An experimental and theoretical study of the energy absorption from high voltage radiation by means of ionization measurements with an extrapolation type chamber

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AN

EXPERIMENTAL

AND

THEORETICAL

STUDY

OF

THE ENERGY ABSORPTION FROM HIGH VOLTAGE RADIATION BY MEANS OF IONIZATION MEASUREMENTS WITH AN EXTRAPOLATION TYPE CHAMBER

A T h e s i s s u b m i t t e d t o t h e u n i v e r s i t y o f London f o r t h e D egree o f Ph.D .

in phy sics

by ALY

ABDEL

KERIM

IBRAHIM.

ProQuest Number: 10097957

All rights reserved INFORMATION TO ALL U SE R S The quality of this reproduction is d ep endent upon the quality of the copy submitted. In the unlikely event that the author did not sen d a com plete manuscript and there are m issing p a g es, th e se will be noted. Also, if material had to be removed, a note will indicate the deletion.

uest. ProQ uest 10097957 Published by ProQ uest LLC(2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States C ode. Microform Edition © ProQ uest LLC. ProQ uest LLC 789 East Eisenhow er Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346

A B S T R A C T

T h i s e x p e r i m e n t a l a n d t h e o r e t i c a l s t u d y aim s a t fu rth e r

i n v e s t i g a t i o n , b y means o f a n e x t r a p o l a t i o n t y p e

of i o n i z a t i o n cham ber,

o f th e i o n i z a t i o n m easurement o f

e n e rg y a b s o r p t i o n from h i g h - v o l t a g e r a d i a t i o n s w i t h i n a medium.

W a v e l e n g t h s r a n g i n g b e t w e e n 0 . 0 8 a n d 0 . 5 A°

were u sed . T he w a l l s o f t h e i o n i z a t i o n c h a m b e r w e r e made o f sim p le elem ents

(g rap h ite,

alum inium and c o p p e r)

or

p r e s s e d b a k e l i t e - g r a p h i t e m ix tu re s w hich were lo a d e d w i t h c e riu m o x id e i n o r d e r to c o n t r o l th e e f f e c t i v e atom ic number o f t h e m ix tu r e s . A d istin ct used is

advantage o f th e e x p e rim e n ta l arrangem ent

the p o s s i b i l i t y

o f m easuring th e i o n i z a t i o n p er

u n i t s p a c i n g w hen t h e a i r s p a c e i s v a n i s h i n g l y s m a l l w h i c h th u s e lim in a te s The r e s u l t s fin ite

th e v a r ia b le e f f e c ts

of chamber s i z e .

c f e a r l i e r w o rk e rs w ith cham bers o f f i x e d

d im en sio n s have b een d i f f i c u l t to

in te r p r e t in

term s o f t h e o r e t i c a l c o n s i d e r a t i o n s b e c a u se o f th e s e effects.

F u r t h e r m o r e , by v a r y i n g th e t h i c k n e s s

upper plan e e le c tro d e

cf

th e cham ber, c o r r e c t i o n c o u ld

b e made f o r a b s o r p t i o n o f r a d i a t i o n w hich,

of the

in t h i s

electro d e,

a t l o n g w a v e l e n g t h s , maybe c o n s i d e r a b l e

m e d ia o f h i g h e r a t o m i c n u m b e r .

in the

-

The r e s a l t s

11 -

o h t r à n e d w i t h a chamber o f g r a p h i t e

w a l l s show t h a t g r a p h i t e b e h a v e s a p p r o x i m a t e l y a s a i r w alled m a te ria l, co n stan t i .e . V where V i s

t h e i o n i z a t i o n p e r u n i t v olum e i s

th e i o n i z a t i o n I q b e in g p r o p o r ti o n a l to th e a i r volum e.

number g r e a t e r

than th a t

spacin g in c re a se s to a c e r t a i n very ra p id ly .

of a i r

slig h tly

W ith w a l l s o f ato m ic th e io n iz a tio n p er u n it

a s t h e s p a c i n g d e c r e a s e s up

t h r e s h o l d s p a c i n g blow w hich i t

in creases

The i o n i z a t i o n p e r u n i t s p a c i n g a n d t h e

t h r e s h o l d s p a c in g b o th depends upon th e m a t e r i a l of th e electro d es

and t h e w a v e l e n g t h o f t h e r a d i a t i o n .

The i o n i z a t i o n p e r u n i t s p a c i n g a t z e r o d i m e n s i o n s may b e m e a s u r e d i n tw o w a y s . o rig in

a tan g en t

to

th e

F i r s t l y , by draw ing a t th e

i o n i z a t i o n - s p a c in g c u rv e and

se c o n d ly by e x t r a p o l a t i o n to ze ro dim ensions of th e i o n iz a tio n p e r u n it spacing - sp acin g curve. I t was t h u s p o s s i b l e t o c o m p a r e t h e s e e x p e r i m e n c a l o b s e r v a t i o n s w i t h e x p e c t a t i o n s b a s e d upon t h e B ragg G ray t h e o r y o f i o n i z a t i o n w i t h i n a c a v i t y . T his com p ariso n s u g g e s ts

th at

t h e B rag g - Gray

t h e o r y may b e r e g a r d e d a s a s a t i s f a c t o r y d e s c r i p t i o n o f the f a c t s

f o r th e range of w avelengths s t u d i e d ,

l e a s t f o r e l e m e n t s o f a t o m i c n u m b e r up t o t h a t o f

at

-

a l u m i n i u m (Z = I 5 ) .

ill

-

F o r c o p p e r (Z = 2 5 ) a n d t h e

m i x t u r e s .( d e p e n d in g upon th e e l e c t r o n e m i s s i o n from Ce o f Z = ^8)

th e ex p erim en tal r e s u l t s

d isa g re e w ith

th e th eo ry ex cep t f o r th e s h o r t e s t w av elen g th s,

and

th e d is a g re e m e n t i n c r e a s e s w ith i n c r e a s e of w avelength. S u g g e s t i o n s a r e a d v a n c e d and a m o d i f i c a t i o n made to G ra y ’ s e q u a t i o n i n an a tte m p t to c o r r e c t f o r t h i s d isagreem ent.

These a re b a s e d upon a c o n s i d e r a t i o n

o f t h e s o u r c e s and t h e e n e r g y o f t h e p h o t o e l e c t r o n s o m itte d from th e w a ll m a t e r i a l s .

AN

EXPERIMENTAL

AND

THEORETICAL

STUDY

OF

THE ENERGY ABSORPTION FROM HIΔ VOLTAGE RADIATION BY MEANS OF IONIZATION MEASUREMENTS WITH AN EXTRAPOLATION TYPE CHAMBER

A T h e s i s s u b m i t t e d t o t h e u n i v e r s i t y o f London f o r t h e D eg ree o f P h.D . i n p h y s i c s by ALY

ABDEL

KERIM

IBRAHIM.

CONTENTS

Page I.

INTRODUCTION

II.

1

THE RATIO OF THE IONIZATION CURRENTS IN CHAMBER PAIRS OF DIFFERENT MATERIALS ACCORDING TO THE THEORY OF BRAGG AND GRAY.

(a) In tro d u c tio n .

7

(Td ) The T h e o r y .

7

(c) T h e o re tic a l D eterm in atio n of th e e f f e c tiv e A to m ic Number o f t h e d i f f e r e n t m i x t u r e s u s e d f o r cham bers. (d)

The E l e c t r o n D e n s i t y o f t h e C hamber W a ll m aterial. (i) (ii)

(e)

(g) III.

For sim ple ele m e n ts.

16

For p l a s t i c m ix tu re s.

17

D eterm in atio n o f th e a b s o rp tio n c o e f f ic ie n ts f o r v a r io u s w all m a t e r i a l .

18

(i)

20

(ii) (f)

15

The e v a l u a t i o n o f

a n d e ®~a

E v a lu a tio n o f th e p h o to e le c tr ic ab so rp tio n c o e ff ic ie n t p er e le c tro n .

The s t o p p i n g p o w e r p e r e l e c t r o n ” S‘*. C a lc u la tio n o f the r a t i o c u r r e n t " R".

23 33

o f the io n iz a tio n 3^

EXPERIMENTAL DETERMINATION OF THE RATIO "R^'

(a)

The p r o c e s s i n g o f t h e p r e s s e d e l e c t r o d e

38

(b)

The E x t r a p o l a t i o n I o n i z a t i o n Chamber

I4.O

(c)

The l e a d s

41

il

-

P age (d) E l e c t r o d e s M a t e r i a l s .

I|.2

(e) A p p aratu s f o r m easuring t h e r a t i o o f th e i o n i z a t i o n c u r r e n t s i n p a i r s o f cham bers. (i) (ii) (iii)

(iv ) (v) (v i) (v ii) (v iii)

The e l e c t r i c a l

U3

circ u it.

The t h e o r e t i c a l c o n s i d e r a t i o n s th e ap p aratu s.

of

P r a c tic a l c o n s tru c tio n of th e ap p aratu s.

k3 k3

1.

T he C a p a c i t y P o t e n t i a l d i v i d e r .

2.

The B a l a n c e P o t e n t i a l I n d i c a t o r .

U7

3.

S e n s i t i v i t y C ontrol f o r th e E lectro m eter.

U8

O ther p a r t s o f t h e c i r c u i t .

hS

T he E a r t h i n g K e y s .

50

A djustm ent o f th e o r d e r o f opening th e sw itch es.

51

P r e c a u t i o n s and P r o c e d u r e .

5%

CALIBRATION OP THE APPARATUS 1.

2.

R e l a t i o n b e tw e e n S c a l e Reading and C a p a c ity P o t e n t i a l D iv id e r R atio .

56

R e l a t i o n b e tw e e n S c a l e R eading and c h a rg e r a t i o .

57

( f ) E x p erim en tal R e s u lts .

63

-

IV.

iii

-

DISCUSSION AND CONCLUSIONS (a)

The I o n i z a t i o n - Volume C u r v e s .

(h)

The I o n i z a t i o n p e r U n i t S p a c i n g a s t h e volum e t e n d s to z e r o I d d = o (i) (ii)

F i r s t M e th o d . S e c o n d M e th o d .

(c)

The A b s o r p t i o n F a c t o r ( f )

(d)

The R a t i o o f I o n i z a t i o n b e t w e e n c h a m b e r s o f h i g h a t o m i c Number a n d A i r w a l l e d m aterial.

(e)

C o m p a r i s o n b e t w e e n T h e o r e t i c a l and P ra c tic a l values.

(f)

E l e c t r o n R a nge a n d I o n i z a t i o n - E l e c t r o d e sp acin g curve. ( i) ( ii)

(iii)

R e l a t i v e n u m b e r s o f R e c o i l and P h o to electro n s. The a b s o l u t e v a l u e o f t h e r a n g e . The mean R a n g e o f t h e e l e c t r o n s

(g) A M o d i f i c a t i o n t o Grays t h e o r y .

in a ir.

I.

I N T R O D U C T I O N

The i o n i z a t i o n p r o d u c e d i n a n a i r f i l l e d c a v i t y by h i g h v o l t a g e r a d i a t i o n w i t h i n a medium h a s b e e n a s u b j e c t o f c o n s i d e r a b l e t h e o r e t i c a l and e x p e rim e n ta l in v e s tig a tio n fo r th e l a s t

t h i r t y years or so.

P ro v id ed t h a t c e r t a i n c o n d itio n s a re f u l f i l l e d seems p o s s i b l e , th eo ry ,

a s shown b y t h e B r a g g

to ex p ress the

i t now

- G ra y

i o n i z a t i o n w ith in such a c a v ity

in term s o f th e r e a l a b s o r p t i o n c o e f f i c i e n t s o f th e medium a n d i t s

s to p p in g power f o r e l e c t r o n s .

i f t h e s e c o n d i t i o n s may b e f u l f i l l e d

C onversely,

sa tisfa c to rily ,

a

m e a s u r e m e n t o f t h e i o n i z a t i o n w i t h i n t h e c a v i t y may b e used to i n f e r the r e a l energy a b s o r p t i o n o f h ig h v o lta g e r a d i a t i o n w i t h i n t h e m edium . The e x p e r i m e n t s o f p r e v i o u s w o r k e r s ,

who h a v e made

m easurem ents o f th e i o n i z a t i o n p ro d u c e d by h i g h v o l t a g e r a d i a t i o n i n i o n i z a t i o n cham bers h a v in g w a lls o f v a r io u s atom ic num bers,

in d ic ate

th a t alth o u g h th e c o n d itio n s

r e q u i r e d by th e t h e o r y a r e s a t i s f a c t o r i l y

fu lfille d

for

s m a l l i o n i z a t i o n c h a m b e r s o f l i g h t a to m m e d i a when v e r y h ig h energy r a d i a t i o n i s used ( e .g .

radium

Y rays)

the

-

2 -

m e a s u r e m e n t s do n o t g i v e t h e r e s u l t s p r e d i c t e d b y t h e t h e o r y when t h e c h a m b e r w a l l s a r e o f h i g h e r a t o m i c num bers o r t h e r a d i a t i o n s u s e d a r e o f l o n g e r w a v e le n g th s . The d i m e n s i o n s o f t h e c h a m b e r a l s o

a f f e c t th e d iscrepancy

b e t w e e n t h e tw o . M ayneord

u se d t h i n w a lle d cham bers o f d i f f e r e n t

m a t e r i a l s a n d f o u n d t h a t t h e r e was a d i s a g r e e m e n t b e t w e e n th e e x p e rim e n ta l v a lu e s and th o s e c a l c u l a t e d , being l e s s th an th e l a t t e r .

th e form er

C l a r k s o n a n d M a y n eo rd

made i o n i z a t i o n c h a m b e r s o f c a r b o n (Ac h e s o n g r a p h i t e ) e l e c t r o p l a t e d on t h e i n s i d e w i t h a c o p p e r l a y e r o f t h i c k ­ ness

•

They f o u n d t h e i o n i z a t i o n c u r r e n t s to b e

ap p reciab ly l e s s

than th e th e o r e t i c a l v alu es.

They i n f e r r e d

t h a t t h e d i f f e r e n c e was d u e t o t h e t h i c k n e s s o f t h e c o p p e r la y e r bein g i n s u f f i c i e n t to g iv e f u l l

eq u ilib riu m e le c tro n ic

e m i s s i o n o v e r t h e s h o r t wave r e g i o n .

I n o rd e r to

study th e

q u a l i t y o f t h e r a d i a t i o n s u s e d i n r a d iu m Y- r a y t h e r a p y ( 5 - 20 X . U . )

W ilson

m a g n e s iu m w i t h w a l l s k mm. o n e mm. t h i c k . M ayneord'

p r e p a r e d cham bers o f c a rb o n , t h i c k and o f copper w ith w a l l s

He f o u n d a c o n s i d e r a b l e d e v i a t i o n f r o m ex perim en tal v alu es.

He a t t r i b u t e d t h e

d is c r e p a n c y p a r t l y to th e f a c t t h a t t h e cham bers c o u ld n o t be regarded as b eing s u f f i c i e n t l y th in .

C larkson (6 ),

in

- 3 -

h i s endeavour to use the i o n i z a t i o n c u r r e n t produced in a gas c o n t a i n e d i n a s m a ll i o n i z a t i o n chamber as an i n d i c a t i o n o f the r a t e

o f a b s o r p t i o n o f energy f o r X -

r a d i a t i o n o f w av e le n g th 0.208

u s e d chambers o f

c a r b o n , m a g n e s iu m ,

alum inium ,

copper,

e le k tro n m etal,

z i n c and l e a d .

iro n ,

He came t o t h e c o n c l u s i o n t h a t

the e x p e rim en ta l v a lu e s f o r th e i o n i z a t i o n c u r r e n ts are l e s s th a n th o se o b ta in e d from th e t h e o r e t i c a l c o n s i d e r a ­ t i o n s o f G ray n um be r ( l e s s

e x c e p t f o r s u b s t a n c e s o f lo w a t o m i c th an 1 2 ).

He s u g g e s t e d t h a t t h e d e v i a t i o n

i n t h e c a s e o f m edia o f h i g h a to m ic number i s due t o th e f a c t t h a t t h e b i n d i n g e n e rg y o f th e e l e c t r o n removed rises re la tiv e ly

to

t h a t o f t h e e q u a n t u m , ( s e e l a t e r p p . 137-139)

A ll th e p re v io u s i n v e s t i g a t i o n s cham bers c o n s t r u c t e d from m a t e r i a l s elem en ts.

R ecen tly ,

co n d u ctin g ,

were made w i t h

c o n s i s t i n g o f sim ple

^’t h e r m o - s e t t i n g ’’ r e s i n s

have been u s e d f o r t h e l a r g e s c a l e p r o d u c t i o n o f i o n i z a t i o n cham bers f o r t h e f o l l o w i n g r e a s o n s . 1)

It is

cham bers i d e n t i c a l effectiv e th e

p o ssib le to p ress

sm all c o n d e n s e r i o n i z a t i o

in co n stru ctio n , but d if fe re n t in

a t o m i c number, w h i c h a r e l i k e l y

to be u s e d f o r

s i m u l t a n e o u s m e a s u r e m e n t s o f ’’d e p t h q u a l i t y ” and

’’d e p t h d o s e ” . ^

- 4 -

2)

It

is also p o ssib le

chambers w hich a r e

su itab le

t o m o u ld v e r y s m a l l

f o r th e study of th e q u a lity

o f t h e s c a t t e r e d r a d i a t i o n g e n e r a t e d i n a medium by X - rays

For th e se

in v e stig a te d

the b e h a v io u r of such p re s s e d i o n iz a t io n

c h a m b e r s an d t h e i r r e s u l t s 1)

show ed t h a t :

-

C h a m b ers m o u l d e d f r o m b a k e l i t e m i x t u r e s a r e

sa tisfac to ry in t h e i r

r e a s o n s A ly a n d V /ils o n (

e l e c t r i c a l c o n d u c t o r s and b e h a v e c o n s i s t e n t l y

in te r a c ti o n w ith the

r a d i a t i o n used (0 .5 -

0 . 0 1 3 A°u) 2)

The r a t i o s o f i o n i z a t i o n c a l c u l a t e d a c c o r d i n g

t o G ra y *s t h e o r y a g r e e w i t h t h e e x p e r i m e n t a l o n e s up t o a w a v e l e n g t h o f 0 . 0 8 A^ •

and beyond t h a t t h e d e g re e o f

d ifferen ce

in c r e a s e s w ith in c re a s e o f w av elen g th v ery

rap id ly .

They s u g g e s t e d t h a t s u c h d i f f e r e n c e s b e t w e e n

t h e t h e o r e t i c a l and e x p e r i m e n t a l f i n d i n g s t o an in c o m p l e t e c o n t r i b u t i o n to

a r e due p a r t l y

t h e i o n i z a t i o n by t h e

p h o t o e l e c t r o n s from th e c h a m b ers o f a to m ic number g r e a t e r than a i r .

T h is c o n t r i b u t i o n b ein g in co m p lete b ecause o f

the r a th e r l a r g e cham bers r e l a t i v e

(approx.

1 . 5 cm .) d im e n s io n s o f th e

to th e range of th e p h o to e le c tro n s .

- 5 -

S p iers

(9)

has s in c e su g g e ste d th a t alth o u g h the

m i x t u r e s u s e d by A ly a n d W i l s o n h a v e a p p r o x i m a t e l y t h e a b s o r p t i o n c o e f f i c i e n t s c a l c u l a b l e f ro m t h e i r e f f e c t i v e a to m ic num bers,

th e o re tica l

th ey w ill n o t g iv e r i s e

to the

e l e c t r o n e m i s s i o n t o b e e x p e c t e d on a c c o u n t o f t h e f a c t t h a t cerium o x id e i s u sed f o r lo a d in g the m ix tu re s . B e c a u s e o f t h e h i g h e n e r g y r e q u i r e d t o remove t h e K e l e c t r o n from c e r iu m

( a b o u t 40

w i l l have re d u c e d e n e r g i e s . p h o to e lec tric co n trib u tio n

ekVc)

th e p h o to e le c tro n s

T h is w ill cause a reduced to

the i o n i z a t i o n in th e

cham ber. C o nsiderin g th e se o r d e r to i n v e s t i g a t e (a) to

the

o b serv atio n s i t

seem ed t h a t i n

su b ject f u rth e r i t

is necessary

stu d y th e i o n i z a t i o n i n cham bers w ith w a ll s

com posed o f s i m p l e e l e m e n t s o f v a r i o u s a t o m i c n u m b e r s i n a d d i t i o n t o t h e m i x t u r e s p r e v i o u s l y u s e d by A ly and W i l s o n and a t

t h e same t i m e

(b)

t o u s e a m e t h o d w h ic h u s e s v e r y

sm all i o n i z a t i o n cham bers or b e t t e r b ility

still,

has th e p o s s i ­

o f e l i m i n a t i n g th e e f f e c t o f chamber d im e n s io n s

alto g eth er. It

se em e d t h a t t h e u s e o f a n e x t r a p o l a t i o n t y p e o f

chamber ( P a i l l a

Quimby ( H ' 1 2 ) ^ o f f e r e d p r o m i s e o f

- 6 -

a c h i e v i n g th e e l i m i n a t i o n o f t h e e f f e c t o f chamber d im e n sio n s and w a ll a b s o r p t i o n . chamber o f t h i s t y p e

For t h i s

reason a

was d e v e l o p e d i n a f o rm w h i c h

a p p e a r e d most p r a c t i c a b l e

fo r th e

e x p e r i m e n t s t h a t were

con sid ered n e c e s s a ry . T his t h e s i s th is

d e s c r i b e s t h e e x p e r i m e n t s made w i t h

type o f cham ber,

u sin g e le c tro d e s o f v ario u s

e l e m e n t s a n d o f t h e same p r e s s e d m i x t u r e s u s e d by A ly an d V /ils o n and c o r r e l a t e

an d a t t e m p t s t o e x p l a i n t h e o b s e r v a t i o n s them w i t h p r e v i o u s e x p e r i m e n t a l a n d

t h e o r e t i c a l w ork.

It

th u s d i f f e r s

i n an im p o r ta n t

p a r t i c u l a r f o r m t h e w o r k o f P a i l l a a n d Quimby who u s e d on ly a i r w a ll m a t e r i a l .

- 7 -

II.

THE RATIO OP IONIZATION CURRENTS IN CHAMBER PAIRS OF DIFFERENT MTERIALS ACCORDING TO THE THEORY OP BRAGG AND GRAY

a . In tro d u ctio n The i o n i z a t i o n p r o d u c e d by x - r a y s i n a n a i r f i l l e d c a v i t y was f i r s t

s t u d i e d by B r a g g w h o

t o t a l le n g th o f the

track s

d e p e n d s on t h e n a t u r e

d e fin e d the range of

trav elled .

substance i . e .

d en sity .

t h e /(?-p a r t i d e s

amount o f m a t t e r t r a v e r s e d T herefore,

medium d i f f e r s

upon i t s

I n o t h e r w o r d s he in

term s o f th e

and n o t t h e d i s t a n c e

i f an a i r c a v i t y

i n t h e medium i t w i l l make no d i f f e r e n c e d e n sity w ithin i t

the

of the /G -p a rtic le s in m a tte r

o f the

a t o m i c nu m b e r and n o t i t s

found t h a t

is in tro d u ced to th e /3-ray

u n l e s s t h e a t o m i c n um be r o f t h e

v e r y much f r o m t h a t o f a i r o r t h e

p re s s u re o f the a i r i s

t o o g r e a t so t h a t a l a r g e f r a c t i o n

o f t h e / 3 - r a y e n e r g y i s u s e d up i n p a s s i n g t h r o u g h t h e cav ity .

To a v o i d t h i s

e i t h e r th e c a v i t y should be sm all

com pared t o t h e ra n g e o f th e e l e c t r o n i n a i r o r t h e p re s s u re reduced, b.

The T h e o r y G ray

found th a t a v ery sim p le r e l a t i o n co u ld

be d e r iv e d by t h e o r e t i c a l r e a s o n in g from c e r t a i n

- 8 —

ex perim ental f a c ts

c o n c e rn in g the

s w i f t l y moving e l e c t r o n s .

l o s s o f e n e r g y by

E sse n tially

t h e same r e l a t i o n

h ad b e e n e n u n i c a t e d i n s l i g h t l y

d ifferen t

a s 1912 by S i r W i l l i a m B rag g

.

It

term s a s e a r l y

had b e e n shown p r e v i o u s l y by G ray

t h a t the

e n e r g y e q u i v a l e n t o f t h e i o n i z a t i o n p e r u n i t v o lu m e i n the c a v ity is i

tim es th e X -ray en e rg y ab so rb ed p e r u n i t

v o lu m e o f t h e s o l i d . somewhat l e n g t h y ,

The d e r i v a t i o n

because i t

of th is re la tio n is

is necessary to e s ta b lis h

th a t th e i n t r o d u c t i o n o f a sm all a i r c a v i t y i n t o a s o lid medium d o e s n o t d i s t u r b

the d i s t r i b u t i o n as re g a r d s

d irec tio n

of the /3 -p a rtic le s c ro ssin g

and v e l o c i t y ,

s u r f a c e which has become a w a l l o f t h e c a v i t y ratio

of

t h e e n e r g y l o s t by an e l e c t r o n

c e rta in d istan ce,

a sm all f r a c t i o n

of i t s

(p i s

the the

in tr a v e r s in g a range in

t h e two

m edia a i r a n d s o l i d ) A ttem pts the c o n trib u tio n s from th e g a s , from th e

h a v e b e e n made t o to i o n i z a t i o n

from the

several w alls,

of these p a r t i c l e s a nd so o n .

estim ate s e p a ra te ly

i n a n e n c l o s e d v o lu m e ,

co rp u scu lar

rad ia tio n s

em erging

from th e e f f e c t o f th e r e f l e c t i o n

f r o m t h e o p p o s i t e f a c e s o f t h e v o lu m e

In the case o f a i r ,

the p r o p o r t i o n o f t h e

- 9 -

w h o le e n e r g y l o s t o r a b s o r b e d w h ic h i s p r e s e n t e d by io n iz atio n ,

has been th e

s u b j e c t o f n e a r l y a s c o r e of

s e p a r a te ex p e rim e n ta l i n v e s t i g a t i o n s as w e ll as a very th o rou g h t h e o r e t i c a l t r e a t m e n t . c o n s i d e r a t i o n of th e e v id e n c e co n clusio n s (1)

From a d e t a i l e d

t h e r e em erg e t h e f o l l o w i n g

(G ray).

T h a t t h e a v e r a g e m e r g y W l o s t by a ^ - p a r t i c l e f o r each io n p a i r form ed, 5«2 X 10

ergs

i s c e r t a i n l y n o t f a r from

( 3 2 .5 e volts)^^^^

T his v alu e

m i g h t w e l l b e i n e r r o r by 2 p e r c e n t i n o f e v i d e n c e t o be p r e s e n t e d higher value

is

a slig h tly

to be p r e f e r r e d .

W = 5*3 X l O " ^ ^ =

la te r,

the l i g h t

33 e - v o l t

ergs. has been

p ro v is io n a lly adopted. (2)

That W i s

t h e same f o r a l l ^ p a r t i c l e s

having

e n e r g i e s b e t w e e n a t h o u s a n d an d a m i l l i o n The f i r s t energy in

v o l t s .(^5)

c o n c l u s i o n e n a b l e s one t o i n f e r t h e

e r g s l o s t by s e c o n d a r y e l e c t r o n s

in passin g

t h r o u g h a n y v o lu m e o f a i r f r o m a m e a s u r e m e n t o f t h e t o t a l io n iz a tio n

produced in a i r .

-

10 -

The s e c o n d i m p l i e s t h a t t h e c o n v e r s i o n f a c t o r f r o m i o n i z a t i o n to en erg y i s t h e

same o v e r a v e r y w i d e r a n g e

o f e n e rg y o f th e s e c o n d a ry e l e c t r o n s and hence o f a l l q u a l i t i e s o f r a d i a t i o n from th e

s o f t e s t x - ra y s to th e

hardest ^ -ra y s . The c o n c l u s i o n i s t h u s a r r i v e d a t , in fin ite ly

s m a ll a i r volum e,

th e t o ta l

th a t,

f o r an

e n e rg y , E, o f

s e c o n d a r y e l e c t r o n s g e n e r a t e d i n u n i t v o lu m e o f t h e medium i s g i v e n "by. E

S3

.

J

=

-B .

tJ.

or,

PW

(1)

where J i s t h e num ber o f i o n - p a i r s p r o d u c e d p e r c . c . i.e .

t h e i o n i z a t i o n p e r u n i t volum e. S in c e t h e r a t e a t w hich t h e c h a rg e d p a r t i c l e s

(electro n s)

lo s e energy i s

du o t o t h e i r e n c o u n t e r i n g t h e

e l e c t r o n s o f t h e medium t h r o u g h w h i c h t h e y p a s s ,

/> i s

p r o p o r t i o n a l to th e e l e c t r o n d e n s i t y and i s a s fo llo w s : nn

Si

n.

8

w h e r e n^ a n d n ^ a r e t h e e l e c t r o n

(2) d e n s i t i e s o f t h e medium

and the a i r r e s p e c t i v e l y and 8% and S a r e t h e e l e c t r o n i c s t o p p i n g p o w e r i n t h e medium a n d t h e a i r r e s p e c t i v e l y .

-

11

-

S u b s t i t u t i n g th e v a lu e of p in

'

(1) we f i n d

=

.......... n^S

B ut, E

w here I i s

=

( e% + e^l) I

(i^.)

t h e i n t e n s i t y o f r a d i a t i o n f a l l i n g on t h e

m a t e r i a l and i s c o n s i d e r e d c o n s t a n t t h r o u g h o u t t h e volum e,

and

p h o to e lec tric

a r e th e a b s o r p t i o n s c a t t e r i n g and

ab so rp tio n c o e ff ic ie n ts per electro n

resp ectiv ely . f r o m ( 3 ) a n d (U) we h a v e T,

^1

(G5,

s i n c e we a r e i n t e r e s t e d o n l y i n

m a t e r i a l s o f a t o m i c n um be r g r e a t e r t h a n 5*

r 25 T

a = O.OOOOU b = 0.00728 c = O .O llU d = 0.0 0 0 3 8 e = 0.0 0 1 5 2 f = 2 .350 The v a l u e s o f Te a r e

then o b ta in e d from th e fo llo w in g

form ula, I 6.06

^ P

X 10^3 n , ^

______ M_________ 6 . 0 6 X 10^3 n,,

M

For w av elen g th s g r e a t e r than the values of ^ form ula

^

the K a b s o r p t i o n l i m i t

th en o b ta in e d from th e f o llo w in g

(30) e'^L

where r ^ i s

M

=

t h e a b s o r p t i o n jump r a t i o .

-

26 -

TABLE The l i n e a r a b s o r p t i o n

f>

X i n A°

+ e'^a

(2) c o e f f i c i e n t f o r C a rb o n

( e^a

= 2 .3 0 g m /c .c.

+ e°"a X 10^5

n

= 6 . 9 6 9 x 10^^ e . / c . c .

y

0.01

0 .0 2 6 8

0 .6 1 6 3

0 .0 4 2 9 5

0 .0781

0.02

0.0295

0 .6 7 8 5

0 .0 4 7 2 9

0 .1 0 5 1

0 .03

0.0296

0 .6808

0 .0 4 7 4 4

0 .1 2 1 9

0 .04

0.0288

0 .6 6 2 4

0 .0 4 6 1 7

0 .1 3 4 9

0 .0 5

0 .0 2 7 9

0 .6 4 1 7

0 .0 4 4 7 3

0 .1 4 4 2

0 .0 6

0 .0 2 6 9

0.6187

0 .0 4 3 1 2

0 .1 5 2 3

0.08

0 .0 2 4 9

0 .5 7 2 7

0 .0 3 9 9 1

0.1648

0 .10

0.0235

0 .5 4 0 5

0 .0 3 7 6 7

0 .1 7 4 3

0.12

0 .0224

0 .5 1 5 2

0 .0 3 5 9 1

0 .1822

0 .1 5

0.0216

0 .4 9 6 8

0 .0 3 4 6 2

0 .1 9 2 3

0 .2 0

0 .0 2 3 0

0 .5 2 9 0

0 .0 3 6 8 7

0 .2 0 7 6

0 .2 5

0 .0281

0 .6 4 6 3

0 .0 4 5 0 4

0 .2 2 5 5

0 .3 0

0 .0 3 7 2

0 .8 5 5 6

0 .0 5 9 6 4

0 .2 4 6 6

0 .3 5

O . 0 5 O8

1.1684

0 . 0 8 139

0 .2 7 3 7

0 .4 0

0 .0 7 0 2

1 .6 1 4 6

0 .1 1 2 6

0 .3 0 9 1

0 .4 5

0 .0 9 5 5

2 .1 9 6 5

0 .1 5 3 1

0.3528

0 .5 0

0 .1280

2 .9 4 4

0 .2 0 5 1

0 .4 0 7 7

r 2/ -

TABLE

(3)

The l i n e a r a b s o r p t i o n c o e f f i c i e n t f o r A lum inium — (e^a + ^ ^

)-^z

= (e0) c u r v e s ( l & l )

-----------------------------

Thickness of e le c tro d e in cm.

0.977 0.889

3 1 .5 2 8 .5

4.5 5.0

i

0 .4 4 3 5

3.468

I

0 .0 0 7 5 1 1 !1

0.01

! 1 :

1 2.63 2.361

M o n i t o r f a c t o r = ^^0504

J

See f i g u r e (31) c u r v e ( l )

1 I!

-vj H

zo -j 1

d

(3)

T hickness o f A ir in MM.

fZ)

(î)d.»

.Sï

16 O55

08

(3)

w

F igure

( 32).

I o n i z a t i o n p e r u n i t s p a c i n g - E l e c t r o d e S p a c i n g Curves E f f e c t i v e w avelength

=

0.425 A®.

( 1 ) E l e c t r#*o d e s : - P r e s s##e d m i x ##t u r e f*o f ^- z 1 2 . 8 4 . = 1 7 . 04 . (2) " : = 2 0 . 84 . (3)

m

%-

vri,’

1

2

3

4

Thicknmss o f A ir in K4M.

- ■-I

I 575 0 20

SI

#

F igure

( 33 ).

I o n i z a t i o n - E le c tro d e S pacing Curves. E l e c t r o d e s : - P r e s s e d m ix tu re of - = 12. 84. ( 1 ) E f f e c t i v e w avelength (2)

= 0.425 A^. = 0.172 A°.

_

V.1

T h ic k n n s o f E lm ctrod» in MM.

F ig u re ( 34). E x tr a p o la tio n of I to

zero e l e c t r o d e t h i c k n e s s .

E f f e c t i v e w avelength

=

0.425

( 1 ) E l e c t r o d e s P r e s s e d m ix tu re of % = 12. 84. (2) ^ ^ = 17. 04. (3 ) z = 20. 84.

TABLS ()4_)

TABLE ( 55) 5 m .a.

80 KVp.

E x t r a p o la t io n of I to zero E lectro d e Spacing

2 nun. A lu m in iu m ( P r i m a r y f i l t e r ) \

6

= 0 . 4 2 5 A°

T h i c k n e s s o f t h e u p p e r e l e c t r o d e 0*5 M.M. S cale R eading

A ir th ic k ­ ness in M. M.

1.4 2 5 8

0.6 4

1.191

1.1 9 1

5 5.1

0.6655

1.505

1.002

2 .0

2 0.1

0.5571

1.862

.9 5 1

2 .9

82.0

0.4567

2.190

0.876

5 .0

0 5.2

0 .40

2 .50

0.855

5-5

55.0

0.5585

2 .797

0.799

4 .0

4 2 .9

0.5255

5.095

0.7 7 5

4-.5

5 6.0

0.2967

5.5 7 0

0.74.9

28.5

0 .2717

5.681

0.7562

4 0 .1

1.0

57.5

1.5

. -

. . .

1

-

Z = 12 * 8if e l e c t r o d e ( S e p a r a t i o n b e t w e e n e l e c t r o d e s if M.M.) \ = 0.425 e

I d

I

0 .7 1 1 9

0.5

1 5 -0 !

1 Î

12 . 8if)

(Z

T hickness of e le c tro d e in cm.

I 1 !

0.5 7.5

-N K) 5.095

1

2 .9 2 6

1.25

2.752

1.75

2.625

! '

. . . .

See f i g u r e s (52 & 55) curve ( l & l)

See f i g u r e (jif) curve ( l )

j

J

0 8

0-6

0-4

0-2

Thickntss o f Air in MM. O 55

0 8

O 30 0-2

06

02

T h ic k n a s s o f A i r in K fM .

F igure

( 3 5 ).

I o n i z a t i o n - E le c tro d e S pacing Curves. E l e c t r o d e s : - P r e s s e d m i x t u r e o f -z % 17.04 ( 1 ) E f f e c tiv e w avelength (8) (3) (4 )

0.485 AO. 0 .1 8 A°. 0 .1 7 2 AO. 0 . 1 A°.

TABLE ( 56)

TABLS (55)

80 5 2 mm. Aluminium (prim ary f i l t e r ) A = 0.4.25 A° e T h i c l m e s s o f t h e u p p e r e l e c t r o d e 0^5 M.M. ( z = 17.04.) A ir th ic k ­ S cale R eading n ess in M. M.

1 1

!

I

E x t r a p o l a t i o n of I to Zero E le c tro d e Spacing Z = 1 7 * 0if e l e c t r o d e ( s e p a r a t i o n h e t i ; e e n e l e c t r o d e s 4. M.M.) V =. 0.4.25 Ao e

d

A ir th ic k n e ss i n M. Mo

0.5

17.5

0 .25

0 .4 6

1.0

4.7.5

0 .3 4

0 .5 4

1.5

6 .6

0 .42

0 .2 8

0.5

0 .7 4

2 .0

1 5. 8

0.485

0.2425

0.75

0 .7 0

2.5

2 1 .9

0 .5 5 0

0.220

1.0

0 .6 8

5 .0

2 8 .9

0.615

0.204

1.5

0.6 6

3 .5

5 6.2

0 .6 7 7

0.193

4..0

44-. 6

0 .7 4

0 .1 8 5

5 2 .8

0 .8

0.178

5 9 .8

0.8 6

0.17 2

4.. 5

5

1

I -sj

See f i g u r e s (52 & 55) curves (2 & l)

1

!1 I

M o n i t o r f a c t o r _= 1 .2

See f i g u r e ( 54*) curve ( 2)

V>1

TABLE ( 5 7 )

TABLE ( 5 8 )

KVp, 5 s. 2 mm. A l u m i n i u m ( P r i m a r y f i l t e r ) 80

= 0.4.25 A° e T h i c l a i e s s o f t h e a p g e r e l e c t r o d e 0^5 M.M< (Z = 2 0 . 8if)

E x t r a p o l a t i o n o f I t o Zero E le c t r o d e Spacing

Z = 20 .84. e l e c t r o d e ( s e p a r a t i o n h e t n e e n e l e c t r o d e s 4 M.M.) o

X = 0.425 A A ir t h i c k ­ n ess in M. M. 0.5

i

:'

Scale R eading

ifO.

e

I

■I

d

0 .3 1 1

0.6 2 2

0 .4 4

0 .4 4

T h i c k n e s s Of e lectro d e in cm.

I

1 .0

9.1

1.5

2 0 .0

0.537

0 .358

0.05

0.9 2 6 7

2 .0

29. 8

0 .62

0 .32

0.075

0 .86

2 .5

5 9 .0

0 .7 0

0 .2 8

0 .1 0

0.74.

5*0

4 9 .9

0.777

0 .259

5.5

58-9

0.8 5 3 3

0.24.38

4-.0

68.1

0.9267

0 .2317

if. 5

77.5

0 .9 9 3 3

0 .2207

5

8 6 .7

1 .06

0.2 1 2

See f i g u r e s

.

(52

& 29)

curves

( 5 & 2)

i ! M onitor f a c t o r =

See f i g u r e

(34)

curve

(3)

ji T H I C K N E S S O F AIR

IN M M .

- --■) ■'I

F igure

I o n i z a t i o n - E le c tro d e S pacing Curves. E le c tr o d e s :- P ersp ex co a te d w ith dag.

k#;_ #

«

( 36).

#

'

I

( 1 ) E f f e c t i v e w avelength (2) " ” (3) " "

= = =

0 .3 2 8 A°. 0.172 A°. 0.256 A°.

TABLE ( 3 9 )

TABLE (4 0 )

lo o KVp. 3 ro* 4- mm. Aluminium ( P r i m a r y f i l t e r )

170 KVp. 15 m .a. Z ero f i l t e r

\ e = 0 . 5 2 8 AP. Upper e l e c t r o d e P e r s p e x c o a t e d v;ith dag o r ("Z = 7 . 54 )

Air thickness in M.M.

Scale Reading

E"

Xe = 0 .2 5 6 A° Upper e l e c t r o d e P e r s p e x c o a t e d w i t h dag o r (2 = 7 . 64 )

Air thickness in M.M.

R'

Scale

Reading 0.1 2 2 5

2 .0

15

0.22

5-5

5 .6

2.5

29.5

0 .2 7 5

4 .0

1 1 .5

0.14

■3.0

4 5.2

0.55

4.5

16.0

0.157

5-5

60.7

0.385

5 .0

2 4 .5

0.1 7 4 5

4 .0

8.0

0.44

5.5

7.5

0 .1 9 1 7

4.5

15.6

O..495

6.0

1 2 .5

0.210

5 .0

21.8

0 .5 5

6 .5

17.5

0 .2 2 8 5

5.5

28.0

0 .6 0 5

6 .0

5 4 .5

0.66

6.5

4 1 .0

0 .7 1 5

The s l o p e o f t h e c u r v e = 0 . 1 1 See f i g u r e

(3 6 ) curve ( l )

The s l o p e o f t h e c u r v e = 0 . 0 ) 5 See f i g u r e

(3 6 ) c u r v e ( 3 )

-

/é

—

TABLE il^ l) 150 KVp. 3 m.a$ O o mm. c o p p e r + 1 mm. Aluminium ( P r i m a r y f i l t e r ) \e

= 0 . 1 7 2 A°

u p p e r e l e c t r o d e P e r a p e x c o a t e d w ith d a g .

A ir th ic k n ess i n M.M.

Scale R eading

e

"

2.5

14.2

0.16

3 .0

6 .8

0.19

3 .5

15.0

0 .22

4.0

22.9

0.25

4.5

31.5

0.28

5 .0

39.6

0.31

5.5

47.5

0.34

6 .0

56.5

0.37

6.5

65.1

0.4 0

The s l o p e o f t h e c u r v e = O. 0 6 Se e f i g u r e

(3 6 ) curve

(2)

m

o

”

O- 34 0 6

09

(3)

F igure

( 41).

I o n i z a t i o n p e r u n i t s p a c i n g - E l e c t r o d e S p a c i n g Curves. E f f e c ti v e w avelength

=

0 ,32 8 A^.

( 1 ) E l e c t r o d e s : - P r e s s e d m ix tu re of - = 12, 64. (2) " " " " I : 17. 04. (3 ) ” " " " T = 20. 84.

T h ic k n e s s

e< E h ^ frodm »n A / M*

F igure E x t r a p o l a t i o n of I to

(4 2 ).

zero e le c tr o d e th ic k n e s s .

E f f e c tiv e w avelength

=

0 .3 8 8 AO.

( 1) E l e c t r o d e s : - P re s s e d m ixture of - = 12. 84. I = 17 . 0 4 . (8) I = 20. 84. (3)

TABLE (Jf6 )

100 I{Vp.

TABLE ( i f 7 )

5 m. a . E x t r a p o l a t i o n o f I to Zero E le c tr o d e Spacing

if mm. A lu m in i u m ( P r i m a r y f i l t e r ) = 0 . 5 2 8 A° e T h i c k n e s s o f t h e u p p e r e l e c t r o d e 0*5 M.M.(Z = S cale R eading

A ir th ic k ­ n ess in M. M.

0.28

1.0

17.5

0.2285

0.2285

1.5

57.2

0.5008

0 .2008

2 .0

5 5 .0

0.5664.

0.1852

2 .9

7 .1

0 .4250

0 .1 7 0 0 0

15.5

0.480

0.160

19.5

0 .550

0.151

if.O

25.2

0 .5 8

0.145

4 .5

; 5 0.6

0.627

0.159

5 .0

55.9

0.675

5 .5 _______

4 1 .4

0 .72

5*5

L

I

O .lif

5 .0 :

See f i g u r e s

( if l & 26)

\

I a

1 1.6

0.5

12 8if) ^

Z = 12 . 8if e l e c t r o d e b e t w e e n e l e c t r o d e s if M. M. )

curves

:

e

T hickness electro d e cm.

= 0 . ) 2 8 AP

of in

I

0.05

0 .5 8

0 .10

0.565

0.15

0.55

0.20

0.54.

"N VO

0 .1546 0 .151 ( l & 2)

See f i g u r e

(if2)

curve

(l)

TABLE ( i f 8 )

TABLE ( i f 9)

1 0 0 KVp. 5 m. a . ij. mm. A l u m i n i u m ( P r i m a r y f i l t e r )

; = 0 ,)28 T h i c k n e s s o f t h e u p p e r e l e c t r o d e 0 .5 M.M< (Z = l / . O i f )

A ir t h i c k ­ Scale n ess i n Reading M. M.

1

i

I

Z = 1 / . Olj. e l e c t r o d e ( S e p a r a t i o n h e t u e e n e l e c t r o d e s 5 M.M.) \

e

= 0.528 £

: T hickness of e le c tro d e in cm*

0.5

2 0.0

0.2572

0 . if 744

1.0

52.6

0.5567

0.5567

1.5

8 .9

O.ififO

0 .295

0.05

0.9 2 6 7

2 .0

18.6

0.52

0.26

0. 1

0.8995

2.5

27.5

1 0.60

0 . 2if

0.15

0.8 8 5 5

5 -0

5 5 .7

0. 67

0.225

0.2

0.8626

0 .74

0 .2 1 1

0.805

0 .2 0 0 8

0.8 6 7

0.195

5.5

4-.0

52.2

4 .5

6 1.0

^

;

I d

E x t r a p o l a t i o n o f I to Zero E le c tr o d e Spacin g

:

i I (

5 .0

68.1

5.5

75.7

:

o . i 855if

0.9 2 6 7 ■

See f ig u r e s

;

0 .9 8 0

(ifl & 28 ) cu rves

0.178 (2 ÔC 2 )

See f ig u r e

(if2)

curve

(2)

GO

O

o 8

O X-

Th ic k ness o f A ir in MM. O 88

(Il

0 35

T h ic k n e ss o f A i r in MM.

F igure

( 4 3 ).

I o n i z a t i o n - E le c tro d e S pacing Curves. E l e c t r o d e s : - P r e s s e d m i x t u r e o f -Z = 2 0 . 8 4 . ( 1 ) E f f e c t i v e w avelength »T TT (2 ) ri ri (3 ) T1 rt (4)

= _ = _ = ” =

U.256 0 .172 AO. 0 . 1 A ^.

TABLE ( 5 0 ) 1 0 0 KVp. 5 m. a . if mia. A l u m i n i u m ( P r i m a r y f i l t e r )

TABLE ( 5 1 ) E x t r a p o l a t i o n o f I to Zero E le c tr o d e S p acin g

= 0 . ) 2 8 A° e T h i c k n e s s o f t h e u p p e r e l e c t r o d e 0«5 M.M, (Z = 2 0 . 8if) S cale A ir th ic k ­ ness in R eading M. M.

!

i

Z = 2 0 . 8if e l e c t r o d e ( ' S e p a r a t i o n betvveen e l e c t r o d e s 5 M.M.) A = 0 . 5 2 8 A°

1 I

I

a

I

0.5 1 .0

if2.2

-

0 .52

1 6 .1

-

0 .5 0

0 .6 4 0 .5 0

1.5

5 2.2

0 . 64.

0 .i f 2 6

2 .0

4-9.3

0 .78

0 .3 9

2.5 5 .0

92.3

1 .1 1

0 .9 0

0 .5 6

76.1

o.985if

1.015

0.558

3.5

éif • 0

0 .8 9

1 . 1 2 if

0.521

if.O

5 4 .9

0.8 2 5 6

1.212

0.505

^ .3 5 .0

4.9.5 4.5.0

0 .7 8

1 .2 8 2

0 .285

0 . 7if8if

1.337

0.267if !

5-5

ifO .l

0.7119

1.4.05

0.255

6 .0

5^. ^

0.6 8

1.4 7 1

0 . 2if 8 I

See f i g u r e s

(ifl & ifj)

curve

(5

& l)

T hickness of e le c tro d e in cm.

I

00 f-»

0.05

1-357

0.075

1.516

0 .1 0

1.282

See f i g u r e

( if 2 )

curve

(5)

TABLE (5 2 )

TABLE ( 5 5 )

170 lO/po 15 m. a . Zero f i l t e r ^

E x t r a p o l a t i o n of I to Zero E le c tr o d e Spacing

= 0 . 2 5 6 A°

T h i c k n e s s o f t h e u p p e r e l e c t r o d e 0.75 M.M. A l . A i r t h i c k -1 S cale ness in , R eading M.M.

1 .0

20 .9

0 .2417

0.2417

1.5

!

4 .0 .0

0 .5 1 1

0 .2 0 7

2 .0

I

0

0 .5 6 0

0 .1 8 0

4 .7

1

0.4.05

0 .1 6 2 0

j

10.0

j

0 .4 4 8

0.149

5-5

1

1 5.0

i

0 .4 9

0 .1 4

if-.O

1

19.5

!

0,550

0 .1 5 2

1

2if. 0

I

0 .5687

0.1 2 6

1

2 8 .1

!

0 . 605

0.1210

2.5

!

5 .0

if. 5 5 .0

A = 0 . 25^6 Ap e

I d

|

11

A lu m in i u m e l e c t r o d e ( S e p a r a t i o n h e t i v e e n e l e c t r o d e 2f M.M.)

T hickness of e lectro d e in cm. GO

I

\ j

0.075

j

0.550

0.125

;

0.5155

0.2

I

0.4 9 1 2

1

j

1

See f i g u r e s

(57 & 5 8 )

curves

( 2 & 2)

See

fig u re

(20)

curve

(if)

o 56-

O16 O08

IZ)

013 O Z6

O 60

F igure

( 4 4 ).

I o n i z a t i o n p e r u n i t s p a c i n g - E l e c t r o d e S p a c i n g C a rv e s E ffe c tiv e vav elen g th

0 .256 A°.

=

f 1 ) ' E l e c t r o d e s : - P r e s s e d m i x t u r e o f - - i ? p,a (3)

:

:

:

:

|

:

o 4.-

0 3-

O %.

T h ickn ess o f A ir in MM. /d * o

O 13

0-3-

o X-

*

T h ic k n e s s o f A ir in MM.

F igure

(45).

I o n i z a t i o n - E le c tr o d e S pacing C urves. E l e c t r o d e s : - P r e s s e d m ix tu re of - = 12. 84. z ( 1 ) E f f e c t i v e w a v e l e n g t h = 0.1 2 A.^. (2 ) (3)

0.256 0 . 1 AO.

TABLE ( 5 4 )

TABLE ( 5 5 )

170 KVp. 15 m .a . Zero f i l t e r

170 ICVp, 15 m. a. Z e ro f i l t e r

= 0.256 e T h i c k n e s s o f t h e u p n e r e l e c t r o d e 0.5 M.M. (z

= 12.84.)

'A ir t h i c k - ; S c a le ness in 1 Reading 1 M. M. 1 1 .5

I

1

4' 6

i ! 1 1

I

i .

I

i

1

A = 0 . 2 5 6 A° e T h i c k n e s s o f t h e u p p e r e l e c t r o d e 0.5 M.M. ( z = 17 . o w ' Scale A ir th ic k ­ R eading ness in M. M.

I

1

i

i

r ' •-

1 0 .1 2

0 .0 8

1

1 .0

5 .8

0.180

0.18

1

2 .0

1 1 .5

j 0.14.1

0 .0 7 0 5 I

1 .5

1 7 .5

0 .2 5 0

0 .1 5 5

i {

2 .5

20.2

1 0 .1 6 1

0 .0 6 4 4 1

2 .0

2 8 .1

0 .2 7 0

0 .1 5 5

1

5 .0

5 .0

j : 0 .1 7 7

0 .0 5 9

1

2 .5

5 7 .0

0 .5 0

0.12

1

5-5

7 .6

1 0 .1 9 5 5

0 .0 5 5 5 1

5 .0

45-5

0 .5 2 5

0 .1 0 8

I

4-.0

1 1 .4

0 .0 5 2 2

5 0 .4

0 .5 5 0

0.1

1

1 6 .5

j I !

5-5

4.5

! 0 .2 0 9 1i 1 0 .2 2 5

4..0

5 8 .1

0 .5 7 5

0 .0 9 5 7 5 j

5 .0

2 0 .5

j

0.24-0

0 . 04-8 1

4-. 5

6 5 .0

0 .4 0 0

0 .0 8 8 9

5 .5

24.. 2

; 0 .2 5 5

0.04.65 1

5 .0

7 2 .5

0 .4 2 5

0 .0 8 5 0

5.5

8 0 .0

0 .4 4 8 7

0 .0 8 1 6

0 .0 5

!

M onitor f a c t o r = See f i g u r e s

(44

& 4 5 ) curves

( l & 2)

See f i g u r e s

1

1 1

i

1

i

0.265

(44- & 2 8 )

curves

(2 & 5 )

00

0 64

1 -------------- i -------------- 4

Thickness

0) [1

o f Air m M M.

]

019

I d / d >o

.i

(Z)

0 3

(3)

0 64

F ig u re ( 46).

'

I o n i z a t i o n p e r u n i t s p a c i n g - i î i l e c t r o d e S p a c i n g u u rv es E f f e c t i v e w avelength (1)

(2)

(3 )

=

0.172 A°:

E l e c t r o d e s : - P r e s s e d m ix tu re of

"

"

"

"

•’

"

- = 12 . 8 4 .

I = 17 .04 . ^ = 2 0 . 84 .

TABLE ( 5 é) I / O KVp. 15 m. a . Zero f i l t e r -

= 0 .2 5 6

TABLE ( 5 7 ) 1 5 0 KVp. 15 m .a.

0 . 5 mm. Cu + 1 mm. A l . (prim ary f i l t e r )

A°

■e '• = 0 . 1 7 2 A° e T h i c k n e s s o f t h e u p p e r e l e c t r o d e 0 . 5 M.M. T h i c k n e s s o f t h e u p p e r e l e c t r o d e 0 . 5 M. M, ( z = 20.82)-) ( z = 12.84.) Scale I iA ir t h i c k A ir th ic k - 1 S cale I I d R e a d i n g R eading I n e s s i n : ness in ! i :i M.M. 1 M. M. ! i 1 t ^ — — *H 1 o .iif6 0.58 0.146 1.0 1 .0 1 59.5 0.58 15*9 ! 0.1855 0.1252 0.287 1 o . 2f 5 .5 .0 1*5 « 7i f . i i 1.5 ! 0.110 0 .2 5 5 0.220 15.0 2 .0 2.0 j 8 6 .5 o . 2f 7 ( ! i C .1020 0.20 I 0.50 0 .2 5 5 2.5 i 16.1 2if .5 2.5 i

!

j

;

5.0 5.5

1

I

! I

I

1 5 .5

j 0.55

0.177

5 .0

5 4.0

25.0

1 0.56

0.16

5-5

27.0

! 0.59

0.14.7

if.O

55.0

0.290

0 . 0 9 6 7

0 .5 2 5

0.0929

0.5585

0.0891 !

i f . O

1 ( !

if. 5

!

2 9.8

1 0.62

0.158 1

if. 5

5 .2

0.59

0.0867

5 .0

1 55.2

1 0.65

0.150

5.0

6 .5

0.if2

0.082,.

5.5

1 5 6.7

1 0.68 ) ' ...............

0 . 122f

5.5

10.0

0.2,48

0.0814.

L ............

! '

1

M o n i t o r f a c t o r = 22.^1 0 .2 6 5 See fig u r e s

( # . & 4-))

curves

(5

& 2)

See f i g u r e s

(4-6 & 5 5 )

curves

( l & 2)

TABLE ( 5 8 ) 150 KVp. 15 m .a. 0.6 mm. Cu + 1 mnu A l . (P rim ary f i l t e r )

TABLE ( 5 9 )

150 KVp. 15 m .a . 0 . 5 mm. Cu + 1 mm. A l. (Prim ary f i l t e r ) X = 0 . 1 7 2 A° T h i c l d i e s s o f t h e u p p e r e l e c t r o d e 0.6 M.M,

Xg = 0 . 1 7 2 A° T h i c k n e s s o f th e u p p e r e l e c t r o d e 0*5 M.M. (Z = l / . O i f )

1 S cale A ir th ic k ­ i I R eading ! n ess in M.M. __ j___ _ ____ I 10.2558 1 .0 19.5

I

i-

^

(Z

I A ir t h i c k - j Scale 1n e s s i n ! Reading i M. M.

= 20.84.)

;

I

! !

i

55.1

i ; '

!

0.2558 1 1 0.2925 : 0.1950

j

1 .5

1 60. é 1 1 2 .5

1 0.5487 ! 0.1745

j

2 .0

j 0.16

i

1 0 .1 5

1

2 .0

50.0

2.5

4.. 2

5.0

10.2

i ! 0.4.50

5.5

15.4.

i 0.495

4-.0

20 . 4-

if. 5 5.0

1 0.4.

1 i

10.141

i 0 .5 8 5

i 0 .4 7 0

! 0 .5 1 5

2 1 .1

*0.545

I 0 .2 7 2

2 .5

2 8 .7

j0 . 6 1

I 0 .2 4 4

5 .0

5 5 .6

j o . 67

5 .5

45-0

jo . 75

10 .2 2 5 1{ 0 .2 0 9

5 0 .7

j o . 79

1: 0 .1 9 8 1I

jo . 85

! 0 .1 9 0

i

I

1

1 0.5585 ! 0.1546

4 .0

25.5

1 0.5816 ! 0.1292

4 .5

!1 5 8 . 7

50.0

! 0.6 2 4

5 .0

66 . 5

55.1

; 0.6655 10 .1209

10.124.8

I

!: i

(

5.5

See f i g u r e s

( 4.6 & 55)

curves

(2 & 5)

1

i 1 ... ........... i

jO.585

1 .0

i

1

I d

5 . 5

:

See f i g u r e s

7 5 . 5

10 . 9 1

00

VJl

1

!

; 0 .1 8 2

1

j

1

10 .9 6 5

i 0 .1 7 5

(46 & 4 ) )

curves

(5 & 5)

f

iEff»,:': -.:6l-’i F igure ( 47) I o n i z a t i o n - E l e c t r o d e S p a c i n g C urves E l e c t r o d e s : - P e rsp e x c o a te d w ith dag. ( 1) E f f e c tiv e w avelength (2)

I'.

' ''

= =

0.12 A^. 0 . 1 AO.

TABLE ( é o )

200 KVjp.

1 . 5 mm. Cu. + 1 rnra. A l .

l_f, rti. a. (Prim ary f i l t e r )

TABLE ( 6 l ) 220 T(V-p. 15 m .a . 2 mm. Cu. + 1 mn. A l . ( P r i m a r y f i l t e r )

X o = 0 .1 2 A^.

\ e = 0 . 1 A°.

U pper e l e c t r o d e p e r s p e x c o a t e d w i t h d ag .

Air th ic k n e s s i n M. M. 2 .5 3 .0

9.7 2 0.3

3.5

6.5 1U .6

h .o .

S ca le Reading

k-5

5.0 5 .5

6.0 6 .5

R' 0.135 0.1625 0.19 0.2175

21.7 26 . 6 36.9

0.245 0.2725 0.300

Uk-k

0.3275 0.355

52.0

The s l o p e o f t h e c u r v e = O.O55 See f i g u r e (I4I4) c u r v e ( l )

U pper e l e c t r o d e p e r s p e x c o a t e d w i t h dag

Air th ick n ess i n M.M. 3.0 3.5 4 .0 4 .5 5 .0 5.5

S cale Reading

R'

9.5 11 .5

0.12 0.14

19.5 3 .8

0 .1 6 0 .1 8 0 .2 0 0.22

9.8

6.0

14.9 2 0.5

0.24

6 .5

25.5

0 .2 6

The s l o p e o f t h e c u r v e = O.Oh See f i g u r e (i|U) c u r v e ( 2 )

CO o\

M

I

-1!

o »

I

%. 0 2-

'"N l'.ni

i j

T h /tk n e s s o f A ir in MM.

4 d

O 148

F ig u re ( 48). I o n i z a t i o n p e r u n i t s p a c i n g - E l e c t r o d e S p a c i n g Curves E l e c t r o d e s : - A lum inium . ( 1 ) E f f e c t i v e w avelength (

2)

(3)

0.172 A° 0.12 A°. 0 .1 A°.

0-6

(3)

04 I 0 2-

Thickn»ss o f A ir in MM. O 28

08 I

(2)

0 167

(3)

0160

(2 )

06 0-4

02

Thickness

o f A ir m MM.

m: F igure

( 4 9 ).

I o n i z a t i o n - E l e c t r o d e S p a c i n g C urves E l e c t r o d e s : - A luminium. I I ®

"

(1) (2)

(3)

E f f e c t i v e vm velength ^

z 0.172 A^ = 0 . 1 2 0 A°

= 0 .1 AO.

TABLE (62) 150 KVp. 15 m . a . 0 , 5 mm. Cu + 1 mm. A l . (P rim ary f i l t e r ) ig

TABLE (65) 200 KVp. 15 m .a . 0 . 5 mm. Cu + 1 mm. A l. (P rim ary f i l t e r ) = 0 . 1 2 A°

= 0 . 1 7 2 A°

T h i c k n e s s o f t h e u p p e r e l e c t r o d e 0.75 M.M. A l . A ir th ic k ­ ness in M. M.

S cale R eading

I â

I

1

.

:

T h i c k n e s s o f t h e u p p e r e l e c t r o d e 0.75 M.M. A l.

A ir th ic k ­ ness in M. M. r, -------------

S cale Reading

I d h-"

--------------

1 .0

20.5

0.24.

0 .2 4

1 .0

15.5

0.15

0.15

1.5

4 5 .0

0.5295

0.219

1.5

1 4 .7

0.2 1 7

0.144

2 .0

69.2

0.4155

0.2076

2 .0

5 1.0

0 .2 8 0

0.140

2.5

9 2 .5

0 .4 8 6 7

0.1 9 4 6 8

2.5

4 7.5

0.5 4 1

0.1564

5 .0

22 .0

0.5555

0.184

5 .0

65 .,5

0 .402

0 .154

5.5

2 9 .7

0.6195

0.177

5.5

8 4 .5

0.465

0.152

4..0

57.2

0.6855

0.171

4 .0

1 8.7

0.525

0.1507

^ .5

4 5 .7

0.750

0.1667

4 .5

2 5 .7

0.585

0.129

5 .0

55-7

0.8150

5 .0

5 2.0

0 .6 4 0

0 .128

1

5. 5

62.5

0.88

5. 5

58.1

0.697

0.126

1 i

.1 6 5 0 0 0 .16

---------------------------

See f ig u r e s

(i}-8 & 4 .$)

curves

( l & l)

See fig u r e s

(48

00

& 4-9)

curves

( 2 & 2)

I

08 IZ)

04-

(ijd.o • (3)

'■=

II

= 1 - 6

"

.

0 87

F ig u re ( 5 0 ).

“ÎPaol-d C»,vaa ( 1 ) E f f e c t i v e w avelength 2)

(

(3 )

"

•!

0.172 Ô.O. 0.120 A°'. 0 . 1 A°.

TABLE ( 6 if) 2 2 0 KVp.'

TABLE ( 6 5 )

1 5 0 KVp. 15 m . a . 0 . 5 mm. Gu + 1 mm. A l . (P rim ary f i l t e r ) = 0 . 1 7 2 A°

m. a .

15

2 mm. Cu + 1 mm. Al (P rim ary f i l t e r ) = 0 . 1 A° e

T hickness of the upper e l e c t r o d e 0 . 7 5 M.M. A l . S cale I A ir th ic k ­ I d R eading ness in M.M. _j -

T hickness of th e upper e l e c t r o d e

A i r thick-, S c a le j n e s s in Reading M. M. . .4 11 .....-.....

. . . .

1.0

11.5

0 .1 4

0.1 4

1.5

6.5

0 .1 9

0.1 2 6 7

2 .0

20.5

0 .2 4

0.12

2.5

5 4.0

0 .2 9

5.0

47.5

5.5

6 2 .0

4 .0 4 .5 5 .0 5.5

1

1 .0

76.1

1.5 2 .0

j 55.2 !1 5 8 . 1

1

I

! 0.9854

1.015

0 .81

1.254 1.445 1.6 4 8

)

28.2

0 .116

2.5 5 .0

0.6955 0. 6066

2 2.1

0.5555

1.8 0 7

0 .5 4

0.115

5-5

17.0

0.510

0 .59

0 .11 1

4 .0

1 2.8 9 .0

0.4755 0.4 4 1 7

9.1

0.44

0 .1 1

10.4167

1 4.9

0 .49

0 .1 0 9

69.5 6 5.8

1.96 2.115 2.264 2 .40

1 2 0 .5

0 .54

0 .1 0 8

2 7.0

0 .59

.107

I

4 .5 5 .0 5.5 6 .0 6 .5

7 8

58.5 55.5 ! 49 .1 1 4 2 .8

• 0.5955 0.5 7 6 7 0 .56

;

I

!1 5 7 . 5 10 ! 52.5 — ....... « .. ...................J

9

See f ig u r e s

( 4 .8 & if j )

curves

(5

& 3)

See f ig u r e s

(5 0

ii o.545 ;i o .5 2 2 110.505 0.285 & 22)

i

i1

1.015 0.825 0 .7 2 2 5 0.6592 ! 0.602

1

0 .56 0.5 2 8 0.505 0 .48 0.46

2.55 2.655

I 0 .444

2.778 2.898 5 .106

I 0 .427 j 0 .414 j 0 .588

1 5-510 ! 5.510

j 0 .57 10 . 5 5 1

curves

00

CO

( l & 2)

1 1 j !

TABLE ( 6 6 ) 2 0 0 KVp. 1 5 m .a .

TABLE ( 6 7 ) 2 2 0 KVp. 1 5 m .a .

1.5 mm. Cu + 1 mm. A l. (Prim ary f i l t e r )

2 mm. Cu + 1 mm. A l.

y

= 0 . 1 2 Ap

1

T h i c k n e s s of t h e u p p e r e l e c t r o d e 0 .0 1 2 5 M.M. Copper A ir Scale 1 th ic k ­ ■ I R e a d in g I ness i n M.M. 1.0

50.0

1 .5 2.0 2 .5 5.0

52.5 20.9 8 8 .1 72.5 60.8 52.0 44.9 58.1 155.8 28.8 25.2 22.5 1 8 . if 1 6 .2

5.5 4 .0 4.5 5.0 5 .5 6.0 6 .5 7.0 7 .5 8.0 9.0 10.0

1 1.5 i 7.1

(Prim ary f i l t e r )

0.7858 0.6590 0 .5 4 5 5 0.474 0.4255 0 .5 8 6 0.555 0 .5 2 9 5 0 .5 0 5 5 0 .2 8 9 6 0.2 725 0.2 5 9 0 0 .2 4 6 2 0 .2 55 0.2247 0.2067 0.1917

1.276 1.565 1 .8 4 1 2.11 2 .5 5 2.59 2.817 5 .0 5 5 5.248 5.454 5.657 5 .8 6 0 4.061 4 .2 5 5 4.45 4.858 5.217

e

= 0 . 1 A°

T h i c l a i e s s of t h e u p p e r e l e c t r o d e 0.0125 M.M. Copper A ir I I Scale th ic k ­ a R e a d in g a ness ! i n M.M. f 0.7 1 .2 7 6 1 .0 0.7 59 0 .6 5 5 71.6 0.95 1 .0 4 5 1 .5 0 .5 8 5 2.0 0.9 2 0 5 59.4 0.8547 1.1 7 0 .5 5 5 6 0.720 0.844 1 .5 8 9 2.5 41.5 29.8 5.0 0 .5 5 5 0 . 6 2 5 4 1 .6 0 4 0 .7 8 5 1 .8 1 8 21.9 0.519 0 .5 5 0.74 5.5 0 .5 0 5 2 .0 1 5 if.O 0 .4 9 6 7 15.5 0.704 2.2 8 1 .2 0.49 4.5 0.674 2 . 5 8 0.420 0.476 5.0 0 .6 4 9 6 70.5 62.5 0.464 0.628 0 . 5 9 1 7 2 .5 5 5 5.5 0.609 6. 0 0.454 0 .5 6 7 2 .7 2 5 55.5 6 .5 0 .5 4 5 8 2 . 8 9 5 0.445 49.1 0.594 0.5267 5.060 0 .5 8 0 7.0 0.457 4 5.9 0.450 0.51 0 .5 6 6 5.225 5 9.5 7.5 8.0 0.424 0 .5 5 6 5*59 0 .2 9 5 55.5 0.27 2 8 .5 5.0 0.411 5 .7 0 5 0.557 0.4021 0.2487 4 .0 2 1 2 2 .5 0.5217 10.0 0

.

4

5

5

5

Mon i t o r f a c t o r = ^ See f ig u r e s

(5 0

& 4 0 ) c u r v e s (2 & l )

See f i g u r e s

(5 0

& 5 0 ) curves

(5

& 2)

00

VO

o 48-

O 32-

I

o

03XH O

OZH o

I

%

o'H

ooB-J

T h ic k n e s s o f

(SI'A.-0

A ir in MM.

= 0125

(2)

s ' O 19

(3)

=

F igure

0-3A

( 52).

I o n i z a t i o n p e r u n i t s p a c in g - E l e c t r o d e S p a c in g Curves. E f f e c t i v e w avelength

=

o , l A°.

( 1) E l e c t r o d e s : - P re s s e d m ix tu re of - = 12. 84. (2) " " '' # = 1 7 . 0 4 . (3 ) " " " I _ 20. 84.

TABLE ( 7 0 ) 2 0 0 KVp. 1 5 m .a .

TABLE ( 7 1 ) 2 2 0 KVp. 1 5 m .a .

1 . 5 mm. Cu + 1 mm. A l . (P rim ary f i l t e r ) \

0

'2 mm. Cu + 1 mm. A l . (P rim ary f i l t e r )

1e

= 0 . 1 2 A°

T hickness of t h e upper e l e c t r o d e 0 . 5 M.M. (Z = 2 0 .84.) A ir th ic k ­ ness in

S cale R eading

T hickness of th e upper e l e c t r o d e 0 . 5 M.M. (Z = 12.84.) I d

I

M. M.

1

= 0 . 1 A°

A ir th ic k ­ ness in

S cale R eading

I

I d

M. M.

1 .0

50.4-

0.550

0.550

1 .0

1 .0

1.5

1 0.0

0 .4 4 8

0.299

1-5

2 .0

2 0.1

0.557

0.268

2.5

2 8 .7

0.6 1 0

5 .0

5 7.2

5.5

0 .1 1

0 .1 1

1 4 .1

0.147

0.098

2 .0

2 8 .8

0.185

0.0925

0.244.

2.5

18.5

0 .2 2 5

0.0 8 9 2

0.6 8 5 5

0.228

5.0

2 5 .0

0.2585 0 .0 8 6 1

4 5 .7

0.75

0.214.

5*5

5 5.5

0.294

It-.o

54.5

0 .82

0.205

4 .0

4 5 .0

0.5295 0 .0 8 2 4

4 .5

65.5

0 .8867

0 .1 9 7

4 .5

5 4 .7

0.565

0 .081

5 .0

7 2.2

0 .955

0.1906

5 .0

65.2

0 .4 0

0.0 8

5.5

8 0.0

1.016

0.185

5.5

8.1

0.455

0 .0 7 9 0

.

................ .................... ..

—

0.084.

.

M o n ito r f a c t o r 0 . 8 See f i g u r e s

( 5 I & 29)

curves

(5

& 5)

See f ig u r e s

(52

& 4-5)

curves

(l & 5)

TABLE ( 7 3 )

TABLE ( 7 2 ) 2 2 0 KVp. 1 5 m. a