal to the volume of the interelectrode space. Its calculated by the formula V = LS, where S- is the cross – sectional area of the outer electrode, L- is the length of the electrode. The total number of particles N=nV will be 1020. Then, with one ion energy 700 eV kinetic energy of the flow is 1000 j, then the energy density of the flow is of the order of 10 j/cm2

5.2. Conditions of effective plasma acceleration in coaxial The current mass of the jumper is determined by the mass of the captured gas. Assuming a full of raking gas current jumper is the mass of gas z

m( z)   M i n( z)S ( z)dz , 0





where Mi – ion mass, S   R z  r z -is the area of capture. Described above (section 1) Electromechanical system has two degrees of freedom. The Lagrangian of such a system 2

2

~ mz 2 L q 2 L0 q 2 q 2 ˆ . L    2 2 2 2C0 Here z, q taken as generalized coordinates, q = C0U-is the charge of the capacitor. The Rayleigh dissipative function of the system

93

~ R q 2 Rq 2 . Fˆ  0  2 2

The first member is associated with the dissipation of energy on resistance of the conductive cables. The second reflects an attempt to take into account the loss of ionization of the gas, radiation and ohmic heating of the plasma. The easiest way to consider these losses of energy follows, introducing the price of the electron  , which determines the amount of energy required for one act of ionization. As you know, in a dissipative system the energy loss is twice the dissipative function [95] dE  2 F . dt Assuming that the dissipation processes occur mainly in the current the web, we can rate them so

d N  dm dE   ; dt dt mi dt dm  m  z m ,   z t dt z

~q 2 R  F  mi z 2

  m

here

or

~   m 1 R . m i z q 2 Substituting the obtained expressions into the Lagrange equation

d  Lˆ  Lˆ Fˆ  ,   dt  x i  xi x i and given that L~ L z  t z t

and

94

dm  m  z ,  dt z t

we get the system of differential equations describing the acceleration process of the current layer in the interelectrode gap





~ q ~  L z  L  L0 q   z t  R0  R q  C  0 ,   0  m L   1 1 m z  z 2  q 2  0 .  2 z 2 z

(5.11)

The initial conditions at the time of the breakdown discharge and applying a voltage to the electrodes

q  C0U0 ; z  0, z  0. q  0 при t  0 . The first equation of system (5.11) is the equation of an oscillatory circuit with variable L and R, the second equation is to Meshchersky accelerating jumper with a variable mass. The meaning of each member of the first equation it becomes clear after multiplication there are   ~  Lq 2  1 L   m  q 2  2 2  0.     q  R0 q   mi z  2C 0   2  2 z In the end we get the energy conservation law, showing in what types transformirovalsya energy of the capacitor Bank:

 Lq 2   2

  – the change of magnetic field energy in the circuit 

 q2   2C 0

   – the change in energy of the capacitor battery; 

R0 q 2

– the ohmic losses in the circuit

  m mi z

– the energy dissipation in current jumper

95

~ 1 L 2  q – the power of the forces acting on the jumper 2 z

~ L 2 the power of the forces acting on the jumper will make  q  dt . z 0 t

~ The second term is the accelerating force, 1  L q 2 -the power of 2 z this force is equal . As can be seen from this equation, the energy consumed is not only to increase the speed of the bunch, but actuated rake mass of the gas, that is, the member is decelerating inertial force 1 m 2 z . Thus, the problem reduces to finding the maximum 2 z functionality tk ~ L 2 0 z q  dt . L 2 Because the force acts on the mass of gas is proportional I z U ~ I  , this leads to a rapid acceleration of the current layer and on the end electrodes. Therefore, the output time of the plasma decreases with increasing voltage. Therefore, the voltage of the capacitor Bank should be as high as possible. So as to obtain a high power density while maintaining other parameters necessary to form short pulses, for the efficient operation of the accelerator to reduce the length of the electrodes. More specifically, the accelerator must operate so that the maximum speed of the clot was achieved at the exit end of the electrodes without loss. To do this, the maximum speed of clot should be achieved in the first quarter of the current period. However, the shorter the length, the less inductance. A substantial reduction of the length of the electrodes can be achieved by the system with increasing inductance per unit length L  L0  bz ,

96

b

 L~ . z

An increase in L leads to an increase in the length of the electrodes, and a decrease in b leads to a decrease in buoyancy . Thus, the optimal acceleration can be formulated as: 1) for any ISP with constant and achieving high efficiency depends on parameters of the discharge circuit and the geometry bI 2 .of the electrode system for any ISP with constant and achieven U0 and C0 g high efficiency depends on parameters of the discharge circuit and the geometry of the electrode system



mi 2 . C0U 02

2) to achieve a sufficiently high efficiency of the acceleration ~ process need to so that in the first quarter L of the current period have changed slightly and the current was growing almost as well as the discharge C0 through L0 . In the second quarter of the period, the inductance needs to increase substantially to the exit of the plasma on the end to beat L0. For accelerator with coaxial cylinders inductance per unit length  L~  2  0 ln R / r , z

where R and r are the external and internal diameters of cylinders. This shows that the motion along the coaxial axis inductance of the ~ nonlinear system L increases. Thus, is determined by the position of the current layer at any given time z

R( z) ~ dz . L  2   0 ln r( z) 0 The energy for the acceleration of clot W  ~ must L the thickening of the electrodes z 97

tос

 q  dt . To increase 2

0

~ L 0  R  0  r   ln   ln1   , t 2  r  2  r 

r  2r .

To implement an optimal system usually use the design accelerator with a coaxial cylindrical system. This system ensures a constant increase of the inductance over the length of the electrodes. As shown above, in the accelerator KPU-30 clot goes to the end of the third quarter of the period at 0, 1 Torr, and at the end of the period at a pressure of 1 Torr. In this case, the effective acceleration can only be low pressure, if we assume that the amplitude of the discharge current is not greatly reduced in the second half period. Consider the ratio for the length of the ion-electron collisions in the plasma

2,5 10 4 Te2 ei  Z e2 ni For the range of pressures P0 = (0,05 – 5) Torr this length is in the range (25 – 0,25) see Therefore, at an initial pressure below 0.1 Torr at a distance of ion-electron collisions becomes of the order of the electrode length, and we obtain an efficient acceleration. However, as shown above, in this case, there is a slide current along the anode and its kontrolirana at the end, as well as the formation of erosive plasma, which generally reduces the efficiency of acceleration.

5.3. The conductivity of the plasma and electron temperature Knowledge of the conductivity of the gas discharge gives possibility to determine important plasma parameters such as temperature and concentration. From the waveforms of voltage and current (paragraph 4.1) it is seen that the maximum current in the discharge circuit is achieved with 6-7 µs from the start of discharge, the voltage on the circuit falls to the value of near-electrode potentials. This suggests that the plasma conductivity is increasing and at this point reaches a maximum. Based on the values of voltage and current as functions of time, determined by the active resistance of the discharge. The curve of the plasma resistance is shown in figure 5.3. 98

600 500

R, м О м

400 300 200 100 0 0

1

2

3

4

5

6

7

t, мкс

Figure 5.3 – Dependence of the resistance changes of the plasma on time

Knowing the potential difference between the electrodes of the accelerator, find the change in electric field intensity between the electrodes depending on the radius Е

U , a ln 2 r a1

(5.12)

where U – is the potential difference between the electrodes, a1 -is the radius of the anode, a2- is the radius of the cathode. We assume that the entire current is due to movement of the electronic components, as well conducting plasma the condition

Ie ~ Ii

M , m

99

(5.13)

where Ie – is the current due to the electronic component, Ii – is the current due to the ion component, M – is the mass of the ion, m – is the electron mass. The continuity equation for the electron component of the current record in the form

I  2  GErd,

(5.14)

where G – is the conductivity, d – thickness of skin-layer. The thickness of the skin layer connected with conductivity well known relation

d

t

0G

.

(5.15)

Jointly solving equations (5.13,14 and 15), we obtain 2

 a  I  ln 2   0 a1  . G  4tU 2 2

(5.16)

The concentration of neutral gas in the discharge chamber at a pressure of 0.1 Torr is n0 = 3,6 ·1015см-3. Next, rate the degree of ionization of the gas in the plasma flow. Write the equation of change of electron concentration t dne GE 2  , N   U Idt . dt i  0

(5.17)

Here N – is the number of electrons in the plasma sheath, ε – "the price of the electron", the value of the order of 100 eV. After substitution of numerical values into equation (5.17) we get N =3,3 ·1018. Assuming that the plasma in a current sheet having a disk shape with thickness of skin-layer d = 25 cm (referring to the diffuse mode), 100

calculate the electron concentration in plasma sheath. The volume occupied by the plasma is V= πd· (R2-r2)=1400 cм3. Then the concentration ne = 2,3·1015 cм-3. Thus, the degree of ionization will be about 63%. Thus, in this case, we have a well-ionized plasma. The temperature of the electronic components can be determined by the formula of Spitzer, taking the experimentally obtained conductivity for the conductivity of a fully ionized plasma 2

 a  I  ln 2   0 3 a1  2  0T 2  .  3 1 G 4tU 2  2m 2 2

(5.18)

By the time of reaching the maximum current of 180 kA at a voltage of 1.8 kV have Те = (4±1) эВ. This value corresponds to a relatively hot plasma generated in the accelerator channel. The results show that the electron temperature is almost constant at any pressure in the chamber of the accelerator.

5.4. The influence of pressure on voltage-current characteristic of the accelerator As the results of the experiments with the pressure is actually on the order, the value of the discharge current remains constant. A small change is observed only when the pressure of three orders of magnitude. The presence of shallow high in a wide range of pressures of 10-2 – 10 Torr due to the well-known Paschen law, according to which, for any gas-centered between the two electrodes, there is a minimum breakdown voltage determined by the kinetic processes in the gas. In our case, the minimum breakdown voltage is observed at 0.2 Torr. This is the optimum pressure when using the accelerator in continuous mode, is implemented when the maximum discharge current, and hence the buoyancy force of the ampere. The independence of the current pressure corresponds to the calculations according to the formula of Spitzer, as the plasma current is determined primarily by the degree of ionization of the gas. 101

As we saw above, the dependence of velocity on pressure is not so easy to interpret. If the output from the coax the speed of clot depends weakly on pressure, the inside of the coax it is higher at low pressure in two to three times. Obviously, inside the coax is of great importance and influence of other parameters, for example, slide along the electrodes. Features of this motion will be discussed below. The harmonic dependence of the current on time is determined by the conversion of electrical energy of the capacitor Bank in the energy of the magnetic field, accelerating the plasma jumper, and damping – energy dissipation in the ohmic plasma heating and losses in the discharge circuit. The course stresses a phased array with a current that is indicative of a rather efficient transformation of energy without significant losses. Otherwise, the value of the period would have to increase. It is obvious that the time dependence of the current will be determined by the full impedance of the system. This should take into account the parasitic resistance and inductance of the coaxial system itself. For plasma accelerator maximum period discharge circuit at the time of formation of a plasma clot when applied to the electrodes the full voltage can be estimated by the formula Thomson. According to the electrodynamic model, the discharge circuit of the coaxial plasma accelerator can be considered as a resonant circuit consisting of condenser, inductance and ohmic resistance (i.e., plasma resistance). In the ideal case in this circuit develops damped oscillations with a period of

T  2 LC . The value of the inductance per unit length coaxial cylinders has been defined above. The calculated inductance per unit length made up 2,18·10-7GN/m. When the length of the electrode 45 cm the inductance of the coaxial system will be 1,31·10-7GN. Defined by the formula Thomson the period of oscillations in the discharge circuit will be about 18 µs. The experimental waveform of the CPU (figure 4.1) the period of oscillation is about 14 µs. Calculated above, the inductance of the coax system more parasitic inductance L0, which suggests that the discharge period is determined primarily by the inductance of the coax. Therefore, the pressure change in the chamber 102

has only a minor effect on the period of the discharge current, the period increases only 1-2 microseconds. The current-voltage characteristic the discharge current of the accelerator KPU-30 from the pressure shown in figure 4.6. As can be seen from the figure, the dependence of the current on the voltage is linear, which in General, corresponds to the data of other experiments. The dependence of the discharge current of the CPU 5 from the voltage shown in figure 4.8. As you can see, at low voltages the discharge current is almost proportional to the voltage, however, in the field of voltage above 3.5 kV, the current value begins to increase. In the process of experiments at various pulse accelerators it was found [83, p. 183] that the behavior of plasma in these accelerators is rather extraordinary. It turned out that at low currents the discharge lines of the electric current is close to radial. But if at a constant flow of substance m/ to begin to increase the discharge current J, then at some critical value of J