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An efficient ionizer for an atomic beam of helium and a source of doubly charged helium ions. Vermette, Clifford William Harvey 1964

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AN EFFICIENT IONIZER FOR AN ATOMIC BEAM OF HELIUM and A SOURCE OF DOUBLY CHARGED HELIUM IONS by CLIFFORD WILLIAM HARVEY VERMETTE B.A.Sc. The U n i v e r s i t y o f B r i t i s h Columbia 1962  A Thesis Submitted I n P a r t i a l F u l f i l m e n t of The Requirements f o r The Degree o f MASTER OF APPLIED SCIENCE I n The Department Of PHYSICS We a c c e p t t h i s t h e s i s as conforming t o the required  standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1964  In presenting the  r e q u i r e m e n t s f o r an  this thesis i n partial fulfilment  advanced degree at  B r i t i s h Columbia, I agree that a v a i l a b l e f o r r e f e r e n c e and mission for extensive p u r p o s e s may his  be  study „  Library  written  Department  of  the  Head o f my  permission*  c o p y i n g or  s h a l l not  freely per-  scholarly  Department or  I t i s understood that  The U n i v e r s i t y of B r i t i s h C o l u m b i a , Vancouver 8 Canada ?  s h a l l make i t  I f u r t h e r agree that  c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n w i t h o u t my  the U n i v e r s i t y o f •  c o p y i n g of t h i s t h e s i s f o r  g r a n t e d by  representatives,  the  of  be  by publi-  allowed  ABSTRACT  Part I An e f f i c i e n t i o n i z e r d e s i g n e d f o r t h e i o n i z a t i o n o f a low i n t e n s i t y m o l e c u l a r  beam has been d e v e l o p e d .  The i o n i z e r  w i l l have an e f f i c i e n c y f o r an.argon beam a t room t e m p e r a t u r e and 0.8 amperes p l a t e e l e c t r o n c u r r e n t o f g r e a t e r t h a n 5.3% and for  an h e l i u m  4 beam a t room t e m p e r a t u r e and 0.8 amperes p l a t e  e l e c t r o n c u r r e n t o f g r e a t e r t h a n 0.12%. The  e l e c t r o n bombardment i o n i z a t i o n o c c u r s between two  f l a t p l a t e s b o t h o f w h i c h a r e a t 200 v o l t s p o t e n t i a l w i t h t o t h e cathode.  respect  The two p l a t e s a r e a t a 2 . 5 ° a n g l e t o each o t h e r  so t h a t t h e i o n s once formed e x p e r i e n c e  a field  gradient  produced  by t h i s a n g l e w h i c h a c c e l e r a t e s them out t h e open s i d e o f t h e i o n i z e r 90° t o t h e d i r e c t i o n o f t h e i n c i d e n t n e u t r a l beam.  The  e l e c t r o n s were e m i t t e d from 6, 0.030 x 0.004 i n c h e s , t h o r i a t e d t u n g s t e n r i b b o n f i l a m e n t s heated by d.c. power.  Successful  a c t i v a t i o n o f t h e f i l a m e n t s , however, was n o t a c h i e v e d were used as pure t u n g s t e n f i l a m e n t s .  and so t h e y  The i o n i z e r r a n a t between  1900° K e l v i n and 2600°Kelvin f o r about 8 hours w i t h o u t d i s t o r t i o n , filament sag, or appreciable  significant  outgassing.  Part I I The  d e s i g n o f a s o u r c e o f doubly charged h e l i u m  i o n s was  c a r r i e d out t o p r o v i d e an h e l i u m beam o f t w i c e t h e t e r m i n a l energy o f t h e Van de G r a a f e A c c e l e r a t o r . The Van  u n i t , t o be i n s t a l l e d i n t h e t o p t e r m i n a l o f t h e  de Graaffc, employs a r a d i o f r e q u e n c y i o n s o u r c e f o l l o w e d by  a double f o c u s i n g magnet. pieces with a fringing plane.  The magnet has p l a n e p a r a l l e l p o l e  f i e l d t h a t produces f o c u s i n g i n a v e r t i c a l  The u n i t i s d e s i g n e d so t h a t a t 2.5 k i l o v o l t s  extraction  v o l t a g e a magnetic f i e l d o f 3060 gauss i s r e q u i r e d t o bend t h e He through +  an a n g l e o f 9 0 ° and b r i n g them t o a f o c u s a t 5.S cm.  from t h e e x i t f a c e o f t h e magnet.  The beam a c c e p t a n c e a n g l e o f  t h e magnet i s 1 0 ° a t a s o u r c e d i s t a n c e from t h e e n t r a n c e f a c e o f 5  cm.  ACKNOWLEDGEMENT  I w i s h t o e x p r e s s my deepest g r a t i t u d e t o Dr. J . B. Warren f o r s u p e r v i s i n g P a r t I o f t h i s t h e s i s and f o r p r o v i d i n g me w i t h t h e o p p o r t u n i t y  t o support m y s e l f f i n a n c i a l l y .  Thanks a r e due t o Mr. D. Axen f o r h i s many u s e f u l and  d i s c u s s i o n s and f o r h i s  ideas  cooperation.  I would a l s o l i k e t o thank Mr. D. L. J a s s b y f o r h i s a s s i s t a n c e , cooperation  and h e l p f u l d i s c u s s i o n s .  I w i s h t o thank Dr. K. Erdman f o r s u p e r v i s i n g P a r t I I of t h i s t h e s i s .  H i s v a l u a b l e s u g g e s t i o n s and d i s c u s s i o n s have  been used t h r o u g h o u t P a r t I I . F i n a l l y , t h e t e c h n i c a l a s s i s t a n c e o f Mr. P. Hass i s g r a t e f u l l y acknowledged.  TABLE OF CONTENTS PART I  AN EFFICIENT IONIZER OF AN ATOMIC BEAM OF HELIUM  CHAPTER I  1  INTRODUCTION  CHAPTER I I IONIZATION PRODUCED BY AN ELECTRON BEAM (a) (b) (c) (d) (e)  I o n C u r r e n t from a Beam Ionization Efficiency I o n C u r r e n t due t o a Background Gas I o n i z a t i o n C r o s s S e c t i o n s o f Argon and Helium E s t i m a t e d I o n C u r r e n t f o r t h e P o l a r i z e d H e l i u m 3 Source  CHAPTER I I I  DESIGN OF THE IONIZER  3 3 4 4 5 6 7  (c)  Design Choice Use o f a Space Charge P o t e n t i a l Minimum ( i ) Purpose ( i i k T h e o r e t i c a l E v a l u a t i o n o f t h e P o t e n t i a l Minimum C o n s i d e r a t i o n s i n D e s i g n and C h o i c e o f Parameters ( i ) S i d e V e r s u s End E x t r a c t i o n ( i i ) Filament Considerations ( i i i ) G r i d t o Cathode S p a c i n g ( i y ) Maximum Space Charge L i m i t e d P l a t e Current. (v) C a l c u l a t i o n o f t h e R e q u i r e d G r i d - P l a t e A n g l e  7 9 9 9 11 11 12 14 14 15  (d)  E x t r a c t i o n o f Ions and F o c u s i n g  16  (a) (b)  CHAPTER IV (a) (b) (c) (d)  Cathode Grid Plate Assembly  CHAPTER V (a) (b) (c)  PRACTICAL CONSTRUCTION OF THE IONIZER  TESTING AND  16 17 16* 16* PERFORMANCE  T e s t Chamber Technique o f Performance T e s t i n g Results and'Estimation o f E f f i c i e n c y (i) Total E f f i c i e n c i e s ( i i ) F i l a m e n t Performance ( i i i ) P o s i t i v e Ion N e u t r a l i z a t i o n  CHAPTER V I  CONCLUSION  19 19 20 20 22 23 24  PART I I A SOURCE OF DOUBLY CHARGED HELIUM CHAPTER V I I  INTRODUCTION  26  CHAPTER V I I I  ION SOURCES  27  CHAPTER I X  THE RADIO FREQUENCY DISCHARGE  28  (a) (b)  General Optimum D i s c h a r g e C o n d i t i o n s f o r t h e P r o d u c t i o n o f  28  Doubly Charged Helium  30  CHAPTER X  DESIGN OF THE DOUBLE FOCUSING MAGNET  (a)  P o l e P i e c e Design  (b)  Image S h i f t due t o t h e Extended  31 31  Fringing Field  32  CHAPTER X I  TEST BENCH  33  CHAPTER X I I  CONCLUSION  34  APPENDICES I E q u a t i o n s D e s c r i b i n g t h e P o t e n t i a l and Space Charge L i m i t e d C u r r e n t Between G r i d and P l a t e II E q u a t i o n D e s c r i b i n g t h e P o t e n t i a l Minimum G r a d i e n t as a F u n c t i o n of t h e G r i d - P l a t e Angle I I I The P o t e n t i a l Minimum V a r i a t i o n due t o a D.C. F i l a m e n t Voltage IV D e r i v a t i o n o f an Approximate Formula f o r t h e Maximum R a t i o o f t h e Charge D e n s i t y o f P o s i t i v e Ions t o t h a t o f E l e c t r o n s f o r t h e P o l a r i z e d Beam I o n i z e r V E l e c t r o n P a t h Length I n c r e a s e due t o an A p p l i e d D.C. Magnetic F i e l d , VI (a) T a b u l a t i o n o f |h(y)dy and dx/dy f o r E n t r y t o t h e Magnet (b) T a b u l a t i o n o f / h ( y ) d y and dx/dy f o r E x i t from t h e Magnet BIBLIOGRAPHY .  36 38 39 40 42 44 45 46  LIST OF FIGURES CHAPTER I Figure 1  Graph o f t h e I o n i z a t i o n E f f i c i e n c y o f Helium  To f o l l o w page  and Argon  6  Figure 2  P o t e n t i a l V a r i a t i o n Between G r i d and P l a t e  9  Figure 3  E f f e c t o f a G r i d - P l a t e A n g l e on t h e P o t e n t i a l  Figure 4  E f f e c t o f a D.C. F i l a m e n t V o l t a g e on t h e  CHAPTER ' I I I  Potential Figure 5  11  Sum E f f e c t o f a G r i d - P l a t e A n g l e and a D.C. F i l a m e n t V o l t a g e f o r t h e P o l a r i z e d Beam I o n i z e r  Figure 6  12  Schematic o f t h e P o l a r i z e d Beam I o n i z e r s 1  Operating Figure #  Principle  12  Ion P a t h on M e e t i n g a P o t e n t i a l Bump i n t h e P o l a r i z e d Beam I o n i z e r  Figure 9  11  Schematic o f t h e Weiss I o n i z e r * s O p e r a t i n g Principle  Figure 7  10  12  Graph o f C u r r e n t D e n s i t y Versus Magnitude o f t h e P o t e n t i a l Minimum  15  F i g u r e 10 (a) S i n g l e E x t r a c t i o n E l e c t r o d e T e s t Arrangement 16 (b) P r o b a b l e  Equipotential Lines f o r Figure  10 ( a ) .  16  F i g u r e 11 (a) Double E x t r a c t i o n E l e c t r o d e T e s t Arrangement 16 (b) E q u i p o t e n t i a l L i n e s f o r 11(a) w i t h t h e F i r s t E l e c t r o d e a t 200 v o l t s  16  (c) E q u i p o t e n t i a l L i n e s f o r F i g u r e 11(a) w i t h the F i r s t E l e c t r o d e a t 0 v o l t s  16  F i g u r e 12 Probable Required  E x t r a c t i o n and F o c u s i n g  E l e c t r o d e Arrangement  16  CHAPTER IV F i g u r e 13 Exploded View o f the P o l a r i z e d Beam I o n i z e r  17  F i g u r e 14 Dimensioned View o f t h e P o l a r i z e d Beam I o n i z e r  18"  CHAPTER V F i g u r e 15 Test Chamber F i g u r e 16 Experimental  19 Curves o f Ion Current  Versus  E l e c t r o n Current  20  -CHAPTER X F i g u r e 17 A General Normal P a r t i c l e T r a j e c t o r y  32  F i g u r e 18 Pole P i e c e Dimensions and P a r t i c l e T r a j e c t o r i e s  32  F i g u r e 19 Test Magnet  32  F i g u r e 20 F r i n g i n g F i e l d Curves  32  F i g u r e 21 Coordinate  Axes o f P a r t i c l e s  v  32  CHAPTER XI F i g u r e 22 R.F. T e s t Bench  33  CHAPTER I  INTRODUCTION  The  development o f an i o n i z e r was c a r r i e d out f o r t h e  purpose o f i o n i z i n g as e f f i c i e n t l y as p o s s i b l e a p o l a r i z e d beam o f h e l i u m 3 atoms emerging from a l o w t e m p e r a t u r e p o l a r i z e d beam source c u r r e n t l y being Columbia.  constructed a t the University of B r i t i s h  I t i s a n t i c i p a t e d t h a t t h i s s o u r c e w i l l produce a  beam o f 10-  n e u t r a l atoms p e r second moving w i t h a speed o f ISO 2  meters p e r second and w i t h a c r o s s s e c t i o n a l a r e a o f O . 3 6 cm . The  i o n i z a t i o n must o c c u r i n such a way a s t o r e t a i n t h e s p i n  d i r e c t i o n o f t h e h e l i u m n u c l e i , so t h a t a f t e r subsequent a c c e l e r a t i o n n u c l e a r r e a c t i o n s can be s t u d i e d w i t h p o l a r i z e d h e l i u m 3 b e i n g used as bombarding p a r t i c l e s . One can i o n i z e atoms by q u a n t a , e l e c t r o n s o r i o n s . Ions and atoms o f l o w energy a r e v e r y i n e f f i c i e n t a t i o n i z i n g a gas.  At h i g h e n e r g i e s , w i t h speeds n e a r t h a t o f 100 e l e c t r o n -  v o l t e l e c t r o n s , atoms and i o n s have a maximum i o n i z a t i o n c r o s s s e c t i o n which i s g e n e r a l l y lower than that f o r e l e c t r o n s .  Ion-  i z a t i o n by l i g h t q u a n t a , however, i s more e f f i c i e n t i n terms o f i o n i z a t i o n c r o s s s e c t i o n t h a n by e l e c t r o n s .  I t i s interesting  t o i n v e s t i g a t e t h i s comparison f o r t h e case o f h e l i u m . l i n e a r absorption  coefficient^  The  d e f i n e d by t h e d i f f e r e n t i a l  equation dl wdx = /  where dx i s t h e f r a c t i o n a l d e c r e a s e i n beam i n t e n s i t y o f a  monochromatic beam o f w a v e l e n g t h A a f t e r p a s s i n g t h r o u g h a F o r 500 angstrom l i g h t p a s s i n g t h r o u g h  l e n g t h dx o f a b s o r b e r . h e l i u m /A  i s 1#5.  N e g l e c t i n g s c a t t e r i n g , t h i s v a l u e o f f*n ft  o  c o r r e s p o n d s t o an i o n i z a t i o n c r o s s s e c t i o n o f 52 x 10" w h i l e t h e i o n i z a t i o n c r o s s s e c t i o n o f h e l i u m by 130 i s 3.5  x I O ' ' cm?. -1  cm.  ev. e l e c t r o n s  Thus a g i v e n i n t e n s i t y beam o f monochromatic  l i g h t - q u a n t a o f w a v e l e n g t h 500 angstroms w i l l produce 150  times  as many i o n s p e r second as t h e same i n t e n s i t y beam o f e l e c t r o n s . 5 2 Thus, a l i g h t beam o f 3 x K r ergs p e r second p e r cm. will produce t h e same r a t e o f i o n i z a t i o n as an e l e c t r o n c u r r e n t o f 0.16  amperes p e r cm.  .  The n o n a v a i l a b i l i t y a t t h i s t i m e o f such  an h i g h i n t e n s i t y , h i g h l y monochromatic source makes t h i s method somewhat i m p r a c t i c a l . T h i s a p p r o a c h , however, i s t h e o n l y  way  o f i n c r e a s i n g a p p r e c i a b l y t h e e f f i c i e n c y of i o n i z e r s used f o r low p r e s s u r e beams.  Of t h e p r e c e d i n g t h r e e methods t h e most  p r a c t i c a l and s i m p l e s t way  o f i o n i z i n g atoms i s by e l e c t r o n s .  I o n i z e r s employing e l e c t r o n bombardment i o n i z a t i o n can be c l a s s i f i e d g e n e r a l l y as f o l l o w s : (1) H i g h and low v o l t a g e d i r e c t c u r r e n t (2) H i g h f r e q u e n c y (3) In types  discharges.  discharges.  E l e c t r o n beam s o u r c e s . (1)  and  (2) t h e gas i s l e a k e d i n t o a d i s c h a r g e  chamber  where t h e gas m o l e c u l e s undergo c o l l i s i o n s w i t h t h e w a l l s i f t h e p r e s s u r e i s h i g h enough, w i t h each o t h e r .  A plasma i s  formed by t h e a c c e l e r a t i o n o f i o n s and e l e c t r o n s i n t h e f i e l d s that are i n i t i a l l y present.  The  and,  strong  pressures required f o r  t h e f o r m a t i o n o f a s u i t a b l e plasma a r e u s u a l l y i n t h e range o f  -3from 1 t o 10Q m i c r o n s .  Only i n t h e case o f c a p a c i t y c o u p l e d  r a d i o f r e q u e n c y s o u r c e s has o p e r a t i o n been extended down t o 10"^ mm. 10  The f a c t t h a t t h e beam p r e s s u r e w i l l be about  mm. and t h e r e q u i r e m e n t t h a t t h e p o l a r i z e d beam atoms  must n o t undergo c o l l i s i o n s o r e x p e r i e n c e any changing  magnetic  f i e l d s t o a v o i d a change i n d i r e c t i o n o f t h e n u c l e a r s p i n r u l e s out t h e s e two t y p e s .  I t i s , t h e r e f o r e , n e c e s s a r y t o use some  form o f e l e c t r o n beam s o u r c e .  The c h o i c e o f t h e most s u i t a b l e  t y p e o f e l e c t r o n beam s o u r c e i s examined i n p a r t 3 ( a ) .  CHAPTER I I  IONIZATION PRODUCED BY AN ELECTRON BEAM  The performance  o f an i o n i z e r can be e v a l u a t e d from  a knowledge o f e x p r e s s i o n s f o r t h e i o n c u r r e n t from a beam o f atoms, t h e i o n i z a t i o n e f f i c i e n c y , and t h e i o n c u r r e n t r e s u l t i n g from a background g a s . (a) I o n C u r r e n t from an Atomic Beam If N  b  i s t h e number o f beam m o l e c u l e s i n c i d e n t p e r  second i n t o t h e i o n i z i n g r e g i o n , L i s t h e l e n g t h o f t h e i o n i z i n g r e g i o n and v , t h e most p r o b a b l e v e l o c i t y o f t h e i n c i d e n t beam m o l e c u l e s t h e n t h e number o f m o l e c u l e s i n t h e i o n i z i n g r e g i o n a t any i n s t a n t o f t i m e i s N L v b  The p r o b a b i l i t y o f an i o n i z i n g c o l l i s i o n f o r one e l e c t r o n o f  -4-  energy eV i s N LQ(V) H  vA  where V i s t h e p o t e n t i a l t h r o u g h which t h e e l e c t r o n has f a l l e n , e i s t h e e l e c t r o n i c c h a r g e , Q(V) i s t h e i o n i z a t i o n c r o s s s e c t i o n a t p o t e n t i a l V and A i s t h e e f f e c t i v e a r e a e v e r which t h e beam i s s p r e a d and t h r o u g h which t h e e l e c t r o n s p a s s .  With i p / e  e l e c t r o n s p e r second p a s s i n g t h r o u g h a r e a A t h e number o f i o n s formed p e r second,assuming  each c o l l i s i o n o f a beam m o l e c u l e  w i t h an e l e c t r o n produces a s i n g l y i o n i z e d h e l i u m a t o m ^ i s N  =  NKLQ(V)ip  ions/second  vAe  (1)  where i p i s t h e e l e c t r o n c u r r e n t t h r o u g h a r e a A. (b) I o n i z a t i o n E f f i c i e n c y The i o n i z a t i o n e f f i c i e n c y , , d e f i n e d a s t h e f r a c t i o n a l number o f beam atoms i o n i z e d , i s Eff.  _ N _ LQ(V)i "  N  B  "  vAe  r  (2)  K  (c) I o n C u r r e n t due t o a Background Gas The p r o b a b i l i t y t h a t one m o l e c u l e o f a background gas w i l l be i o n i z e d by i p / e e l e c t r o n s w i t h energy eV t r a v e l l i n g t h r o u g h a r e a A p e r second i s  SlYiip where Q ( V ) i s t h e i o n i z a t i o n c r o s s s e c t i o n o f t h e background gas w h i c h may o r may n o t be d i f f e r e n t from t h e beam gas f o r e l e c t r o n s o f energy eV. each second i s  F o r /° kji  m o l e c u l e s t h e number o f i o n s formed  where P  i s t h e number o f background gas m o l e c u l e s p e r u n i t  volume and H  i s t h e path length o f t h e e l e c t r o n s through t h e  ionizing region.  The i o n c u r r e n t c o r r e s p o n d i n g  to Ni s  I = /*<3(v)i i  ( 4 )  p  (d) I o n i z a t i o n C r o s s S e c t i o n s o f Argon and Helium The i n a c c u r a c y i n e s t i m a t i n g t h e expected  theoretical  performance o f an i o n i z e r l i e s m a i n l y i n t h e u n c e r t a i n t y w i t h w h i c h t h e i o n i z a t i o n c r o s s s e c t i o n a s a f u n c t i o n o f bombarding e l e c t r o n energy f o r gases i s known. Most e x p e r i m e n t e r s  express t h e i r r e s u l t s i n terms o f  q u a n t i t i e s other than t h e i o n i z a t i o n cross s e c t i o n .  Sometimes  t h e e f f i c i e n c y o f i o n i z a t i o n , S , i s u s e d , and t h i s i s d e f i n e d e  as t h e number o l p o s i t i v e i o n s formed by each e l e c t r o n i n t r a v e r s i n g 1 cm. o f p a t h t h r o u g h a gas a t a p r e s s u r e o f 1 mm. o f mercury and a t a t e m p e r a t u r e o f 0°C.  The i o n i z a t i o n  efficiency  i s r e l a t e d t o t h e i o n i z a t i o n c r o s s s e c t i o n , Q, by t h e f o r m u l a S  e  = 3.56 x 1 0  where 3*56 x 10-*-" i 0  s  1 6  Q  t h e number o f gas m o l e c u l e s p e r c u b i c  cent-  i m e t e r a t a p r e s s u r e o f 1 mm. o f mercury and a t e m p e r a t u r e o f 0°C.  The f o r e g o i n g c o n c e p t s a r e d i s c u s s e d i n r e f e r e n c e s (5)  and (6). The most a c c u r a t e d e t e r m i n a t i o n s  of S  e  t o date have  been made by P.T. S m i t h (1) b u t even t h e s e v a l u e s c o u l d be i n e r r o r by a s much as 40%.  The v a l u e s o f S m i t h have been t a b u l a t e d  i n t h e r e g i o n o f i n t e r e s t i n t a b l e 1 and a r e shown g r a p h i c a l l y i n f i g u r e 1 t o g e t h e r with t h e values  o f two other  experimenters,  A. Hughes and E. K l e i n (2) and K. Compton and C. van V o o r h i s ( 3 ) .  TABLE I Electron Energy ( v o l t s )  EFFICIENCY OF IONIZATION S  f o r Helium  e  S  f o r Argon  e  100  1.245  12.90  120  1.250  12.53  150  1.22$  11.63  200  1.149  10.53  250  1.060  9.43  300  0.971  3.5&  (e) Estimated  Ion Current  1  f o r t h e P o l a r i z e d Helium 3 Source  From t h e e f f i c i e n c y e x p r e s s i o n  o f p a r t 2(b) i t i s seen  t h a t t o make t h e e f f i c i e n c y as h i g h as p o s s i b l e one must make the i o n i z e r as l o n g as p o s s i b l e , choose t h e p o t e n t i a l s so t h a t the bombarding e l e c t r o n s have energies  such t h a t t h e c r o s s  s e c t i o n f o r i o n i z a t i o n i s a maximum, and arrange t o make t h e e l e c t r o n c u r r e n t d e n s i t y , ip/A, as l a r g e as p o s s i b l e .  The 10 cm.  l e n g t h o f t h e i o n i z i n g r e g i o n o f t h e i o n i z e r was f e l t t o be a reasonable  compromise between lengthness  focusing d i f f i c u l t i e s . the maximum o b t a i n a b l e minimum a l l o w a b l e  and c o n s t r u c t i o n and  As e x p l a i n e d more f u l l y i n p a r t 3 ( c ) ( i v ) c u r r e n t d e n s i t y which was s e t by t h e  s e p a r a t i o n o f t h e e l e c t r o d e s bounding t h e  i o n i z i n g r e g i o n i s approximately 0.13 amperes/cm. . The  To f o l l o w page 6  o  -7-  e l e c t r o d e p o t e n t i a l s were chosen such t h a t t h e i o n i z a t i o n c r o s s s e c t i o n o f h e l i u m was t h a t v a l u e o c c u r r i n g a t about 130  electron-  v o l t e l e c t r o n n b o m b a r d i n g energy, namely, 3.5 x 1 0 " ^ c m . . 2  the  v e l o c i t y o f t h e h e l i u m 3 atoms i n t h e low t e m p e r a t u r e beam  w i l l be about 180 meters p e r second t h e i o n i z a t i o n for  Since  t h e p r e c e d i n g v a l u e s w i l l be 0.016.  efficiency  I f a l l t h e i o n s so  formed a r e c o l l e c t e d , t h e c u r r e n t f o r a n e u t r a l beam o u t p u t o f atoms p e r second w i l l be about 2.6  microamperes.  CHAPTER I I I  DESIGN OF THE  (a)  IONIZER  Design Choice As was p r e v i o u s l y s t a t e d i n t h e I n t r o d u c t i o n t h e o n l y  s u i t a b l e t y p e o f e l e c t r o n bombardment i o n i z e r i s t h e e l e c t r o n beam s o u r c e . the  Here t h e r e i s a c h o i c e between two b a s i c t y p e s ^  u n i d i r e c t i o n a l e l e c t r o n s o u r c e and t h e o s c i l l a t i n g  source.  The F i n k e l s t e i n Source (6) and t h e von Ardenne  electron Source  (7) a r e t h e most w e l l known examples o f t h e l a t t e r t y p e o f i o n i z e r . T h e i r performance d a t a p e r t a i n s t o o p e r a t i o n a t r e l a t i v e l y h i g h p r e s s u r e s ( g r e a t e r t h a n 0.1 m i c r o n s ) i n which a plasma i s formed and t h e e x t r a c t e d c u r r e n t from t h i s plasma w h i c h i s space charge l i m i t e d , t h e r e f o r e , depends on t h e geometry o f t h e e x t r a c t i o n e l e c t r o d e s as w e l l as on t h e plasma i o n d e n s i t y and potentials.  electrode  The d e s i g n o f such i o n i z e r s i s p r e s e n t e d i n ( 8 ) .  The p r e s e n c e o f an a p p r e c i a b l e number o f p o s i t i v e i o n s due t o t h e  -8high pressure  beams and t h e a s s o c i a t e d l a r g e amount o f i o n -  i z a t i o n due t o secondary e l e c t r o n s from t h e s e i o n s r e s u l t i n g from t h e s m a l l e l e c t r o n mean f r e e p a t h and hence l a r g e  col-  l i s i o n r a t e w i t h atoms makes t h e d e s i g n and performance o f these i o n i z e r s completely intensity ionizers.  d i f f e r e n t from t h a t o f low beam  As w i l l be suggested from l a t e r d i s c u s s i o n  t h e number of e l e c t r o n s one  can put i n t o a g i v e n r e g i o n w i t h a  g i v e n e l e c t r o d e geometry depends o n l y on t h e geometry p o t e n t i a l of the e l e c t r o d e s .  Thus, a l t h o u g h an  and  oscillating  e l e c t r o n source o f f e r s lower f i l a m e n t current f o r a given i o n i z a t i o n e f f i c i e n c y , t h e maximum o b t a i n a b l e i o n i z a t i o n e f f i c i e n c y s e t by t h e e l e c t r o n c u r r e n t d e n s i t y would p r o b a b l y be t h e same as t h a t o f a u n i d i r e c t i o n a l t y p e s o u r c e w i t h t h e same geometry. The  c o n s t r u c t i o n s i m p l i c i t y of the l a t t e r type, provided  filament emission  that  the  does not l i m i t t h e e f f i c i e n c y , makes i t  s l i g h t l y more a t t r a c t i v e .  The  most s u c c e s s f u l u n i d i r e c t i o n a l  e l e c t r o n beam i o n i z e r t o d a t e d e s i g n e d f o r low i n t e n s i t y beams i s t h a t d e v e l o p e d by R. Weiss (9) argon a t room t e m p e r a t u r e .  which has a 2%%  efficiency for  Another i o n i z e r of the  oscillating-  e l e c t r o n t y p e w h i c h p r o b a b l y has performance comparable t o t h a t o f t h e Weiss I o n i z e r and  i s of q u i t e simple c o n s t r u c t i o n i s t h a t  developed by C l a u s n i t z e r (10).  However, no performance d a t a of  enough s i g n i f i c a n c e has been p u b l i s h e d t o p r o v i d e an comparison.  Thus, because o f i t s s i m p l i c i t y and  accurate  provenperfor-  mance, t h e o p e r a t i n g p r i n c i p l e and r e c t i l i n e a r geometry o f Weiss I o n i z e r was  chosen.  the  -9(b) Use  o f a Space Charge P o t e n t i a l Minimum  ( i ) Purpose The  beam i o n s when formed have speeds c o r r e s p o n d i n g t o  a f r a c t i o n o f an e l e c t r o n - v o l t and  can have t h e i r d i r e c t i o n o f  t r a v e l a l t e r e d by even s m a l l p o t e n t i a l bumps. bumps due  Since p o t e n t i a l  to patches of i r r e g u l a r l y e m i t t i n g tungsten or g r i d  warpage a r e d i f f i c u l t t o e l i m i n a t e , a p o t e n t i a l g r a d i e n t t o keep the i o n s t r a v e l l i n g i n t h e d e s i r e d  d i r e c t i o n i s introduced.  T h e r e f o r e , t o a c h i e v e an h i g h i o n c o l l e c t i o n e f f i c i e n c y one  must  arrange the  ions  electrode  geometry and  p o t e n t i a l s such t h a t t h e  once formed e x p e r i e n c e a f o r c e o r p o t e n t i a l g r a d i e n t w h i c h f o c u s e s and  d i r e c t s them t o t h e e x i t .  The  way  shape o f t h e p o t e n t i a l s between t h e e l e c t r o d e s region  i s d e t e r m i n e d can be i n v e s t i g a t e d  ( i i ) Theoretical I f two  Evaluation  i n which i n the  the  ionizing  quantitatively.  o f t h e P o t e n t i a l Minimum  f l a t p l a t e s , g r i d and  p l a t e , of p o t e n t i a l  V  c  w i t h r e s p e c t t o t h e cathode a r e p l a c e d p a r a l l e l t o each o t h e r a distance  d apart with a current  density  of e l e c t r o n s , J ,  flowing  f r o m g r i d t o p l a t e t h e n the p o t e n t i a l i s governed by e q u a t i o n derived  i n Appendix I .  where x i s t h e p e r p e n d i c u l a r d i s t a n c e grid/plate potential, V and  (S)  m  frpm t h e g r i d , V  c  i s the  i s t h e v a l u e o f p o t e n t i a l a t t h e minimum,  d i s the g r i d t o p l a t e d i s t a n c e .  c o r r e s p o n d i n g t o e q u a t i o n (£)  The  potential variation  i s shown g r a p h i c a l l y i n f i g u r e  2.  To f o l l o w page 9  G-R1D  0  PLATE.  d  J/2. X,  Figure 2  DISTANCE  FROM  G-KfD  -10The v a l u e o f t h e p o t e n t i a l minimum i s g i v e n by a q u a t i o n (7) o f Appendix I as £^1%= where a  2  ^-(VB/VcJ^l+alVB/Vc)*"  = 2.335 x 10  (7)  2  amp./volt.  I f a s m a l l a n g l e i s i n t r o d u c e d between g r i d and p l a t e t h e r e w i l l r e s u l t a p o t e n t i a l minimum w h i c h d e c r e a s e s as t h e grid-plate separation increases* f i g u r e 3«  t h i s e f f e c t i s shown i n  The e q u a t i o n g o v e r n i n g t h i s p o t e n t i a l minimum change  w h i c h i s d e r i v e d i n Appendix I I i s AY = -2 6/ J \ Vmo 3 mo > A\ c m e  1  a  v  ,.l -(l W V m nV/^y n l *1 J W ' . ,, 2V 7Vc-(V /V ^]  (9)  g  m o  m o  where 6 i s t h e g r i d t o p l a t e a n g l e , V p o t e n t i a l minimum a t Y= 0 and A m e ^ v  i s the value of the  m o  s  t  c  h  e  c n a n  minimum over a d i s t a n c e W f o r a g i v e n a n g l e  6  e  i  n  potenial  0.  I t s h o u l d be n o t e d t h a t e q u a t i o n (9) ceases t o h o l d a t V /V -£:i. mo  c  At t h i s p o i n t i n s t a b i l i t i e s  i n the electron  c u r r e n t c h a r a c t e r i s t i c o f a t e t r o d e s e t i n (11).  T h i s phenomenon  p r o v i d e s a f u n d a m e n t a l l i m i t a t i o n t o t h e amount o f c u r r e n t one can pass t h r o u g h t h e i o n i z i n g r e g i o n . A f u r t h e r v a r i a t i o n i n t h e p o t e n t i a l minimum o c c u r s i f a v a r i a t i o n i n cathode-grid p o t e n t i a l with distance along the ionizer exists.  Such an e f f e c t o c c u r s when t h e f i l a m e n t s a r e  h e a t e d by d.c. power.  The e q u a t i o n i n t h i s case w h i c h i s  d e r i v e d i n Appendix I I I i s AVmf. = - i If L  1  . AZ  (10)  |_1 - 4 ( V c / V ) i ] n  where z i s t h e d i s t a n c e a l o n g t h e f i l a m e n t s towards t h e p o s i t i v e end o f t h e f i l a m e n t v o l t a g e , A V ^ f i s t h e change i n p o t e n t i a l  To f o l l o w page 10  POTENTIAL  Figure 3  E f f e c t of a G r i d - P l a t e  Angle  -11minimum w h i c h r e s u l t s when a g r i d t o cathode p o t e n t i a l o f t h e form Vcg = V  G  - V li  f  z  e x i s t s , and ^ z i s t h e d i s t a n c e over which t h e f i l a m e n t v o l t a g e , Vf, i s applied.  The p o t e n t i a l minimum change r e s u l t i n g from  t h i s d.c. f i l a m e n t v o l t a g e o c c u r s a l o n g t h e l e n g t h o f t h e i o n i z e r a s shown i n f i g u r e 4 * I n t h e Weiss I o n i z e r t h e g r i d - p l a t e s e p a r a t i o n i n c r e a s e s a l o n g t h e l e n g t h o f t h e i o n i z e r so t h a t t h e sum e f f e c t o f d.c. f i l a m e n t v o l t a g e and g r i d - p l a t e a n g l e i s t o produce a potential variation similar t o that of figure 3 . I n t h e i o n i z e r t o be d e s c r i b e d h e r e t h e g r i d - p l a t e separation increases i n a d i r e c t i o n perpendicular t o the length o f t h e i o n i z e r so t h a t t h e sum e f f e c t o f d.c. f i l a m e n t v o l t a g e and g r i d - p l a t e a n g l e produce a p o t e n t i a l minimum v a r i a t i o n and p o t e n t i a l v a r i a t i o n as shown i n f i g u r e 5. the e q u i p o t e n t i a l s corresponding L =  to V  c  Numerical values of  = 200 v o l t s , W = 0.6 cm.,  z = 1Q cm., 0 = 2£°, V f = 10 v o l t s , and J = 0.13 amp./cm.  have been r e c o r d e d . be d i s c u s s e d  The r e a s o n s f o r c h o o s i n g t h e s e v a l u e s  will  later.  (c) C o n s i d e r a t i o n s i n D e s i g n and C h o i c e o f Parameters ( i ) S i d e v e r s u s End E x t r a c t i o n I n t h e Weiss I o n i z e r i o n s were removed from t h e end o f t h e i o n i z e r i n a w e l l f o c u s e d p e n c i l a s shown s c h e m a t i c a l l y i n f i g u r e 6.  However, v a r i a t i o n s i n g r i d t o p l a t e d i s t a n c e as  s m a l l a s 0.005 i n c h e s c o u l d d i s t u r b t h e p o t e n t i a l g r a d i e n t  2  POTENTIAL  Figure k  Effect  of a D , C . F i l a m e n t V o l t a g e on the  Potential  Figure 5  Sum E f f e c t  of a G r i d - P l a t e Angle and a . D . C . F i l a m e n t V o l t a g e on the  Potential  -12-  s u f f i c i e n t l y t o prevent c o l l e c t i o n o f a l l ions preceding variation.  this  F u r t h e r m o r e , beam i n t e n s i t i e s o f about 1015 atoms  per second p e r cm.*" may y i e l d enough p o s i t i v e i o n s t o n e u t r a l i z e t h e charge d e n s i t y o f e l e c t r o n s i n t h e i o n i z i n g r e g i o n  suf-  f i c i e n t l y t o d e s t r o y t h e p o t e n t i a l g r a d i e n t n e c e s s a r y f o r an high c o l l e c t i o n e f f i c i e n c y . I t i s possible t o avoid the f i r s t d i f f i c u l t y and extend t h e upward range o f beam i n t e n s i t i e s by a  ;  f a c t o r o f a t l e a s t t e n by employing s i d e e x t r a c t i o n as shown i n f i g u r e 7.  I n s i d e e x t r a c t i o n on meeting a l a r g e p o t e n t i a l bump,  t h e i o n r a t h e r t h a n b e i n g t u r n e d back goes around t h e bump as shown p i c t o r i a l l y i n f i g u r e o.  Positive ion neutralization i s  l e s s i n s i d e e x t r a c t i o n t h a n i n end e x t r a c t i o n because a t t h e p o i n t o f maximum p o s i t i v e i o n p i l e u p which o c c u r s a t t h e e x i t side of t h e i o n i z a t i o n region only those ions along the width of t h e i o n i z e r have c o n t r i b u t e d t o t h e n e u t r a l i z a t i o n . I n t h e Weiss d e s i g n t h e p o i n t o f maximum p o s i t i v e i o n p i l e u p o c c u r s a t t h e e x i t end and a l l t h o s e i o n s a l o n g t h e l e n g t h o f t h e i o n i z e r c o n t r i b u t e t o n e u t r a l i z a t i o n . The r e l a t i v e amounts o f n e u t r a l i z a t i o n i n t h e two methods o f e x t r a c t i o n a r e ,  therefore,  approximately i n the r a t i o of length t o width of the i o n i z i n g region. ( i i ) Filament The  Considerations most i m p o r t a n t r e q u i r e m e n t o f t h e f i l a m e n t s i s  that f o r t h e values  o f p l a t e / g r i d p o t e n t i a l and geometry chosen  t h e y must have an e m i s s i o n  o f a t l e a s t 0.3 amp./cm.  2  t o achieve  maximum i o n i z a t i o n e f f i c i e n c y . S i n c e under space charge l i m i t e d f l o w between two p a r a l l e l p l a t e s t h e c u r r e n t depends on t h e square o f t h e cathode  To f o l l o w page 12  figure 6  Weiss I o n i z e r * s O p e r a t i n g P r i n c i p l e  NE.UTRAL ATOM  -O  figure 7  P o l a r i z e d Beam I o n i z e r s Principle  Operating  To f o l l o w page 12  NrtA&lvMTUDE. O f POTEKfTiAL. l*iMlMUIv\  y Figure £  I o n P a t h on M e e t i n g a P o t e n t i a l Bump f o r t h e P o l a r i z e d Beam I o n i z e r  -13-  to g r i d distance, small v a r i a t i o n s i n filament to grid  distance  l e a d t o l a r g e v a r i a t i o n s i n c u r r e n t d e n s i t y and hence l a r g e v a r i a t i o n s i n t h e p o t e n t i a l minimum between g r i d and During a c t u a l operation as much as k mm.  i t i s estimated  plate.  t h a t t h e g r i d warped  Such a v a r i a t i o n f o r a 1.6  mm.  t o t a l grid to  cathode d i s t a n c e w o u l d u n d e r space charge l i m i t e d o p e r a t i o n ^ 7  l e a d t o a 30 % change i n c u r r e n t d e n s i t y .  To a v o i d t h i s e f f e c t ,  i t i s n e c e s s a r y t o o p e r a t e t h e f i l a m e n t s under t e m p e r a t u r e limited conditions. emission  Thus, t h e f i l a m e n t s must have u n i f o r m  over t h e i r s u r f a c e .  T h i s c o n d i t i o n means t h a t  c o a t e d cathodes whose e m i s s i o n  oxide  i s extremely v a r i a b l e over t h e i r  s u r f a c e cannot be used under t e m p e r a t u r e l i m i t e d o p e r a t i o n . A n o t h e r more secondary c o n s i d e r a t i o n i s t h e o f h a v i n g f i l a m e n t s w i t h low o p e r a t i n g t e m p e r a t u r e s .  desirability Excessive  r a d i a t i o n o f heat which i s p r o p o r t i o n a l t o t e m p e r a t u r e r a i s e d t o t h e f o u r t h power causes e x c e s s i v e g r i d d i s t o r t i o n and The  above c o n s i d e r a t i o n s r e s t r i c t t h e c h o i c e  filaments to t h o r i a t e d tungsten,  outgassing. of  pure t u n g s t e n o r the porous  o x i d e impregnated t u n g s t e n used i n t h e P h i l i p s Type L T h e r m i o n i c Cathode.  The most a t t r a c t i v e o f t h e s e t h r e e i s t h e  Philips 1200  Type L Cathode w h i c h has an o p e r a t i n g t e m p e r a t u r e between and  1400  K e l v i n and a maximum e m i s s i o n  0  amp./cm. . $200.  The  One  0  12  cathode a t t h e p r e s e n t t i m e , however, c o s t s o v e r  n e x t most a t t r a c t i v e cathode m a t e r i a l i s t h o r i a t e d  t u n g s t e n w h i c h has a maximum e m i s s i o n 1900  o f about tt t o  K e l v i n and  o f about 1 amp./cm.  i s r e l a t i v e l y inexpensive.  Pure  2  tungsten,  t h e most i n e f f i c i e n t of t h e t h r e e m a t e r i a l s , has a maximum emission  o f about 0.3  amps./cm. a t 2500 2  0  Kelvin.  at  -14( i i i ) G r i d t o Cathode S p a c i n g As w i l l be shown i n t h e n e x t s e c t i o n t h e maximum o b t a i n a b l e p l a t e c u r r e n t d e n s i t y i s about 0.13 amps./cm. . 2  T e s t s have shown t h a t t h e g r i d : p l a t e c u r r e n t d i v i s i o n i s 1:1 so t h a t a t o t a l o f 0o26 amp,/em. o f c u r r e n t i s r e q u i r e d from 2  the f i l a m e n t s .  To ensure o p e r a t i o n under t e m p e r a t u r e l i m i t e d  c o n d i t i o n s , t h e f i l a m e n t t o g r i d d i s t a n c e must be l e s s t h a n t h a t corresponding  t o space charge l i m i t e d o p e r a t i o n f o r a c u r r e n t  d e n s i t y o f Go26 amp./cm. . 2  A lower estimate  of t h i s  distance  can be o b t a i n e d from t h e e x p r e s s i o n f o r space charge l i m i t e d c u r r e n t between two p l a n e p a r a l l e l p l a t e s  d  2  = aJLlc J  where V , t h e g r i d p o t e n t i a l , i s t a k e n as 200 v o l t s f o r reasons c  t o be mentioned l a t e r , J i s 0.26 amps./cm. , and a i s 2.335 x 10"  ampo/volto*" F o r t h e p r e c e d i n g  v a l u e s d i s 1.6  mm.  Thus, t h e f i l a m e n t t o g r i d d i s t a n c e must be l e s s t h a n 1.6 mm. t o ensure t e m p e r a t u r e l i m i t e d  operation.  I n r e a l i t y , t h i s d i s t a n c e w i l l be somewhat g r e a t e r because t h e r i b b o n - l i k e n a t u r e o f t h e f i l a m e n t s causes h i g h e r f i e l d g r a d i e n t s t o e x i s t near t h e f i l a m e n t s u r f a c e s .  However, i t  i s d e s i r a b l e t o make t h i s f i l a m e n t t o g r i d d i s t a n c e as s m a l l as p o s s i b l e t o m i n i m i z e p o s i t i v e i o n bombardment caused by t h o s e atoms i o n i z e d i n t h e g r i d - c a t h o d e (iv)  region,  Maximum Space Charge L i m i t e d P l a t e  Current  The maximum a l l o w a b l e v a l u e o f e l e c t r o n c u r r e n t  density  , J , i n t h e g r i d - p l a t e r e g i o n i s s e t by t h e minimum v a l u e o f t h e p o t e n t i a l minimum, t h e maximum g r i d / p l a t e p o t e n t i a l and t h e  -15minimum g r i d t o p l a t e d i s t a n c e a c c o r d i n g t o e q u a t i o n  (7)°  The  beam f o r which t h i s i o n i z e r i s t o be used i s 6 mm. i n d i a m e t e r and so t h e g r i d t o p l a t e d i s t a n c e and t h e w i d t h o f t h e i o n i z i n g r e g i o n were b o t h s e t a t 6 mm„  The c r o s s s e c t i o n f o r i o n i z a t i o n  o f h e l i u m has a b r o a d maximum r a n g i n g from about 75 e l e c t r o n v o l t s t o 200 e l e c t r o n - v o l t s e l e c t r o n bombarding energy. C h o o s i n g t h e g r i d / p l a t e p o t e n t i a l t o be 200 v o l t s p u t t h e c r o s s s e c t i o n n e a r i t s maximum w h i l e a t t h e same t i m e a l l o w i n g a h i g h p l a t e current densityo  The maximum v a l u e o f c u r r e n t d e n s i t y  o b t a i n a b l e i s l i m i t e d by t h e l o w e r l i m i t o f t h e p o t e n t i a l minimum Y^jY  c  unstableo  = £ a t w h i c h p o i n t t h e space charge becomes  W i t h t h e above c h o i c e o f parameters t h e v a l u e s o f J  f o r v a r i o u s v a l u e s o f Y^Y^  as c a l c u l a t e d from e q u a t i o n (7)  a r e shown g r a p h i c a l l y i n f i g u r e ( 9 )<>  I f the g r i d - p l a t e angle i s  s e t so t h a t t h e p o t e n t i a l minimum v a r i e s between 80 and 105 v o l t s t h e n t h e average v a l u e o f maximum o b t a i n a b l e v a l u e o f J i s 0ol3 ampso/cm. . 2  (v) C a l c u l a t i o n o f t h e R e q u i r e d  G r i d - P l a t e Angle  To a c h i e v e an h i g h i o n c o l l e c t i o n e f f i c i e n c y , e f f e c t s due t o p o t e n t i a l bumps must be m i n i m i z e d potential gradient.  by p r o v i d i n g a l a r g e  The maximum a l l o w a b l e v o l t a g e g r a d i e n t a t  the i o n i z e r entrance without t h e p o t e n t i a l a t t h e i o n i z e r d r o p p i n g below Vm/Vc = u n s t a b l e , i s &Y  me  exit  t h e v a l u e below w h i c h t h e c u r r e n t i s  = 25 v o l t s .  F o r an i o n i z i n g r e g i o n w i d t h o f  o.6 cm., a g r i d / p l a t e v o l t a g e o f 200 v o l t s , and a p o t e n t i a l minimum a t t h e i o n i z e r e n t r a n c e , V  m e  , o f 105 v o l t s , e q u a t i o n  (9)  g i v e s © = 2^°. The t o l e r a n c e on t h i s a n g l e can be a p p r e c i a t e d by n o t i n g a \ degree change i n 0 c o r r e s p o n d s t o a 5 v o l t change i n  ^ Qm  Figure 9  CURRLWT  v  DE.MSITV (AH\PS./OA?) •IS  H  -16-  (d) E x t r a c t i o n o f Ions and F o c u s i n g " P l a c i n g t h e g r i d and p l a t e a t an a n g l e w i t h t h e c o l l e c t i o n p l a t e a t ground p o t e n t i a l as shown i n f i g u r e 10(a) p r o v i d e s a p o t e n t i a l g r a d i e n t as shown i n f i g u r e 10(b) w h i c h t e n d s t o s l i t f o c u s and a c c e l e r a t e t h e i o n s out o f t h e i o n i z i n g region.  The n a t u r e o f t h e e x t r a c t e d beam o f i o n s w i l l  require  t h e use o f an e l e c t r o d e s t r u c t u r e s i m i l a r t o t h a t shown i n f i g u r e 12 i n o r d e r t o spot f o c u s t h e s e i o n s *  With the arrange-  ment shown i n f i g u r e 11(a) i t was found t h a t v a r y i n g t h e p o t e n t i a l on t h e m i d d l e e l e c t r o d e produced no e f f e c t on t h e i o n current reaching the c o l l e c t i o n plate* was deemed t o be u n n e c e s s a r y .  Thus, t h e m i d d l e p l a t e  The p r o b a b l e e q u i p o t e n t i a l l i n e s  a t t h e extreme v o l t a g e s on t h e m i d d l e e l e c t r o d e a r e shown i n f i g u r e s 11(b) and 1 1 ( c ) .  CHAPTER IV  PRACTICAL CONSTRUCTION OF THE IONIZER  (a) Cathode The cathode c o n s i s t e d o f s i x 0.030 x 0.004 i n c h e s t h o r i a t e d t u n g s t e n r i b b o n s s u p p o r t e d a t e i t h e r end by aluminum supports.  To p r e v e n t sag due t o t h e r m a l e x p a n s i o n , t h e  filaments  were clamped a t one end and k e p t t a u t by a s p r i n g arrangement a t t h e o t h e r end.  The s p r i n g arrangement c o n s i s t s o f a p i a n o  w i r e s p r i n g pushing a s t e e l f i l a m e n t holder along s t e e l t r a c k s . Any uneven e x p a n s i o n o f t h e f i l a m e n t s i s t a k e n up by i n d i v i d u a l  TEST EXTRACTION  ARRANGEMENTS  CORRESPONDING  PROBABLE  EQUIPOTELMT/AL LINES.  PLAN  VIEW  S T R O N G  ELEVATION  FIELD  Vf.EW  FOCUSING  FOCUSING ELECTRODES  IONS  NEUTRAL B E A M  IONIZER  P L A T E  GRID  (-3  O  ,o H H  * O Figure  12  Probable  Required E x t r a c t i o n  and F o c u s i n g E l e c t r o d e  Arrangement SB  era CD  -17movement  of the leafs  o f a 0.005 i n c h t a n t a l u m l e a f  which t h e f i l a m e n t s a r e spot welded. prevent t h e f i l a m e n t s from aluminum f i l a m e n t high heat  supports<,  heat  c o n t a c t i n g t h e l e s s heat The f i l a m e n t  shields resistant  s u p p o r t s were made o f  c o n d u c t i v i t y aluminum so t h a t t h e p i a n o w i r e  w o u l d be a d e q u a t e l y the  Tantalum  spring to  exploded  view  cooledo  of figure  The c a t h o d e  assembly  spring  i s shown i n  13»  B e f o r e o p e r a t i o n t h o r i a t e d t u n g s t e n f i l a m e n t s must be activated.  The a c t i v a t i o n p r o c e s s i n v o l v e s t h r e e s t e p s .  Initiallyp minutes thoria  t h e f i l a m e n t s a r e f l a s h e d a t 2300  K e l v i n f o r two  t o c l e a n t h e t u n g s t e n s u r f a c e and reduce to metallic  thorium.  The t e m p e r a t u r e  some o f t h e  i s then reduced t o  2100 ° K e l v i n a n d k e p t t h e r e f o r 15 t o 30 m i n u t e s  to allow  diffusion  9  of the thorium t o the surface.  ature i s lowered region.  The f i l a m e n t  Stefan-Boltamann and  t o 1300 o r 1900  Kelvin  temperature  Finally s  t h e normal  operating  c a n be e s t i m a t e d f r o m t h e  E q u a t i o n u s i n g t h e known e m i s s i v i t y  a s s u m i n g a l l t h e i n p u t power i s r a d i a t e d  surface.  t h e temper-  of tungsten  from t h e heated  The f o u r f i l a m e n t s r e q u i r e d a f i l t e r e d  power s u p p l y  c a p a b l e o f s u p p l y i n g 50 amperes a t 12 v o l t s w i t h a r i p p l e of. l e s s than 1 (b)  volt.  Grid The  inchp  grid  0.002 i n c h  i s comprised  diameter  hole  c u t i n a 0.050 i n c h  less  s t e e l b a r screwed  o f a t u n g s t e n mesh, 20 w i r e s p e r  w i r e , s p o t w e l d e d o v e r a 0.6 x 10 stainless  on f i r m l y  steel grid  sheet.  a t the undamped  A  cm.  stain-  end o f t h e g r i d  s h e e t p r e v e n t s b u c k l i n g c a u s e d by e l e c t r o n bombardment a n d h e a t  To f o l l o w page 17  Cathode  Cooling  + 10  Coils  Vb/t F i ! a m * » i t  U a J - T ^ r o ^ h  P l a t e Cool.n^ C o i l  Brass  Flange  Lucite  Flange  Allen-Mead C l a m p u K j Lava  Screw  Insulators  Filament  CJarnj-m..  Bar  P l a t e Cooling C o d " T a n t a l u m Meat raSS Clamping  Srti-Jd.s Bar  Cathode. Cooling  Coils  5taunlcS£ S t « e l  Plate  M i c a +10 V o l t F i l a m e n t Insulator rass  <ST-\CL Plate.  Stainless  Stee/  Separator  Grid  Lava Cathode - Crnd I s o l a t o r  B r a s s Cathod*. B l a c k B r a s s S u p p o r t fear  "Tantalum Heat Shields A l f m m o m .Suppo*^ B l a c k Sbe.tt\ T r a c k  5tamUss Steel Grid 4nti-Wipp B a r  Piano  Wire Spring  FilamentT a n t a l u m L e a f Spring Tahtalwm He>a.t  F i g u r e 13  The P o l a r i z e d Beam I o n i z e r  -Irr a d i a t i o n from t h e f i l a m e n t s . can  b e s e e n i n f i g u r e 14»  (c)  Plate The  steel  plate  sheet  The d i m e n s i o n s o f t h e g r i d  i s made o f 1/16 i n c h  thick  a n d h a s t h e same d i m e n s i o n s a s t h e g i d sheet»  water c o o l i n g  coils  are soft soldered  sheet  stainless Copper  t o t h e p l a t e a s shown i n  f i g u r e 13° (d)  Assembly The  s i d e by b r a s s  plate,  g r i d and f i l a m e n t  sections.  b r a s s and i s t h e o n l y grounded brass grid  The bottom s e c t i o n  part  support b a r .  o f the i o n i z e r i n contact  stainless steel plate  sheets t o t h e bottom s e c t i o n . separation  m i l l e d a t an a n g l e angle.  have \ i n c h cooling  copper tubing  t o prevent  filament  spring.  a n d 0.050  section soft  lava  bottom  section  cathode s e c t i o n  plate  ofthe  i n s u l a t o r s a r e used t o ,  screws from t h e g r i d - p l a t e  5/3 i n c h b r a s s  grid-  t o them f o r w a t e r  e x c e s s i v e outgassing and f a i l u r e Heat t r e a t e d  inch  grid-plate  and t h e s t a i n l e s s s t e e l  soldered  inch  clamping b a r a r e  separate t h e clamping  volt  made o f \  s o a s t o p r o v i d e t h e 2.5 d e g r e e  The bottom b r a s s  inch  with the  The t o p o f t h e b r a s s  b a r and bottom o f t h e b r a s s  on one  i s made o f 5/3  The two r e m a i n i n g s e c t i o n s  clamp t h e l / l 6 i n c h  plate  a r e a l l supported  potential, the  f r o m t h e g r i d a n d t h e p o s i t i v e 10  from t h e grounded  cathode  section.  Figure  lh  The P o l a r i z e d Beam  Ionizer  -19GHAPTER V  TESTING AND PERFORMANCE (a) T e s t Chamber The i o n i z e r t e s t chamber assembly i s shown i n f i g u r e  15°  The i o n i z e r s u p p o r t b a r i s screwed t o a b r a c k e t a t t h e bottom of a 9 inch diameter, i inch t h i c k brass flange which,.in t u r n , i s screwed t o t h e t o p o f t h e t e s t chamber.  C o o l i n g c o i l s and  e l e c t r i c a l l e a d s a r e t a k e n out t h r o u g h t h i s f l a n g e .  The  col-  l e c t i o n e l e c t r o d e which c o l l e c t s i o n c u r r e n t from t h e i o n i z e r i s i n s e r t e d t h r o u g h a p o r t on t h e s i d e o f t h e t e s t chamber.  The  t e s t chamber i s s u p p o r t e d a t and pumped out from t h e bottom -6  a t t h e r a t e o f 300 l i t e r s p e r second.  P r e s s u r e s o f 2 x 10"  mm.  were measured by an i o n gauge p o s i t i o n e d below t h e t e s t chamber. Gas c o u l d be l e a k e d i n from below t h e t e s t chamber and cont r o l l e d t o w i t h i n 10  %  a  (b) Technique o f Performance T e s t i n g The e x p e r i m e n t a l t e c h n i q u e employed t o e s t i m a t e t h e performance c h a r a c t e r i s t i c s o f t h e i o n i z e r was t o r a i s e t h e background p r e s s u r e w i t h a g i v e n gas a n d , f o r a p a r t i c u l a r p l a t e e l e c t r o n c u r r e n t , r e c o r d t h e p o s i t i v e i o n c u r r e n t making background c o r r e c t i o n s .  The p o s i t i v e i o n c u r r e n t was  suitable  collected  by a p l a t e a t ground p o t e n t i a l and measured w i t h t h e c u r r e n t meter o f a vacuum t u b e v o l t m e t e r .  Gas was l e a k e d i n a t a  c o n s t a n t r a t e and i n c r e a s e s i n p r e s s u r e were a t t r i b u t e d t o r e s i d u a l background.  The r e s i d u a l background p r e s s u r e r o s e  To  Figure  15  Test  Chamber  f o l l o w page  -20w i t h i n c r e a s e d e l e c t r o n c u r r e n t because o f g r e a t e r  outgassing  caused by more i n t e n s e e l e c t r o n bombardment o f t h e g r i d p l a t e and h i g h e r f i l a m e n t t e m p e r a t u r e s .  The  ground c u r r e n t v e r s u s p r e s s u r e  obtained i n a  run w i t h t h e l e a k shut o f f .  curve was  and  r e s i d u a l backseparate  The t e m p e r a t u r e and hence gas  p r e s s u r e i n t h e i o n i z i n g r e g i o n was t h a t measured by t h e i o n gauge.  assumed t o be t h e same as  The p r e c e d i n g method p r o v i d e d  only a lower l i m i t to the i o n i z a t i o n e f f i c i e n c y since the a c t u a l gas p r e s s u r e i n t h e i o n i z i n g r e g i o n was t h a t measured by t h e i o n gauge.  The  p r o b a b l y much l e s s t h a n  curves f o r b o t h h e l i u m  and  a r g o n w i t h t h e i r a s s o c i a t e d r e s i d u a l background c u r r e n t s a r e shown i n f i g u r e 16.  The  s e n s i t i v i t y o f t h e i o n gauge r e l a t i v e  t o dry a i r f o r h e l i u m was 4/3  t a k e n t o be l / 7 and t h a t f o r argon  (12).  (c) R e s u l t s and E s t i m a t i o n o f E f f i c i e n c y (i) Total Efficiencies Equation  (4) g i v e s t h e t h e o r e t i c a l r a t i o o f i o n c u r r e n t  t o e l e c t r o n c u r r e n t as (4)  p o t e n t i a l o f 130 v o l t s , Q(180) = 3<>32 x 10~ -5 i n g t o the pressure  5 x 10  mm.  cm.  and  correspond-  o f mercury a t which t h e number  o f m o l e c u l e s p e r u n i t volume of h e l i u m gas a t room t e m p e r a t u r e current to electron current i s  ION CURRL.NT (MICROAMPERE, 10  ARGON  CO^RECTEJS  FOR  BACKGROUND  -V4E.UUl*\  CORRECTED  FOR  BACKG-ROUND  BA«-K6ftOONO FOR &3XH H&-lUt/\ AND AReoM (*A.s L E A K C L O S E . © } X  4 -  _ _ - A - -- A -I  A - - -  L  zoo PLATE. E L E C T R O N F i g u r e 16  J  CURRENT  I  A  ~ 1_  _  _  A  400  (MILLIAMPERLS)  -21-  I ip  =s.  32oS m i c r o a m p s ° / a m p  0  -16 Similarly  f o r argon,  Q(lgO)  = 3.08  ?  x 10  cm,  , and  -6 at  the pressure 54  x 10  mm»  t h e number o f m o l e c u l e s  per  unit  11 10  volume a t room t e m p e r a t u r e i s l o ? S x I _ 32o9 microampso/ampo i« P The determined  that  o f 45%  from  the graph  f o r argon  gas  is  is  23 °S m i c r o a m p s o/amp  The  foregoing results 72%  0  indicate a  f o r argon.,  The  i n t h e c a s e o f h e l i u m may  positive  as  microampso/ampo  f o r h e l i u m and  creased  16  of figure  I  efficiency  Thus,  experimental value of the slope f o r helium  I _~ 14«9 and  molecules/coCo  ion neutralization  collection lower  collection  h a v e b e e n due resulting  from  pressure, d i s c r e p a n c i e s i n the values taken  efficiency  to the i n the g r e a t e r  f o r the  ionization  cross s e c t i o n or i n the values taken f o r the pressure s e n s i tivities u 100%  The  collection  s i n c e t h e gas  ionising  temperature  region could easily Lower l i m i t s  be (2)  efficiencies  calculated w i t h an  collection  and  be  on t h e  hence i n v e r s e  h i g h e r by  factor,  C,  close  density  a factor  efficiencies  f o r beams o f h e l i u m and  additional  are probably  two  i n the  0  of the i o n i z e r  argon  t o account  to  atoms u s i n g for a less  may  equation than  100%  efficiency< > Total  E f f . = 100  L'Q(V) i p C v A e  %  (11)  For argon a t 20 C 0  o  with the f o l l o w i n g  values:  v = 350 meters/second Q = 3<>08 x I O " C =  A = 6  e  2  0.72  L = 10  ip=  cmo  16  cm  u  cm.  OoS  2  amps.  = I 0 6 x 10  -19  coulombs  the t o t a l e f f i c i e n c y i s Total E f f o  =  5o3%  For helium 4 a t 20 ° C v = 1100 Q  =  0  with the following  values:  meters/second  3o32 x 1 0 "  17  cmo  2  C m Oo45 the t o t a l e f f i c i e n c y i s Total E f f o  -  0ol2$  I n t h e a c t u a l beam source i t i s planned t o c a r r y out the  i o n i z a t i o n i n t h e presence o f a 3000 gauss do c« magnetic  f i e l d applied  p a r a l l e l t o the d i r e c t i o n of electron t r a v e l .  In  Appendix V i t i s shown t h a t the i n c r e a s e i n e f f i c i e n c y which a r i s e s from t h e i n c r e a s e d path l e n g t h o f the e l e c t r o n s  is  negligibleo ( i i ) F i l a m e n t Performance Consistent,, prolonged a c t i v a t i o n o f t h e f i l a m e n t s not  accomplished j, however  period  9  was a c h i e v e d  0  was  partial activation for a limited  An average t e s t run l a s t e d o hours and  i n a l l cases t h e f i l a m e n t s were used as j u s t pure t u n g s t e n f o r at l e a s t 7 o f these hours»  The f a i l u r e a t a c t i v a t i o n may  have  -23b e e n due c h i e f l y t o i n t e n s e p o s i t i v e or  improper a c t i v a t i o n  filament  temperatures  probable since  resulting  from i n c o r r e c t  The l a t t e r  0  i o n bombardment  w i t h measured f i l a m e n t  reason i s f e l t  in  failed  deterioration  to gain better  plained  of filament  (iii)  Positive  intensity  It  s h o u l d be Ion  i s useful  ived  i n A p p e n d i x »'IV  Since  could  of positive  flashing  o n l y be ex-  i o n bombardment.  g r i d t o cathode s p a c i n g ,  success-  possible,  f o r which t h i s  ion neutralization  to electron  performance.  resulted  t o make an a p p r o x i m a t e e s t i m a t e o f t h e  A measure o f t h e l a t t e r density  that  Neutralization  maximum beam i n t e n s i t y positive  i t was n o t i c e d  response.,this e f f e c t  by t h e i n c r e a s e d  activation  well  v o l t a g e f r o m 20G t o 300 v o l t s  W i t h a l o w e r vacuum a n d c l o s e r ful  temperatures  emissivityo  the filament-grid  rapid  t o be im-  corresponded reasonable  During the course of t e s t i n g raising  poisoning  estimation of  t h e method o f e s t i m a t i n g f i l a m e n t  when o p e r a t e d a s p u r e t u n g s t e n  s  affects  effect  density  ionizer  c a n be u s e d  before  the c o l l e c t i o n e f f i c i e n c y .  i s the r a t i o of positive ion  at a given point.  f o r the region  The r a t i o  s  der-  o f maximum p o s i t i v e i o n  density, i s (12)  which f o r helium k having t h e f o l l o w i n g  Q = 3-32 x 1 0 " R = 0.3  1 7  cmo  cm.  Nb=10l5  atoms/seco  A —Oo36  cm.  2  2  values  -24-  E = 2 5 volts/cm m v  i o n  =  x lO  6o7  ^ °?>  elo  ^  x  0  - 2  ^ grams  cmo/sec  u  the r a t i o i s / ^ i o n z= /©el.  1 2  0  0  0  The background pressure corresponding to a beam i n t e n s i t y of IO* 5 atoms/second t r a v e l l i n g at 1 1 0 0 meters/second speed spread 1  over  0 » 3 6  2  cm<>  cross sectional area i s 7  pressures of 1 » 4 x 1 0  mm  0  » 2  x  -7  1 0 " '  mm» At  the r a t i o i s down to l/lOO which  gives a 1 % change i n the second derivative of the p o t e n t i a l at a given point„ 10  17  Thus, at beam i n t e n s i t i e s above approximately  atoms per second per cm  o &  0  p o s i t i v e ion n e u t r a l i z a t i o n  becomes s e r i o u s .  CHAPTER VI  CONCLUSION  The most important consideration i n the design of a n i o n i z e r i s the achievement of a high c o l l e c t i o n efficiency<> The c o l l e c t i o n e f f i c i e n c y achieved by t h i s i o n i z e r was at l e a s t 7 2 % f o r argon at 5 4 x 1 0 "  mm. pressure and at least 4 5 % f o r  -5  helium at  5  x  10  nrnio  o f mercury  pressure.  Because of the uncertainty of gas temperature i n the i o n i s i n g region only lower l i m i t s of i o n i z e r performance could be obtained..  The estimated e f f i c i e n c y at 0o# amperes plate  current f o r an argon beam at room temperature i s at least  5°3%°  -25while that  f o r helium 4 i s at least The W e i s s  0ol2%  I o n i s e r had a  a r g o n a t room t e m p e r a t u r e w i t h a p l a t e  0  total  efficiency for  current  of O d B  amperes.  CHAPTER V I I  A SOURCE OF DOUBLY CHARGED HELIUM  INTRODUCTION  The carried  design o f a doubly  out f o r t h e purpose  charged  of providing  h e l i u m s o u r c e was a h e l i u m beam w i t h  d o u b l e t h e V a n de G r a a f e t e r m i n a l energy„  The r e q u i r e m e n t s o f  the source a r e : (1) t h a t  i t produce  a mono-energetic,  c h a r g e d h e l i u m beam o f r e l a t i v e l y (2) t h a t  well focused, high  intensity,  i t a c h i e v e s s e p a r a t i o n o f t h e s m a l l doubly  component f r o m t h e n o r m a l l y l a r g e  doubly  singly  charged  charged  helium  component j, a n d (3) t h a t The  t h e u n i t be s m a l l and simple  i n construction.  He beam s h o u l d be o f s u f f i c i e n t l y  high intensity  m i c r o a m p e r e o r g r e a t e r ) so t h a t  good s t a t i s t i c s  in nuclear reaction  and mono-energetic  energy  so t h a t  good  g e t a 1 micoampere He*beam f r o m a n i o n s o u r c e i t  usually necessary t o extract  Separation  more t h a n 1  o f t h e two h e l i u m c h a r g e  t e r m i n a l o f t h e V a n de G r a a f e dissipating charged  may be a c h i e v e d •  r e s o l u t i o n may be o b t a i n e d . To  is  experiments  (1  o f beam.  components a t t h e t o p •  i s essential, therefore, to avoid  e x c e s s i v e power i n a c c e l e r a t i n g  component  railliampere  the large  singly  o f t h e beanie  Because space and f a c i l i t i e s  at the top terminal are  -27liroited,  the source should  be s m a l l  and s i m p l e i n c o n s t r u c t i o n .  T h e r e were two methods c o n s i d e r e d  t o achieve  separation  t + and  focusing  o f t h e He, c r o s s e d  and. a d o u b l e f o c u s i n g simplicity consists  electric  magnetic  field.  o f an i o n s o u r c e f o l l o w e d  ION  High  In type  (1)  a beam o f e l e c t r o n s  Focusing  i s generally  may  many  down v e r s i o n yielded  cross  obtained  (6),  (7) .  region  focused,  only  once  e t . a l . (14)  Moak  mono-energetic  The  (13)  or they  built  Duo P l a s m a t r o n  a  scaled  which  5 m i c r o a m p e r e beam  ,  {,4.  o f He i o n s .  The d i s a d v a n t a g e o f t h i s  same t y p e a r e t h a t operation  from a  j e t t o produce t h e i o n s .  o f von Ardenne's o r i g i n a l  a steady, w e l l  emitted  by a m a g n e t i c f i e l d .  the ionising  times  be u s e d t o p r o d u c e t h e  sources  c o l l i d e s w i t h an atomic  may  magnets  sources  filament  electrons  by a double f o c u s i n g  could  e l e c t r o n beam  frequency  therefore,  These a r e , g e n e r a l l y :  +  (2)  The He u n i t ,  SOURCES  m i x t u r e o f He a n d H e i o n s » Focused  design  VIII  Numerous i o n s o u r c e s  (1)  fields  Because o f i t s  t h e l a t t e r method was c h o s e n .  CHAPTER  cross  and magnetic  they  by f i l a m e n t In type  are limited  i o n i z e r and others  t o l e s s t h e n 1500  of the  hours o f  life.,  (2) a r a d i o  m a i n t a i n s an e l e c t r o d e l e s s  frequency  discharge  field  e x c i t e s and  i n a pyrex v e s s e l .  The  -26-  absence o f a hot cathode and, hence, t h e a s s o c i a t e d l o n g the mono-energetic y i e l d s make t h i s  type  a p p l i c a t i o n s than source  o f source  type  more a t t r a c t i v e  (1) sources«  large current  f o r accelerator  Because a r a d i o  frequency  h a s b e e n s u c c e s s f u l l y u s e d i n t h e Van de G r a a f e  number o f y e a r s Duo P l a s m a t r o n this  i o n p r o d u c t i o n , and r e l a t i v e l y  He source  life  for a  a n d p r o m i s e d t o compare f a v o u r a b l y w i t h t h e f o r He o u t p u t ,  i t was c h o s e n a s t h e i o n i z e r f o r  +  0  CHAPTER IX  THE  (a)  RADIO FREQUENCY  DISCHARGE  General To b e a b l e t o p r e d i c t  the effect  of discharge  conditions  on He o u t p u t , i t i s h e l p f u l t o i n v e s t i g a t e q u a l i t a t i v e l y of  t h e To f o d i s c h a r g e e  A radio frequency  discharge  when a v e s s e l c o n t a i n i n g g a s a t a l o w p r e s s u r e a  coil  c a r r y i n g high frequency  inductively fields  coupled  induced„  current<>  the order o f 1 volt/meter next  to  n e a r l y zero at the center.  electric  from t h e v o l t a g e d i f f e r e n c e a c r o s s t h e tank c o i l  an  o f 50 k i l o v o l t s  electrically  p e r meter.  w h i c h a r e many o r d e r s  o f magnitude l e s s  field  results  and i s o f t h e  the electric than  i s only  decreases  After the discharge  n e u t r a l plasma i s formed  electric  magnetic f i e l d ,  t o t h e b o t t l e and  The o t h e r  inside  i n an  arrangement., t h e r e a r e two d i f f e r e n t  of  order  i s excited  i s placed  Initially,  One, due t o t h e c h a n g i n g  the physics  those  has o c c u r r e d fields i n  which would  -29exist in  i f the  the  negative  c h a r g e s were removed.  p l a s m a , h o w e v e r , must be  electrons  sufficiently  energies  great  electric  high  are  accelerated  The  current  obtainable  f r o m an  r. fo  d e t e r m i n e d l a r g e l y by  plasma i o n  density  and  gas  to  The  so  fields  that  enough t o  ionize  atomso source  is  extraction  conditions o The  main f a c t o r s g o v e r n i n g  (1)  D i f f u s i o n of ions  (2)  Gas  (3)  R°  a given  fo  power  walls  input  close proximity  point  lose their  of walls  of the  charge through recombination with  plasma i o n  extent  present  indication  high  o f gas  application  density  of  As  energy t o  density  determines the  yield  e x c i t a t i o n as has  determine  that  pressure  been found t o  value  gyromagnetic frequency  number  and  increase  so  the molecules  Eubank et a l . . ( 1 5 )  a high  same low  a  low  visible  power.  upon  o r l o n g i t u d i n a l magnetic  case p a r t i c u l a r l y ,  i s exhibited at  jointly  in  number o f  q u a n t i t a t i v e l y the  either a transverse  walls  c a u s e i o n i z a t i o n and  o b s e r v e d by  power c a n  ion density  transverse  which the  pressure  r . f . power d e t e r m i n e s t h e  pressure  ionised.  The  the  The  sufficient  while the  and  ion  electrons.  of i o n i z a t i o n of those molecules present  t o be  pressure  For  density.  electrons with  discharge  decreases the  s i n c e most i o n s w h i c h c o l l i d e w i t h t h e  R a d i o f r e q u e n c y power and the  are:  pressure  The at  t o the  equilibrium ion density  field.  a l a r g e maximum i n t h e  o f d.  of the  c. m a g n e t i c f i e l d electrons  is in  ion  at  resonance  -30with the a p p l i e d o s c i l l a t o r y f i e l d . Komarov & P e t r o v to  (16) found t h i s t r a n s v e r s e d. c. magnetic  be 30 gauss corresponding  30 megacycles.  F o r a 25 megacycle o s c i l l a t o r field  t o an e l e c t r o n gyro frequency o f  P h y s i c a l l y , t h e e f f e c t can be e x p l a i n e d by  assuming t h e magnetic f i e l d r e v e r s e s t h e d i r e c t i o n o f t h e e l e c t r o n , without  l o s s o f energy, as the a p p l i e d e l e c t r i c  r e v e r s e s d i r e c t i o n , so t h a t , although  t h e magnetic  field  field  s u p p l i e s no energy t o t h e e l e c t r o n s , the e l e c t r o n ' s d i r e c t i o n i s a l t e r e d i n such a way t h a t i t can r a p i d l y g a i n energy from the e l e c t r i c f i e l d , p r o v i d e d t h a t t h e motion i s not f r e q u e n t l y i n t e r r u p t e d by c o l l i s i o n s w i t h gas molecules (17)o The to  amount o f e x t r a c t e d c u r r e n t i s extremely s e n s i t i v e  e x t r a c t i o n e l e c t r o d e design and v o l t a g e .  o f these  The proper  design  e l e c t r o d e s has been i n v e s t i g a t e d by many people (18)  and ( 1 9 ) . (b) Optimum Discharge  Conditions f o r the Production  o f Doubly  Charged Helium To o b t a i n an a p p r e c i a b l e d e n s i t y o f He^the mean f r e e path o f an e l e c t r o n i n t h e plasma must be l o n g enough so t h a t the e l e c t r o n can a c q u i r e an energy g r e a t e r o r equal t o t h e second i o n i z a t i o n p o t e n t i a l o f helium. be  The r a d i o frequency  f i e l d must  s u f f i c i e n t l y i n t e n s e so t h a t t h e e l e c t r o n s r e c e i v e t h i s  b e f o r e h i t t i n g gas molecules o r t h e w a l l s o f t h e v e s s e l .  energy Hence  gas p r e s s u r e must be below a c e r t a i n c r i t i c a l v a l u e f o r a p p r e c i a b l e amounts o f He t o be formed. A l l i s o n and Norbeck ( 2 1 ) .  T h i s e f f e c t has been observed by  -31CHAPTER X  DESIGN OF THE DOUBLE FOCUSING MAGNET  (a) P o l e P i e c e The  Design basic  magnet was s e t t l e d  design o f t h e double on f r o m  simplicity  o f machining  acceptance  angle. Sternheimer  focusing  considerations of physical  pcle pieces,  image i n t e n s i t y  (22) h a s c a l c u l a t e d  fringing  a n d beam  field.  different  field  I f one c o n s i d e r s  c a s e a s shown i n f i g u r e 17 o f p a r t i c l e s . f r o m a s o u r c e a t P  t r a v e l l i n g t o w a r d s t h e magnet, b e i n g d e f l e c t e d § a n d imaged a t a p o i n t  Th  T  v  an a n g l e field,  focusing i s  = R c o s . t sine_,£> co.s.s + _S' s i n e ( t p - t - s )  vertical  through  I , then i n t h e case o f a uniform  t h e image d i s t a n c e f o r h o r i z o n t a l  for  size,  curves o f double  f o r v a r i o u s d e f l e c t i o n s and s e v e r a l  v a r i a t i o n s assuming a sharp the  focusing separation  Scos.(.Q-s)  (13)  - cos.fj) - t c o s . s .  focusing i s  - RlQ + s ' d - P t a n s)1  ^ _  (14)  S t a n s + [i-§>tan s) t a n t - ( 1 - $ t a n t ) where s ' i s t h e o b j e c t d i s t a n c e d i v i d e d by t h e r a d i u s o f c u r v a t u r e , R,  o f t h e p a r t i c l e s , T i s t h e image d i s t a n c e , s i s t h e a n g l e t h e  normal  r a y makes w i t h t h e n o r m a l  magnet, t i s t h e a n g l e t h e n o r m a l the  exit  vertical  t o the entrance face o f the r a y makes w i t h t h e n o r m a l t o  f a c e o f t h e magnet, a n d <p i s t h e a n g l e o f d e f l e c t i o n . I n o r d e r t o g e t maximum beam a c c e p t a n c e , most o f t h e f o c u s i n g was c h o s e n t o t a k e p l a c e a t t h e e n t r a n c e f a c e  -32of the  magneto  This  choice  the  magnet n o r m a l t o t h e  and  (14)  making t h e  c a n be  correspondingly  reasonably  s' =  small  the  o f 3-33  of curvature  sized pole  image  (13)  image  intensity,  cm.  was  For a 2i  pieceso  chosen t o  kilovolt  r e q u i r e s a 3060 g a u s s m a g n e t i c  t h i s value  size,  9=90°, the  hence, the  considerations  object  distance  on was  1*5.  allow  extraction  field.  o f t h e beam h o l d e r  settled  5 cm,  and  so  pole  that  ! o f p a r a m e t e r s and  c o n d i t i o n t h a t the  image d i s t a n c e s  f o c u s i n g , be  equations  equal,  angle  s = 4 4 . 2 ° and  piece  design  (13)  those parts  of the  (b)  Image S h i f t  due  The  effect  Fringing f i e l d  (14)  give the  and  c o u l d be  t o the Extended F r i n g i n g of the  I i s the  dimensionso  finite  extent  for fringing field The  obtained not  normal entry  i s d e r i v e d by  Bainbridge  the  t r a j e c t o r y i n c l u d i n g t h e more g e n e r a l  vertical entrance The  pole  cover  by  flux  cutting  the  beam.  fringing  field  Field  I shown i n f i g u r e  exist  t r a j e c t o r y i n the  for  the  A greater  of the  field  which would  cm.  (19).  p o l e p i e c e s w h i c h do  computed n u m e r i c a l l y  of i n f i n i t e  and  i s shown i n f i g u r e s (18)  off  from  f o r h o r i z o n t a l and  image d i s t a n c e , T = 5.5  the  d e n s i t y f o r a g i v e n magnet c u r r e n t  is  leave  i n equations  d e f l e c t i o n angle,  F o r the above c h o i c e  was  so t h a t  to  high.  From d e s i g n piece  face  made s m a l l and,  A radius  voltage,  exit  particles  t=0. By  distance  required the  (23).  f o r pole horizontal The  pieces plane  formula  case o f o b l i q u e  20.  for  entry  Figure  21  C o o r d i n a t e Axes of  Particles  SCiV-E- —  D/MEMSlbNS SP£C I RED  PULL  S>IT-£-  IN INCHES  TRAJECTORIES FRIN&IM&  UNLESS  OTHERWISE  FOR eJCTtNOE.0  FieLD  I  NORVlAL TRAJECTORY FOR SrfARP  FRINGIN&  FlE-LD  IMAGE- FOR, ExTENDE-0  J F i g u r e 18  Particle  Trajectories  MATERIAL MASVtT — pote. Ne.ce« SCALE -  MILD  — CAVT  STCtL. IRON  -pdL-E  Pieces-  •-H.5 —J,4T*--l-5  9.5 15.5  F i g u r e 19  T e s t Magnet  F i g u r e 20  Fringing Field  DISTANCE.'  FROM  POLE  Curves  FACE.  \KI  <&Ap  WIDTHS  ^>  -33-  j h ( y ) d y + R cos. 6  dx _ d  y  (15)  ±(R*-[R COS 9 + f n ( y ) d y ] M p  The c o o r d i n a t e a x e s , x and y, and t h e a n g l e © a r e as shown i n f i g u r e 21.  At a g i v e n y c o o r d i n a t e t h e v a l u e o f t h e f i e l d i s  H h ( y ) where H 0  0  i s t h e u n i f o r m f i e l d i n s i d e t h e magnet.  The  t e c h n i q u e employed t o e v a l u a t e f o r m u l a (15) was f i r s t t o determine  ('h(y)dy by n u m e r i c a l i n t e g r a t i o n u s i n g Simpson's R u l e  p. w i t h an i n t e r v a l l e n g t h o f 0 . 1 5 S gap w i d t h s .  Then, t h e s l o p e s  dx/dy a t t h e even i n t e r v a l p o i n t s wpre computed and t h e t r a j e c t o r i t r a c e d i n . The r e s u l t i n g image s h i f t i s as shown i n f i g u r e 18. S i n c e t h e measured f r i n g i n g f i e l d s , A and C, f a l l o f f more s h a r p l y t h a n does f r i n g i n g f i e l d I , t h e a c t u a l image s h i f t  will  be s l i g h t l y l e s s t h e n t h e computed s h i f t f o r f r i n g i n g f i e l d I . '  The s l o p e s dx/dy t o g e t h e r w i t h t h e i n t e g r a l  y  j h ( y ) d y f o r both  e n t r a n c e and e x i t cases a r e t a b u l a t e d i n Appendix V I . S i n c e t h e a n g l e between t h e f i e l d l i n e s and p a r t i c l e t r a j e c t o r i e s can n o t be determined a c c u r a t e l y , c a l c u l a t i o n o f t h e v e r t i c a l f o c u s by t h e extended f r i n g i n g f i e l d was n o t attempted. CHAPTER X I  TEST BENCH A diagram o f t h e t e s t bench i s shown i n f i g u r e 2 2 . P o l y e t h y l e n e t u b i n g c o u p l e s a p r e s s u r e measuring  P i r a n i gauge  head and a gas l e a k t o e i t h e r end o f a T-connector  at the top  T5  (JfiS  F i g u r e 22  L&PiK  SCALE.  'A  77777*  R . F . T e s t Bench  SIZE.  ASS ALUM-MUM  Y// A  STAINLESS  STCEL  (A)  EXTRACTOR  ELECTRODES, (FULL  EVn  1  Size)  7 i-3 O  o  iup SOPPOFCT  A N P.  (Vs.")  TO  ' O N :>  IN  p-i  .  o  PUMp <D  -34A 0.040 i n c h t u n g s t e n  of the r . f . b o t t l e .  between probe and e x t r a c t i o n e l e c t r o d e . made o f s i l v e r end.  stainless  soldered stainless  The beam h o l d e r i s  s t e e l with brass  The i o n c u r r e n t m e a s u r i n g d e v i c e  steel  cup s i l v e r  which, i n t u r n , i s s i l v e r brass  posts  soldered to a stainless soldered to a brass  soldered t o a f i x e d brass  image c a n b e l o c a t e d a n d p r o f i l e d .  t o be u s e d  i n this  test  steel  flange.  tube  The  and t h r e e  flange allows  o f t h e beam cup i n t h r e e p e r p e n d i c u l a r d i r e c t i o n s the  flanges at  consists of a  f l a n g e w h i c h i s made m o v a b l e by a b e l l o w s  support  serves as  The e x t r a c t i o n v o l t a g e , 0 t o 5 k v . , i s a p p l i e d  the probe.  either  wire  movement  so t h a t  A d i a g r a m o f t h e magnet  b e n c h i s shown i n f i g u r e 19»  CHAPTER X I I  CONCLUSION  The by  a double  He source +  f o c u s i n g magnet.  o f He^ i t i s e x p e c t e d be  below a c e r t a i n  d.Co the  magnetic  that the discharge pressure  critical  field  sizeably  followed  I n o r d e r t o g e t a p p r e c i a b l e amounts  value.  of a value  such  i n c r e a s e t h e plasma  will  have t o  Application of a transverse t h a t t h e gyro  e l e c t r o n s i s i n resonance with the o s c i l l a t o r  should ion  c o n s i s t s o f a r . f . i o n source  frequency  of  frequency  i o n d e n s i t y a n d , h e n c e , He  output. The  horisontal  finite  extent  of the fringing  image b y no more t h a n  field  s h i f t s the  0.6* cm. f r o m t h e image f o r no  fringing will  field.  be b r o u g h t  numerical  Although closer  calculations  by  i t i s expected the v e r t i c a l the f r i n g i n g  field,  c o u l d be made t o c h e c k  no  image  accurate  this  effect.  -36APPENDIX I Equations Describing Charge L i m i t e d Consider plane p a r a l l e l be  described dx  where V i s the  Current  the £  2  i s the  The  one  Space  Between G r i d and  Plate  (= l / ( 3 6  dimensional  Poisson's  are can  equation  p o i n t x between t h e s e  at t h i s  p o i n t and  x 10^)  farad/meter).  charge d e n s i t y  produce a current  plate  p o t e n t i a l between t h e s e p l a t e s  p o t e n t i a l a t any  I f the  and  e  charge d e n s i t y  o f a vacuum  P o t e n t i a l and  case i n which both g r i d  the  sheets.  by  the  density  J  plates <P 9  £ i s the p e r m i t t i v i t y Q  c o n s i s t s only  of  electrons  which  then  v where v i s t h e in  v e l o c i t y of the  e l e c t r o n s a t p o i n t x.  terms of the p o t e n t i a l through which the  Writing  e l e c t r o n has  fallen  gives  P= where  >£=  e/m  J for electrons.  f o r /° inVo Poisson's d Y 2_ 2  d^  The  J  equation  Thus, s u b s t i t u t i n g t h i s gives  V"^  TpTl  p o t e n t i a l i s c o n c a v e upwards and  of g r i d  and  p l a t e are  shown i n f i g u r e  equal,  has  by  symmetry, i f t h e  a minimum, V , m  i n the  potential  center  2.  M u l t i p l y i n g both sides of the 2 d\^ and dx  expression  integrating yields  preceding  equation  by  as  -37-  The  c o n d i t i o n dV/dx = 0 a t V = V  the  above equation  m  g i v e s C_ ]  =  -i^JV^  Therefore,  becomes  k  dx  (5)  Letting  m  1  and  making t h e s u b s t i t u t i o n U =  - V ^ m  1 eads t o  I = 4 U * ( U 4-V*] s u b s t i t u t i n g again  i Hence  =|  equation  p  f o r U gives  (v*  -  4)H^^4)  (5) i n t e g r a t e d becomes ijj  Applying ^2  = ktyc  t h e boundary ~ t ) ^ ^c-t" v  +  V  where a = 3_ \ 4 4 Using  2 7  !) •  T  h  a squaring  p  V = V  complete equation  e  both  gives  i s therefore  (6)  ' (6) t h a t V = V  m  at x - d gives  = -(V|-v|)(v|-r2v|)  2  c  A + ( V * - V * ) ( 7 * + Zvi)  t h e c o n d i t i o n i n equation  A  2  c o n d i t i o n t h a t a t x=0  ( 4- |)i(v4 2V|) V  x 4- C  2  sides 1+2  Vm  (7)  4 la Substituting  for  i n equation  ( 6 ) from equation  (7) g i v e s  -38-  1 -  x = d 2  v  c  (8)  1 i  I t : s h o u l d be n o t e d  t h a t t h e above e q u a t i o n  i s valid  only f o r  a n d 0<x<  1 > V(x)> Vm  d where V(x) i s t h e v a l u e o f t h e p o t e n ' Ve ' Vc 2 i a l a t any p o i n t between x = 0 a n d x = d o 2 APPENDIX I I Equation Gradient  D e s c r i b i n g t h e P o t e n t i a l Minimum  as a F u n c t i o n o f t h e G r i d - P l a t e Angle  C o n s i d e r t h e square  r o o t o f e q u a t i o n (7)  • (^rf- [ -te)*][ d  Taking  a  l  the d i f f e r e n t i a l  distances  o f both  l + a  W*I  sides treating the grid-plate  d„ a n d t h e p o t e n t i a l minimum, V , m  ,1* = V &  m  1 [(Va^IrJ^-  2(V /V )l m  (Wv )i)  'c  as v a r i a b l e s c  e  I f W i s d e f i n e d s o t h a t 6 = fed t h e n t h e p r e c e d i n g  &V v  Equation  m a  m  _  20 ->  (9) i s v a l i d  a*-V?A  r  i  o n l y f o r 1< V < 1 Vn 4 m  ij  equation i s  (9)  -39-  APPENDIX I I I The Potential Minimum Variation Due to a Do C o Filament Voltage Assume a cathode-grid voltage exists of the form V  cg = o " < f/Dz V  v  where z i s the distance along the length of the filaments from the entrance to the ionizer^ V p o t e n t i a l at s=0  s  V  0  i s the value of grid-cathode  i s the grid-cathode potential at z=z, Vf  G g  i s the d o C o filament voltage with respect to the potential at z=0, and L i s the length of the filaments.  Substituting V  c g  into equation (7) gives dJ £a"  =  2  2  Taking d i f f e r e n t i a l s of the above equation t r e a t i n g z and V as variables gives &V  m  =  _ 1 V 2  1  f  (l-i(V /V )*)  L  c g  For V g = V C  Q  Sv 6%  - VfZ L m  =  = V  c  _ l Vf 2 L  m  the preceding equation becomes  (l-|(V /V P) 0  m  m  -40-  APPENDIX IV Derivation  o f t h e Approximate  Maximum R a t i o Ions t o t h a t  o f t h e Charge  of Electrons  Formula  Density  f o rthe  of Positive  f o r t h e P o l a r i z e d Beam  C o n s i d e r an a t o m i c beam o f c i r c u l a r incident  between g r i d  a n d p l a t e a s shown  Ionizer  cross  section  below  The number o f beam m o l e c u l e s i n t h e d a s h e d  element  &V=-  A»l  is  S A Nb A v b  where A i s t h e c r o s s  s e c t i o n a l area  number o f atoms p e r s e c o n d e n t e r i n g the  o f t h e beam, N  b  i s the  the i o n i z i n g region, v ^ l s  most p r o b a b l e v e l o c i t y o f t h e beam m o l e c u l e s , a n d &A  element  o f cross  s e c t i o n a l area  shown  i s the  above.  The p r o b a b i l i t y o f an e l e c t r o n i o n i z i n g 1 atom i n Sv i s  where Q i s t h e c r o s s cules,  and S y  s e c t i o n f o r i o n i z a t i o n o f t h e beam  i s a s shown a b o v e .  moleJ6y  The p r o b a b i l i t y o f e  electrons  i o n i s i n g 1 atom i s QJ &X e &y  The number o f i o n s  formed p e r second i n & V i s , t h e r e f o r e ,  dN .- &A Nh Q J A v e b  The v e l o c i t y a t y=W  o f an a b o v e  i o n f o r m e d a t y=y w h i c h t r a v e l s  -41in  the p o s i t i v e y - d i r e c t i o n  is  2eE(W-y) m ion where E i s t h e and  field  e x p e r i e n c e d by t h i s  ion»  m. „ i s t h e mass o f t h e i o n . ion If  y=W  as  then The  effective electric  dN  one  assumes a f o c u s i n g o f i  now  sketched  b e t w e e n y=y  and  below  ions/second with  contribution  speeds Vy pass  through  o f t h e s e i o n s t o the charge  area x . l at  W.  density at W i s  d/>y = M  where C = NhQJ2 Avb \2~eW  Won The SV  t o t a l charge  d e n s i t y o f i o n s a t W due  t o i o n s formed i n  is 2x '8 A W-y = C = C J  2x d v c 2W-y x  dy_ W-y  where D i s t h e d i a m e t e r  o f t h e beam  = 2G ( {W - Jw-T? ) The  a b o v e e x p r e s s i o n has  a maximum v a l u e a t W  = D,  / ° m a x = 2C{TT  = 4NhQJfD" eAv fgelP T  b  m ion  (12)  -42APPENDIX V Electron Path Length Increase due to an Applied Do C . Magnetic  Field  The effect of application of a uniform magnetic  field  p a r a l l e l to the d i r e c t i o n of electron t r a v e l i s to cause those electrons which leave the filaments at an angle not p a r a l l e l to the magnetic f i e l d to s p i r a l with an angular frequency given by the formula UJ  r eB m  where LO i s the angular frequency of s p i r a l l i n g , B i s the magnetic f i e l d f l u x density, and e/m i s the charge to mass r a t i o of the electron,. The time taken to traverse the g r i d to plate distance assuming an average electron energy corresponding to V i s X - dp /v g  =4fi^  s  d  pg/ ^  2 7  l^  \ m The t o t a l number of cycles rotated i s R = SAL"*  I f one assumes a cosine d i s t r i b u t i o n of electrons emitted from the surface of the filaments ( 1 1 ) , then the mean angle of emergence i s given by 0 =  Jcos 0 d9  =2  { de The average value of the component of v e l o c i t y perpendicular to the magnetic f i e l d i s , therefore, V j _ = v s i n e 0 = 0.594 v a v  a v  -43H©Fig  v  surfac©  a v  t h © a v t r a g © v e l o c i t y o f § l © e t r o n § ©mittisd f r o m t h ©  iB  e  Th§ r a d i u s o f r o t a t i o n o f §l§etron§ i n a f i e l d B w i t h velocity  p e r p e n d i c u l a r t o t h i magnetic fi§ld i § P * '  eB  I f i i t t h i d i i t a n e t t r a v t l l t d parallel'to th§ m a g n e t i c f i e l d i n one c y c l e f o r h e l i c a l t r a v e l * t h e f a c t o r by w h i c h t h © p a t h length P  i i  i n c r e a s e d is  ABA^.M£A  S  S  But S a d « g / R a i]C\V_ « U i i n g t h i s e s e p r e m i e n f o r S t o g e t h e r  w i t h t h © expression f o r  i n t h i formula f o r P gives  P • Jl-t-xS I t i i interesting t o n o t e t h a t P is ' i n d e p e n d e n t o f t h i a p p l i e d m a g n e t i c f i e l d * 1 ? This r e s u l t i s t o b e expeoted s i n e © t h i o n l y way o f c h a n g i n g t h e t o t a l e l e c t r o n p a t h l e n g t h f o r a g i v e n V i s t o change the § p e e d o f the e l e c t r o n p e r p e n d i c u l a r t o the magnetic field*  T h i § i p e e d i s u n a f f e c t e d by: t h e m a g n e t i c  T h # m e a n e n e r g y o f electrons emitted f r o m t h ©  field, §urfae§  o f t h © f i l a m e n t s i s 0>1 v o l t s (11) w h i c h c o r r e s p o n d s t o a v e l o c i t y I  o f !• #75  K  1°  t cffls/iiCa  Th©  Biian  component o f v e l o c i t y  d i e u l a r t o t h e m a g n e t i c f i e l d is» t h e r e f o r e . v^ « Is 112  perpen-  f  10^ m e t e r s p e r s e c o n d  T a k i n g t h © a v e r a g e e l e c t r o n p o t e n t i a l to b e 150 v o l t s leads t o 2.  m 0s00047  -44APPENDIX V I Tabulation  o f f h ( y ) d v a n d dx/dy f o r E a t r v t o t h e Magnet A s s u m i n g  a Source- D i v e r g e n c e o f 1 0 ° a n d a n I n t e r v a l L e n g t h  o f 0.158 Gap  W i d t h s w i t h t h e C o o r d i n a t e A x e s a s Shown i n F i g u r e 21  Interval  0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  23 24  D i s t a n c e from Entrance Face (gap w i d t h s ) 2.800 2 c 64 5 2 „ 48,7 2.328 2.170  2 .011 1.853  1.694 1.536 1.377 1.219 1.660 0.902 0.743 0.585 0.426 . 0.268 0.108 -0.050 -0.203 . -0.366 -0.525 -0.683 -0.842  dx/ dy Center Path  dx/dy Short Path  dx/ dy Long Path  0.0125  -0.962  -0.807  -1.146  0.14  0.087  -0.902  -0.756  -1.066  0.16 0.18 0.20 0.23  0.121  -0.880  -0.139  -1.039  0.178  -0.840  -0.706  -0.987  0.251  -0.793  -0.668  -0.930  0.312  -0.758  -O.637  -0.888  0.49 0.54  0 o441  -0.604  -0.575  -0 0300  0.64 0.77  0.614  -0.598  -0.500  -0.706  0.856  -0.488  -0.401  -0.574  0.96  1.15  -0.375  -0^.298  -0.451  0.98 1.00 1.00  1.46  -0.267  -0.196  -0.335  1.00  lo77  -O.I67  -O;o0997 -0.230  h(y)  / h(y)dy y  26 0.10 0.11 0.12 0.125  0.145  0.26 0.28 0.35 0.40  0.86 0.92  -45T a b u l a t i o n o f ^h(y)dy and dx/dy f o r E x i t T r a j e c t o r i e s from the Magnet t o -the Image.  The Coordinate Axes a r e Shown i n F i g u r e 21.  (The requirement t h a t the normal r a y be d i r e c t e d a l o n g t h e y - a x i s a t the image s e t s t h e angle 0 which t h e t r a j e c t o r y a t t h e e x i t f a c e makes w i t h the x - a x i s a t 123°^°°  F o r the l o n g e s t t r a j e c t o r y  s  0 = 130.7° and f o r t h e s h o r t e s t , 0 - 116.8°)  Interval  0 1 2 3 4 5 6 7 3 9 . 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  D i s t a n c e from E x i t Face (gap widths) -1.00 -0 o 342 -0c6d3-  -0.525 -O.366 -0.203 -0.050 +0.103 0.263 0.426 0.535 0.743 0.902 1.060 1.219 lo377 1.536 1.694 1.353 2.011 2.170 2.3# 2o437 2.645 2.300  h(y)  Jh(y)dy -1  1.0 1.0 1.0 0.93 0.96 0.92 0^36 0.77 0.64 0.54 0.49 0.40 0°35 0.23 0.26 0.23 0.20 0.13 0.16 0.145 0.14 0.125 0.12 0.11 0.10  dx/dy ' dx/dy Center . . Short Path Path  dx/dy Long Path  0.316  -0.517  -0.663  -0.379  0.626  -0.394  -0.522  -0.270  0.916  -r0.291  -0.404  -0.177  1.16  -0.212  -0.320  -0.103  io33  -0.153  -0.261/  -0.051  1.46  -0.113  -0.213  -0.012  1.55  -0.0906 -0.136  0.015  1.63  -0.0662 -0.164  0.039  1.63  -0.0511 -0.143  .0.054  lo73  -0.0360 -0.133  0.0691  lo77  -0.0240 -0.121  0.0314  1.30  -0.0150 -0.112  0.0904  -46-  BIBLIOGRAPHY  lo  P. T o S m i t h , P h y s . Rev.  2.  A Hughes a n d Eo K l e i n ,  3°  K. Compton and C v a n V o o r h i s , P h y s . Rev.  4o  A o von E n g e l ,  5.  Ho M a s s e y and E . B u r h o p , ' " E l e c t r o n i c Phenomena," O x f o r d P r e s s , 1952  6o  Finkelstein, RoS.L  7.  A r d e n n e , P h y s i k Z. 43,  8.  Mo v o n A r d e n n e , " T a b e l l e n d e r E l e k t r o n e n p h y s i k I o n e n p h y s i k and U b e r m i k r o s k o p i e , " D e u t s c h e r V e r l a g d e r W i s s e n s c h a f t e n , B e r l i n (1956)  9o  Weiss, Ro,  36,  1293(1930)  P h y s . Rev.  " I o n i s e d Gases,'  1  23,  450(1924)  2J7, 724(1926)  Oxford Press, and I o n i c  1955 Impact  11, 94(1940)  R . S . I . 12,  91(1942)  k  9  397(1961)  10o  Clausnitser,  11o  Spangenberg, "Fundamentals o f E l e c t r o n D e v i c e s , " M c G r a w - H i l l Book Company, I n c . , N. Y., 1957  12.  Dushman, " S c i e n t i f i c  Helv»  (1961)  P h y s . A c t a Supp. V I  F o u n d a t i o n s o f Vacuum T e c h n i q u e , " J o h n  W i l e y and Sons, I n c . ,  1949 55,  946(1939)  13.  S m i t h a n d S c o t t , P h y s . Rev.  14°  Moak, B a n t a , T h u r s t o n , J o h n s o n , a n d K i n g , " A ' D u o - P l a s m a t r o n Ion S o u r c e " f o r Use i n A c c e l e r a t o r s , " Oak R i d g e N a t i o n a l L a b o r a t o r y , Oak R i d g e , T e n n e s s e e  15o  Eubank,  I60  Komarov.-and P e t r o v , S o v i e t P h y s i c s - T e c h n i c a l P h y s i c s , 3 1 ,  17„  S a n b o r n C. Brown, " P l a s m a , " C a m b r i d g e  18.  Peck, and T r u e l l ,  R.S.I.  2£,  10,  989(1954)  22?(196l)  t h e M. I . T. (1959)  Thonemann a n d H a r r i s o n , U n c l a s s i f i e d  3p  Technology Press of Report A.E.R.E.  G.P./R.  1190(1955) 19.  M . E . ' A b d e l a z i z , Ph.d. T y n e , E n g l a n d (1956)  Thesis, King's College,  Newcastle-upon-  -47-  20.  P.C. Thonemann, Progress i n Nuclear P h y s i c s 2, 219(1953)  21.  S. A l l i s o n and E. Norbeck, J r . , ' R . S . I . * 3 ,  22.  Sternheimer, R.S.I. 21, 11, 629(1952)  23.  B a i n b r i d g e , "Experimental N u c l e a r P h y s i c s , " Segre, V o l . 1, Page 532  i .  .  285(1956) .  .  

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