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Atomic beam polarized 3He+ ion source Vyse, Robert Norman 1970

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AN ATOMIC BEAM POLARIZED. He ION SOURCE 3  +  by ROBERT NORMAN VYSE B.A.Sc .,• U n i v e r s i t y o f B r i t i s h Columbia, 1965 M.AcSc*, U n i v e r s i t y o f B r i t i s h Columbia, 19&7  A THESIS SUBMITTED I N PARTIAL FULFILMENT OF • THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Physics  We a c c e p t t h i s  t h e s i s as c o n f o r m i n g to the  required standard  ,  THE UNIVERSITY OF BRITISH COLUMBIA J a n u a r y , 1970  In p r e s e n t i n g  this  thesis  an a d v a n c e d d e g r e e a t the L i b r a r y I  further  for  agree  scholarly  by h i s of  shall  this  written  the U n i v e r s i t y  make  tha  it  freely  permission  fulfilment  of  of  Columbia,  British  available  for  for extensive  the  requirements  reference copying o f  I agree and this  for  It  is understood  financial  gain shall  permission.  Depa r t m e n t The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  Columbia  that  not  copying or  for  that  study. thesis  p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t  representatives. thesis  in p a r t i a l  or  publication  be a l l o w e d w i t h o u t my  i  ABSTRACT AN ATOMIC BEAM POLARIZED H e 3  A beam o f p o l a r i z e d atomic  +  ION SOURCE  i o n s has been produced  beam method t e c h n i q u e s .  T h i s method has the a t t r a c t i o n  of  being capable o f p r o d u c i n g an i o n beam w i t h  up  to 1 0 0 $ •  of 3 g  The p o l a r i z a t i o n  e  polarizations  beams p r e s e n t l y produced  by o p t i c a l pumping techniques i s o f the o r d e r o f 5#« apparatus  i s composed o f three main s e c t i o n s ,  beam source c o n s i s t i n g liquid  helium  using  The  the atomic  o f a s u p e r s o n i c n o z z l e c o o l e d to  temperatures  beam, the tapered hexapole  to produce a low v e l o c i t y  atomic  magnet to s p a t i a l l y separate the  p a r t i c l e s i n the two magnetic s p i n s u b s t a t e s , and the e l e c t r o n bombardment i o n i z e r atomic  beam.  $Ee i o n s from the n e u t r a l  to produce  +  3g  Q  The low v e l o c i t y beam i s r e q u i r e d because the  n u c l e a r magnetic moment o f $Ee i s of the order o f 1000 s m a l l e r than the e l e c t r o n i c  magnetic moment used  times  to separate  beams i n c o n v e n t i o n a l S t e r n - G e r l a c h magnets and to a c h i e v e a high i o n i z a t i o n beam produced helium  efficiency.  by the atomic  temperature  The measured i n t e n s i t y o f the beam source c o o l e d to l i q u i d  was 1 x 1 0  x  o  atoms/sr-sec,  the most probable  v e l o c i t y was 3 1 0 m/sec, and the v e l o c i t y f u l l w i d t h a t h a l f maximum was 5"0 m/sec. i n c r e a s e s by a f a c t o r  The beam f l u x  through  the i o n i z e r  o f 1 . 3 when the hexapole  field  i s turned  on, i n good agreement w i t h the t h e o r e t i c a l l y expected i n c r e a s e .  ii  This i n c r e a s e corresponds atomic beam.  A 12nA3jj + i e  to a p o l a r i z a t i o n of 65% o f the o  n  beam was obtained c o r r e s p o n d i n g  to an i o n i z a t i o n e f f i c i e n c y o f approximately  0»15%*  iii TABLE OF CONTENTS Page CHAPTER I  INTRODUCTION  CHAPTER I I  METHODS FOR PRODUCING POLARIZED 3rfe BEAMS  7  A.  The O p t i c a l Pumping Method  7  B,  The Atomic Beam Method  9  -  PRODUCTION OF MOLECULAR BEAMS  ^  A.  M o t i v a t i o n f o r Development Beams.  B.  P r o p e r t i e s o f the M o l e c u l a r Flow Beam  C.  P r o p e r t i e s o f the Nozzle Beam  15  (1)  Gas Flow Through the Nozzle  17  (2)  The Free J e t Expansion  (3)  The F r e e z i n g S u r f a c e  (k)  V e l o c i t y D i s t r i b u t i o n of P a r t i c l e s i n the Beam  CHAPTER I I I  (5)  1  of Molecular  ....  CHAPTER IV  3  26  I n t e n s i t y A v a i l a b l e from Nozzle  (i)  (7)  18 2  30  Beams  (6)  l l f  F r e e l y Expanding J e t I n t e n s i t y . .  30  (ii) Beam I n t e n s i t y Downstream from the Skimmer. D e v i a t i o n s from I d e a l Behaviour  30 31  Low Temperature Nozzle Sources and t h e i r Uses  33  THE POLARIZED  A.  The Low Temperature Atomic Beam Source....  37  (1)  37  $ E e  +  BEAM SOURCE......  37  -  General D e s c r i p t i o n  ..  iv Page (2) (3)  CHAPTER V  CHAPTER VI  CHAPTER V I I  CHAPTER V I I I  Thermal T r a n s p i r a t i o n C o r r e c t i o n s to P r e s s u r e Measurements Carbon R e s i s t o r  . 4 - 2  Temperature  B.  The Hexapole Magnet  C.  The E l e c t r o n Bombardment I o n i z e r  -  TECHNIQUES FOR MEASUREMENT OF ATOMIC  ,  . 52  BEAM INTENSITY AND VELOCITY  58  A.  Measurement of the Atomic Beam I n t e n s i t y . .  58  B.  The T i m e - o f - F l i g h t  59  -  RESULTS OF STUDIES OF THE ATOMIC BEAM  66  A.  The Atomic Beam I n t e n s i t y .  66  B.  The Atomic Beam V e l o c i t y  82  -  POLARIZATION AND IONIZATION OF THE 3Re BEAM  Measuring Apparatus....  8  8  A.  The T r a j e c t o r i e s o f Atoms through the Hexapole Magnet  88  B.  The C a l c u l a t e d Beam  90  C.  The P o l a r i z a t i o n Measurement and I o n Beam Y i e l d  95  -'  CONCLUSIONS  99  A.  Comparison w i t h Other Sources o f P o l a r i z e d 3 H e + Ions  99  B.  Measurement o f the 3He D(3He,P) He R e a c t i o n  P o l a r i z a t i o n o f the Atomic  +  Beam by the  l+  C.  P o s s i b l e Improvements o f the P o l a r i z e d 3fle + Beam Apparatus  1  0  1  10h  V  Page (1)  Improvements I n c r e a s i n g Beam I n t e n s i t y . . .  the Atomic  (2)  Improvements Reducing the Atomic Beam V e l o c i t y  (3)  Improvements i n I o n i z a t i o n E f f i c i e n c y and E x t r a c t i o n  10M105" 106  (k)  O v e r a l l System Improvement P o s s i b i l i t i e s by Changing Geometry... 1 0 7  (5)  Improvements i n Vacuum System Reducing Background Ion Y i e l d  1°9  vi Page APPENDIX A,  INTENSITY FROM A FREELY EXPANDING JET....  APPENDIX B,  INTENSITY AND VELOCITY DISTRIBUTION OF PARTICLES IN THE JET AFTER PASSING THROUGH A SKIMMING ORIFICE  APPENDIX C, 1. 2. 3.  111  113..  ,  TRAJECTORIES OF PARTICLES PASSING THROUGH A HEXAPOLE MAGNET  120  E q u a t i o n of Motion o f a Magnetic D i p o l e i n a A x i a l l y Symmetric M u l t i p o l e F i e l d . . . .  I  T r a j e c t o r i e s o f a Magnetic D i p o l e i n a P a r a l l e l Hexapole Magnet  l  2  2  0  , ^ "  T r a j e c t o r i e s o f a Magnetic D i p o l e i n a Tapered Hexapole Magnet  126  APPENDIX D,  CALCULATION OF THE SIGNAL SHAPE FROM THE TIME-OF-FLIGHT APPARATUS  13  APPENDIX E,  A LOW TEMPERATURE NOZZLE BEAM FOR A POLARIZED 3 + I O N SOURCE by R. Vyse, J.C. Heggie and M.K. Craddock r e p r i n t e d from 6 t h I n t ' l Symposium on R a r e f i e d Gas Dynamics. 2 , Academic Press I n c . New York (1969) <  138  LOW TEMPERATURE ATOMIC 3 He BEAM FOR USE IN A POLARIZED 3fte ION SOURCE by ' R. Vyse, D. Axen and M.K. Craddock Rev. S c i . I n s t r . I n p r e s s  1*3  2  H e  APPENDIX F.  +  BIBLIOGRAPHY  vii LIST OF FIGURES Page 1. 2.  3«  Energy L e v e l s of 3 n e Atoms i n an E x t e r n a l Magnetic F i e l d (not to s c a l e )  8  General Arrangement o f the Components of the P o l a r i z e d ^He Apparatus showing the d i f f e r e n t i a l pumping r e q u i r e d to handle the JRe gas flow  10  Nuclear P o l a r i z a t i o n of S i n g l y I o n i z e d 3ffe Atoms f o r E q u a l F i e l d s i n the I o n i z i n g and Target Regions  h.  Schematic R e p r e s e n t a t i o n of Nozzle Beam Source  5.  Discharge C o e f f i c i e n t v s . Reynolds Number based on E x p e r i m e n t a l Flow and V i s c o s i t y a t Stagnation Conditions  1  ,  19  6 . . Schematic R e p r e s e n t a t i o n of Flow from an O r i f i c e i n t o an Evacuated Region 7. 8.  9.  D i s t r i b u t i o n of Mach Number Along Symmetry of the Expanding J e t  2  0  21  -  the A x i s of  Terminal Mach Numbers as a F u n c t i o n of Inverse Knudsen Number based on S t a g n a t i o n C o n d i t i o n s a t the Nozzle Schematic R e p r e s e n t a t i o n of R a d i a l l y Expanding Flow through a Skimmer to a Detector.  5  2  2  7  10.  The  11.  The A d j u s t a b l e Nozzle-Skimmer Assembly  ^3  12.  C o n d i t i o n s f o r Thermal T r a n s p i r a t i o n E f f e c t . .  kh  13.  Thermal T r a n s p i r a t i o n C o r r e c t i o n s to Measurements of Nozzle-Skimmer and SkimmerC o l l i m a t o r Pressure  "+6  1*+.  Low  Temperature 3 e  2  H  Atomic Beam Source...  A.C. B r i d g e Used to Monitor R e s i s t a n c e Carbon R e s i s tor . Thermometer  of  38  ^9  Input Power Induced Heating o f Carbon R e s i s t o r Thermometer w i t h R e s i s t o r a t Near C a l i b r a t i o n o f Carbon R e s i s t o r Thermometer... Dimensions o f the Components o f the Hexapole Magnet Magnetic F i e l d S t r e n g t h i n the Region o f the Pole T i p s as a F u n c t i o n of the E l e c t r i c a l C u r r e n t Through the C o i l s Measured Value o f the Magnetic F i e l d S t r e n g t h as a F u n c t i o n o f the R a d i a l D i s t a n c e from C e n t r a l A x i s Schematic R e p r e s e n t a t i o n o f I o n i z e r and Ion Measurement Apparatus (A) D.C. C u r r e n t Measurement (B) Chopped C u r r e n t Measurement Two S l i t Chopper.. I o n i z e r Ion Y i e l d as a F u n c t i o n o f Background Hydrogen Gas Pressure Schematic R e p r e s e n t a t i o n o f T i m e - o f - F l i g h t V e l o c i t y Measurement Equipment P h o t o t r a n s i s t o r Reference  Signal C i r c u i t . . . . .  Schematic o f Ion Gauge S i g n a l C i r c u i t , Reference S i g n a l and O s c i l l i s c o p e D i s p l a y . . . . Broadening o f E x p e r i m e n t a l S i g n a l due to F i n i t e Width Shutter F u n c t i o n . Nozzle Beam Curve I n c l u d e s C o r r e c t i o n f o r a 2.5 cm D e t e c t o r Length Assumed I n t e n s i t y P r o f i l e o f P a r t i c l e s P a s s i n g through the Chopper Opening ( S h u t t e r Function). T a n g e n t i a l Chopper V e l o c i t y = 35 m/sec Room Temperature Beam I n t e n s i t y P r o f i l e s f o r a 0 . 2 cm Diameter Nozzle Room Temperature Beam I n t e n s i t y P r o f i l e s as a F u n c t i o n o f Nozzle-Skimmer S e p a r a t i o n  ix Page 30. 31. 32.  Continuous Beam P r o f i l e Taken w i t h A d j u s t a b l e Nozzle-Skimmer Assembly Beam I n t e n s i t y P r o f i l e s f o r a 0.2 - Nozzle Operated a t 77°K  cm  70  Diameter 72  L i q u i d N i t r o g e n Temperature Beam I n t e n s i t y P r o f i l e s as a F u n c t i o n o f Nozzle-Skimmer Separation  73  Beam I n t e n s i t y P r o f i l e s as a F u n c t i o n o f Nozzle-Skimmer S e p a r a t i o n w i t h the Nozzle a t L i q u i d Helium Temperature...  . 75  3*+.  Beam I n t e n s i t y P r o f i l e s f o r 0.2 cm Diameter Nozzle Operated a t L i q u i d Helium Temperature.  76  35.  ^ e Beam I n t e n s i t i e s as a F u n c t i o n o f Nozzle S t a g n a t i o n P r e s s u r e Po f o r Three Temperatures To. The dashed l i n e s p a s s i n g through the o r i g i n are f i t s to the data a f t e r c o r r e c t i o n for scattering  78  Beam I n t e n s i t i e s f o r 3f}e and ^He Beams a t L i q u i d Helium Temperature Before and A f t e r Correction f o r Scattering. Only the u n c o r r e c t e d e x p e r i m e n t a l p o i n t s are shown when the c o r r e c t i o n i s s m a l l  79  The U n c o r r e c t e d Data o f F i g . 36 D i v i d e d by the Nozzle P r e s s u r e to V e r i f y E x i s t e n c e o f Scattering  80  Normalized I n t e n s i t y P r o f i l e v s . V e r t i c a l Displacement from Beam A x i s . S t a g n a t i o n Pressure Po = k20 T o r r S t a g n a t i o n Temperature.To = 77°K  83  T y p i c a l ^Ee T i m e - o f - F l i g h t Spectrum f o r L i q u i d Helium Cooled N o z z l e . Stagnation P r e s s u r e i s 36 T o r r . H o r i z o n t a l Time Scale i s 0 . 5 m s e c / d i v . The Upper Trace shows the Time Reference L i g h t P u l s e . . .  85  R e s u l t s o f F i g . 39 Converted i n t o a V e l o c i t y Spectrum. The curve shown i s a f i t o f Eq. 17 to the e x p e r i m e n t a l spectrum  86  33-  36.  37.  38.  39.  kO.  T y p i c a l T r a j e c t o r i e s o f Focussed and Defocussed ^He Atoms p a s s i n g through the Hexapole Magnet. The Source-Magnet S e p a r a t i o n i s 15 cm and the F i e l d a t the Magnet Pole Tips i s taken as 9000 Gauss. E f f e c t o f Source-Magnet S e p a r a t i o n on I n t e n s i t y and P o l a r i z a t i o n of Atomic Beam. Nozzle a t +.2°K l  E f f e c t o f Source-Magnet S e p a r a t i o n on I n t e n s i t y and P o l a r i z a t i o n o f Atomic Beam. Nozzle a t 7 ° K Schematic Diagram I n d i c a t i n g R e l a t i v e •Location o f Components Used i n Atomic Beam P o l a r i z a t i o n Measurement. Dimensions i n cm.. Change i n D i f f e r e n t i a l P i r a n i D e t e c t o r S i g n a l when Hexapole Magnet i s Turned On and O f f T y p i c a l I o n i z e r S i g n a l s from Chopped Atomic Beam w i t h Hexapole Magnet Turned On and O f f . H o r i z o n t a l S c a l e 0.5 ms/div. V e r t i c a l S c a l e 0.5 mv/div Enhancement R a t i o o f I o n i z e d Beam as a F u n c t i o n o f Magnet E x c i t a t i o n C u r r e n t . D e f i n i n g Diagram f o r C a l c u l a t i o n o f Flow through Nozzle-Skimmer System D e f i n i t i o n o f C e r t a i n V a r i a b l e s used i n C a l c u l a t i o n o f Flow through Nozzle-Skimmer Sys tern Schematic Diagram Showing Two Poles o f a R a d i a l l y Symmetric Magnet.. Schematic Diagram Showing the,Parameters used to d e s c r i b e the Tapered Hexapole Magnet. R e c t a n g u l a r Chopper Shutter F u n c t i o n . Rectangular D e t e c t o r Response F u n c t i o n Geometry o f T i m e - o f - F l i g h t Apparatus  LIST OF TABLES  Page 1.  2.  3.  D e t a i l e d Summary of Heat Leaks i n t o the C r y o s t a t of the'Low Temperature Atomic Beam Source. Measurements were made a f t e r i n i t i a l c o n s t r u c t i o n of source and a f t e r e x t e n s i v e m o d i f i c a t i o n s n e c e s s a r y to reduce heat l e a k to the expected d e s i g n values  39  S e l e c t e d T r a j e c t o r i e s of Focussed and Defocussed ~>lie Atoms P a s s i n g Through the Tapered Hexapole Magnet  89  Comparison of d i f f e r e n t Methods of Producing P o l a r i z e d 3He Ions... +  100  xii  ACKNOWLEDGEMENTS I would l i k e  to thank my s u p e r v i s o r , D r . M.K. Craddock,"  f o r h i s continued i n t e r e s t throughout described i n this  the course o f the work  thesis.  I would a l s o express my thanks  to Dr. D. Axen, who  o r i g i n a l l y b u i l t much o f the e x i s t i n g p o l a r i z e d helium-3 beam apparatus, f o r h i s continuous i n t e r e s t and u n t i r i n g  help w i t h  many o f the e x p e r i m e n t a l measurements d e s c r i b e d i n t h i s I would a l s o  thesis.  thank D r s . White, Erdman and Warren f o r  t h e i r i n t e r e s t and encouragement d u r i n g the course o f t h i s work. I am extremely g r e a t f u l to the many t e c h n i c i a n s who have c o n t r i b u t e d to t h i s work over a p e r i o d o f many y e a r s ; i n p a r t i c u l a r , Messrs. D. Haines, C. Sedger and D. Stonebridge f o r t h e i r u s e f u l s u g g e s t i o n s and e x c e l l e n t I wish  craftmanship.  to- thank the N a t i o n a l Research  C o u n c i l f o r one  b u r s a r y and three s c h o l a r s h i p s h e l d d u r i n g the course o f t h i s work.  1  CHAPTER I INTRODUCTION The  study o f the nature o f n u c l e a r  they p l a y I n v a r i o u s considerable of  r e a c t i o n mechanisms has been a s u b j e c t of  i n t e r e s t f o r many y e a r s .  these f o r c e s  f o r c e s and the p a r t  has been a s u b j e c t  The s p i n dependent nature  of more r e c e n t  essence the s p i n dependence o f the n u c l e a r  interest.  force implies  In  that  the f o r c e between two i n t e r a c t i n g nucleons depends both on the magnitude and o r i e n t a t i o n o f the s p i n v e c t o r magnetic moment o f the p a r t i c l e s . i n t e r a c t i o n have been p o s t u l a t e d nuclear  c h a r a c t e r i z i n g the  Various expressions f o r this  and are o f t e n r e p r e s e n t e d i n  models by p o t e n t i a l s ; a common example i s the s p i n - o r b i t  p o t e n t i a l Vso oC  where  i s the P a u l i s p i n o p e r a t o r and i_ i s  the o r b i t a l angular momentum o p e r a t o r .  From an  experimentalist's  p o i n t o f view the study o f the nature o f these f o r c e s i s o n l y p o s s i b l e because of the a v a i l a b i l i t y o f s p i n s e n s i t i v e polarized  t a r g e t s or p o l a r i z e d beams. The  reference i  detectors,  s p i n o f a p a r t i c l e i s measured r e l a t i v e to some  a x i s , sometimes a magnetic f i e l d  p a r t i c l e s such as p r o t o n s , and 3He there  magnetic s p i n s u b s t a t e s mj = +-§• o r m-j. = the n u c l e a r  spin lines i t s e l f  up p a r a l l e l  direction.  For s p i n  are two n u c l e a r depending on whether ( s p i n up) or  a n t i p a r a l l e l ( s p i n down) to the d i r e c t i o n o f the magnetic field  axis.  The p o l a r i z a t i o n P o f an ensemble o f such p a r t i c l e s  i s g i v e n by P  •_  N(+i)-N(-£)  —  .  N(+£)+N(-£) where N(+£) i s the f r a c t i o n a l number o f p a r t i c l e s i n the beam  or  target with t h e i r spins  aligned p a r a l l e l  to the magnetic  f i e l d w h i l e N ( - i ) i s the f r a c t i o n a l number a l i g n e d a n t i p a r a l l e l . A beam or t a r g e t w i t h equal p o p u l a t i o n s o f both s u b s t a t e s i s said  to be u n p o l a r i z e d  target with a l l spins  and has zero p o l a r i z a t i o n w h i l e a beam or oriented  i n the p o s i t i v e d i r e c t i o n would  have 100$ p o l a r i z a t i o n . Certain  techniques have been developed  of s p i n dependent f o r c e s . o r b i t force  Because o f the s t r e n g t h  the r e a c t i o n products o f any r e a c t i o n  p a r t i c l e s w i t h nonzero partially polarized. collimated  f o r the study  involving  s p i n and angular momentum w i l l be These p o l a r i z e d p a r t i c l e s can be  i n t o a beam f o r use i n a subsequent  formed i n t h i s manner a r e r e f e r r e d (p,p) e l a s t i c  o f the s p i n -  reaction.  Beams  to as secondary beams.  s c a t t e r i n g c a n be used  to produce  a beam o f p o l a r -  i z e d protons w h i l e the D(D,3R"e)n r e a c t i o n can be used  to produce  a p o l a r i z e d n e u t r o n beam.  U n f o r t u n a t e l y these secondary beams  frequently  p a r t i c l e fluxes  have inadequate  experiments  which might be envisaged  s p i n dependence o f a s e l e c t e d reactions desired  c a n a l s o be used  particles.  to be o f use i n many  to study, f o r example, the  r e a c t i o n mechanism.  to analyze  Certain  the p o l a r i z a t i o n o f  For example, the e l a s t i c s c a t t e r i n g o f  p o l a r i z e d protons o f f carbon or helium r e s u l t s i n a l e f t - r i g h t asymetry  about  the incoming  beam a x i s which can be r e l a t e d to  the incoming p r o t o n p o l a r i z a t i o n . • The p r o d u c t i o n of more i n t e n s e beams o f p o l a r i z e d particles  has become p o s s i b l e  p o l a r i z e d i o n sources.  through  the development o f  These d e v i c e s prepare beams o f p o l a r i z e d  p a r t i c l e s f o r i n j e c t i o n into accelerators. p o l a r i z e d p a r t i c l e s i n t o the a c c e l e r a t o r  By i n j e c t i n g  much higher beam  i n t e n s i t i e s can be produced than by s c a t t e r i n g or r e a c t i o n techniques.  P o l a r i z e d p r o t o n and deuteron i o n s o u r c e s , which  a l l o w the p r e p a r a t i o n  of intense  beams w i t h p o l a r i z a t i o n s o f  near 100$ f o r the case o f the p r o t o n s , have been  extensively  developed and they are now a v a i l a b l e as commercial items. After particles  the p r o t o n and deuteron one o f the next  that c o u l d  simplest  e f f e c t i v e l y be used i n p o l a r i z a t i o n  studies  i s ^He, an atom w i t h n u c l e a r s p i n o f £ and a zero e l e c t r o n i c spin.  U n p o l a r i z e d He has been used e x t e n s i v e l y J  target, and p r o j e c t i l e i n n u c l e a r p h y s i c s Many o f the i n t e r e s t i n g p o s s i b i l i t i e s a p r o j e c t i l e were d i s c u s s e d  f o r many y e a r s .  f o r research  using  Since that  have been w i d e l y s t u d i e d .  time ^He induced  Because o f the strong  dependence o f the n u c l e a r f o r c e none o f these s t u d i e s c o n s i d e r e d complete u n t i l carefully investigated. and  targets  3He as  by Bromley and A l m q v i s t (Br60) i n a  l e n g t h y review a r t i c l e i n i 9 6 0 . reactions  studies  as both a  spin  can be  the d e t a i l e d e f f e c t s o f s p i n have been I n an experiment w i t h u n p o l a r i z e d  and w i t h no o b s e r v a t i o n  beams  o f the p o l a r i z a t i o n o f the  outgoing p a r t i c l e s the d e t a i l e d s p i n dependence o f the r e a c t i o n i s l o s t due to "the average over the magnetic quantum numbers o f i n i t i a l and sum over the f i n a l s t a t e s .  Knowing the p o l a r i z a t i o n  of some combination o f incoming p r o j e c t i l e , t a r g e t n u c l e u s , or the outgoing r e a c t i o n products can r e s u l t i n much more s p e c i f i c information forces.  on the d e t a i l e d behaviour o f the s p i n dependent  For t h i s reason many p r e v i o u s l y  s t r i p p i n g and pickup r e a c t i o n s  studied  inelastic,  may be s u i t a b l e candidates f o r  renewed study*  G.  e x i s t i n g nuclear and  beamso  C. P h i l l i p s  (Ph66)  r e a c t i o n studies  Studies  using  r e c e n t l y reviewed  p o l a r i z e d ^Ee  a t R i c e U n i v e r s i t y using  t a r g e t i n the 3He(d,p) He r e a c t i o n lf  first  has  (Ba65)  tensor forces,,  s t u d i e s w i t h p o l a r i z e d beams and f o r other s t r i p p i n g reactions  H  the.  of s t r i p p i n g  It i s clear  targets  3 e  a polarized  have p r o v i d e d  i n d i c a t i o n that o p t i c a l model t h e o r i e s  p r o c e s s e s must i n c l u d e  targets  need be  to f u r t h e r d e f i n e  that  further  carried their  out  spin  dependence. P o l a r i z e d n u c l e i can a l s o be assignments of s p i n s systems. in  the  and  p a r i t i e s of e x c i t e d s t a t e s of  A g a i n the R i c e group has  study o f  used to help make  used a p o l a r i z e d 3 n e  the u n s t a b l e nucleus ^ L i formed as  i n t e r m e d i a t e s t a t e i n the 3ne(p,p)3He r e a c t i o n have determined i n f o r m a t i o n T = 1 states  of  if  only  targets  elastic are  scattered measured  about the  the mass k system.  b a s i c a l l y impossible  spins  and  an  (Ba67).  They  parities  to deduce a unique s e t of phase  of  shifts  beams  a v a i l a b l e along w i t h s p i n measurements of However, i f s p i n s  the degenerate s o l u t i o n s  target  In t h i s r e a c t i o n i t i s  s c a t t e r i n g data w i t h u n p o l a r i z e d  proton.  nuclear  can  of  the 3 n e  are  and the  also  be r e j e c t e d and  a unique  d e t e r m i n a t i o n o f phase s h i f t s becomes p o s s i b l e . P o l a r i z e d 3ne  beams are  the n e u t r o n that i s p o l a r i z e d ;  a l s o of i n t e r e s t because i t i s  thus i n a sense one  has  a v a i l a b l e a v a r i a b l e energy n e u t r o n beam f o r r e a c t i o n s the n e u t r o n eg.  ( 3 n e , p p ) , and  perhaps  involving  (3He,n).  Another i n t e r e s t i n g p o s s i b i l i t y f o r p o l a r i z e d 3 p w e l l as  a l l other p o l a r i z e d p a r t i c l e s i s the  t e s t i n g of  e  a  s  conservation lavs.  The s e l e c t i o n o f c r u c i a l experiments to t e s t  p a r i t y and time r e v e r s a l i n v a r i a n c e be g r e a t l y aided  i n s p e c i f i c reactions  should  by the a v a i l i b i l i t y of c o n t r o l over the  p o l a r i z a t i o n o f the incoming beam. experiments may be aided  S e l e c t i o n o f these c r u c i a l  by the s y s t e m a t i c c l a s s i f i c a t i o n by  M o r a v c s i k , Csonka and Scadron (M066) o f a l l experimental p o s s i b i l i t i e s ' f o r reactions  i n v o l v i n g four nucleons o f g i v e n s p i n .  To perform many o f these p o t e n t i a l experiments a p o l a r i z e d ^He beam i s r e q u i r e d . o f p o l a r i z e d ^He a t t a i n a b l e  To estimate the p o s s i b l e  as a secondary beam, c o n s i d e r  e l a s t i c s c a t t e r i n g o f He o f f Sle.  flux the  P h i l l i p s and M i l l e r (Ph59)  3  show t h i s s c a t t e r i n g can r e s u l t i n near 1 0 0 $ p o l a r i z a t i o n o f the He under c e r t a i n c o n d i t i o n s . energy o f 5 » 2 Mev, the c r o s s p o l a r i z e d ^He s c a t t e r e d 0.162 300  For a ^He bombarding  laboratory  s e c t i o n f o r the p r o d u c t i o n o f 1 0 0 $  a t *+5° i n the c e n t e r o f mass frame i s  I f a 1 0 0 pA^Ee beam bombards a ^He gas t a r g e t  b/sr.  kev t h i c k ( 5 a tin p r e s s u r e and 1 . 2 cm long) and i f the s o l i d  angle o f the r e s u l t i n g beam i s r e s t r i c t e d to 1 0 " s r then the 2  beam i s 0 . 0 1 nA.  f l u x o f the r e s u l t i n g s c a t t e r e d all  the above c o n d i t i o n s  0.001  could  I t i s unlikely  be achieved i n p r a c t i s e  thus  nA might be a more r e a s o n a b l e estimate o f the p o s s i b l e  p o l a r i z e d ^He i o n c u r r e n t .  This  i n t e n s i t y i s too low to be o f  much use f o r many n u c l e a r s t u d i e s techniques to produce more intense  and thus we must t u r n to o t h e r beams.  Two methods have been proposed f o r the p r o d u c t i o n o f polarized 3  + H  e  i o n beams.  An o p t i c a l pumping technique has been  s u c c e s s f u l l y developed a t R i c e U n i v e r s i t y .  A t U.B.C. an atomic  6 beam method f o r the p r o d u c t i o n o f p o l a r i z e d ^Ee Warren, Axen and K l i n g e r  proposed by  +  ( W a 6 3 ) i s under development.  Initial  d e s i g n , c o n s t r u c t i o n and p r e l i m i n a r y t e s t i n g o f the U.B.C. i o n source has been r e p o r t e d by Axen  (Ax65).  i o n i z e r has been r e p o r t e d by Vermette  The development  (Ve6h)  and the  d i f f e r e n t i a l P i r a n i d e t e c t o r by J a s s b y (Ja6*0 • thesis w i l l discuss  o f the  The p r e s e n t  the d e t a i l e d study o f the atomic beam  f o r m a t i o n and i t s subsequent p o l a r i z a t i o n and i o n i z a t i o n . The c o n t e n t s o f t h i s following chapters. the  In Chapter I I a g e n e r a l d e s c r i p t i o n o f  two techniques used to produce p o l a r i z e d 3jj + ^ e  presented. low  t h e s i s i s d i v i d e d i n t o the  o  n  I n Chapter I I I the t h e o r e t i c a l background  temperature n o z z l e source which i s e s s e n t i a l  o p e r a t i o n o f the U.B.C. i o n source i s reviewed.  beams i s o f the  to the Chapter IV  g i v e s a d e t a i l e d d e s c r i p t i o n o f the mechanical o p e r a t i o n o f U.B.C.'s i o n s o u r c e .  Chapter V d e s c r i b e s  the techniques used  to measure the i n t e n s i t y and v e l o c i t y o f the atomic beam.  The  r e s u l t s o f these measurements are p r e s e n t e d i n Chapter V I . Chapter V I I c o n s i d e r s the  the e f f e c t  the hexapole magnet has on  3jfe t r a j e c t o r i e s and the r e s u l t i n g  P o s s i b l e improvements to the p o l a r i z e d c o n s i d e r e d i n Chapter V I I I .  beam p o l a r i z a t i o n . i o n source a r e  7  CHAPTER I I METHODS FOR PRODUCING POLARIZED 3 H A.  The O p t i c a l  BEAMS  Pumping Method.  The p o l a r i z e d  ^Ee  +  i o n source based on o p t i c a l  pumping t e c h n i q u e s , s u c c e s f u l l y delivers  + 9  developed a t Rice  University,  k pA of ions w i t h a p o l a r i z a t i o n measured by a  n u c l e a r double s c a t t e r i n g  experiment of  0.05~to.01  (Ba68, Fi69).  The emittance of the beam was estimated to be 1 cm»rad*ev^. The energy l e v e l s r e l e v a n t scheme a r e shown on F i g . 1 .  to the o p t i c a l pumping  A weak s e l f - s u s t a i n i n g  electric  d i s c h a r g e i n v e r y pure 3 n e gas, produced by a 50 M H r f  field  z  around an o p t i c a l pumping c e l l , e x c i t e s  some of the ^ S  s t a t e 3 n e atoms to the 23S]_ metastable s t a t e . c i r c u l a r l y polarized along  the a x i s  transitions sublevels  resonance l i g h t d i r e c t e d  of the a p p l i e d  from the lower (m  to the 2 3 P  to the v a r i o u s 2 3 s  1  0  levels.  and  F  Right-hand into  the c e l l  magnetic f i e l d p r o d u c e s ^ m F  = - 3 / 2 , -i)23s^  ?  = +1  hyperfine  Atoms i n the 2 3 p l e v e l s  de-excite  l e v e l s w i t h n e a r l y equal p r o b a b i l i t i e s .  t h i s p r o c e s s i s repeated over many c y c l e s from the n e g a t i v e m  ground  0  As  atoms are removed  h y p e r f i n e l e v e l s o f the metastable atoms  are p l a c e d i n the p o s i t i v e m  t i o n o f the metastable atoms.  p  l e v e l s , producing a p o l a r i z a -  The" n e g a t i v e m^ l e v e l s can be  p o p u l a t e d i n the same way using l e f t - h a n d l i g h t ; a p o l a r i z a t i o n o f the o p p o s i t e s i g n The p o l a r i z a t i o n i s t r a n s f e r r e d atoms to the much more numerous l ^ S  circularly  polarized  results. from the metastable  ground s t a t e  atoms by means  l u l l I ^ u 11 u 11  <  2R 3  4xl0 cm" 4  J  1/2 -1/2  1  9233cm -I  1/2 -1/2  2'S,  F= /2 0.22 cm"  2"S 1.6 x l O c m " 5  1  F=3/2  <  1/2 -1/2 1  3/2 1/2 -1/2 -3/2  -l/2> --I/2  Fig. 1 Energy L e v e l s of 3 n Atoms i n an E x t e r n a l Magnetic F i e l d (not to s c a l e ) * e  of s p i n exchange c o l l i s i o n s , and, under continuous i l l u m i n a t i o n from the pumping l i g h t , equilibrium  the ground s t a t e p o l a r i z a t i o n reaches an  value equal to that of the metastable atoms.  d i s c h a r g e produces both atoms i n the metastable s t a t e the  ions.  cm ) c r o s s  collisions. cell  The ions  The  large  s e c t i o n f o r e l e c t r o n exchange v i a He -He are extracted  by standard r f i o n source  from the o p t i c a l pumping  techniques.  gas p o l a r i z a t i o n i n the o p t i c a l pumping c e l l was  measured to be 0 . 0 5 t o . 0 1 , which, w i t h i n  experimental e r r o r , i s  the measured value o f the i o n p o l a r i z a t i o n . possible  as w e l l as  The i o n p o l a r i z a t i o n comes i n t o e q u i l i b r i u m w i t h the  atomic ground s t a t e p o l a r i z a t i o n because o f a very t-10  Thus i t appears  to e x t r a c t an i o n beam w i t h the same p o l a r i z a t i o n as the  gas  i n the pumping c e l l .  60$  (Ga65)  As p o l a r i z a t i o n s o f approximately  have been a c h i e v e d i n gas samples under optimum  conditions,  further  improvements i n the p o l a r i z a t i o n o f the  i o n beam can be expected.  The p r e s e n t p o l a r i z a t i o n appears to  be l i m i t e d by the s h o r t d w e l l time i n the o p t i c a l pumping T h i s may be overcome by i n c r e a s i n g pumping c e l l , influence B.  The r f  hence a l l o w i n g  cell.  the dimensions o f the  the $Ee atoms to remain under the  o f the pumping r a d i a t i o n f o r a longer  time.  The Atomic Beam Method. The  p a r t i c l e s i n each o f the two p o s s i b l e  nuclear  spin  s u b s t a t e s i n an atomic beam o f ^Ee can be separated by p a s s i n g the n e u t r a l beam through an inhomogeneous magnetic This  field.  technique was suggested by Warren, Axen and K l i n g e r  (Wa63)  He atoms 3  skimm collimator  1~ Polarized H e  3  atoms — P o l a r i z e d  leybold 2heraeus HG45 6" CVC  CVC  8"  IO"  four Fig. 2  stage  differential  pumping  system  G e n e r a l Arrangement o f the Components of the Polarized. ^Ee Apparatus showing the d i f f e r e n t i a l pumping r e q u i r e d to handle the 3 n e gas f l o w .  He  6  ions  11 as a method f o r producing shows a schematic  a p o l a r i z e d ^Ee  view o f t h i s scheme.  +  i o n beam.  Fig. 2  An atomic beam  produced u s i n g a s u p e r s o n i c n o z z l e c o o l e d  to l i q u i d  helium  temperatures i s passed through the inhomogeneous magnetic of  a hexapole magnet.  field  As atomic ^Ee has no e l e c t r o n i c magnetic  moment, those p a r t i c l e s w i t h n u c l e a r s p i n p r o j e c t i o n +•§• i n the d i r e c t i o n o f the a p p l i e d f i e l d p o l e p i e c e s and subsequently of  nuclear spin p r o j e c t i o n  a x i s and f o c u s s e d ^He  into  are d e f l e c t e d towards the magnet  removed from the beam w h i l e  those  are d e f l e c t e d toward the c e n t r a l  the i o n i z e r .  The v e r y s m a l l s i z e o f the  n u c l e a r moment and the need f o r a magnet o f reasonable  length producing  c o n v e n t i o n a l magnetic f i e l d  strengths requires  t h a t the v e l o c i t y o f the p a r t i c l e s e n t e r i n g the magnet be very low.  I n the o r i g i n a l p r o p o s a l an atomic beam w i t h a most  probable  v e l o c i t y o f 180 m/sec was to pass through a tapered  hexapole magnet 50 cm i n l e n g t h . calculated  Under these c o n d i t i o n s i t was  t h a t an atomic beam c o u l d be prepared  polarization,  with near  100$  that i s , a l l the p a r t i c l e s p a s s i n g i n t o the  i o n i z e r would be i n the  nuclear s p i n p r o j e c t i o n s t a t e .  I o n i z a t i o n o f the beam would be achieved w i t h an e l e c t r o n bombardment type i o n i z e r .  The p o s i t i v e ions so produced would  be f o c u s s e d and a c c e l e r a t e d to produce a beam o f p o l a r i z e d ^He  +  i o n s s u i t a b l e f o r n u c l e a r r e a c t i o n s t u d i e s . The percentage  p o l a r i z a t i o n o f the i o n i z e d beam depends on the magnetic s t r e n g t h p r e s e n t a t the i o n i z e r and the t a r g e t . calculated  the ^>Ee n u c l e a r p o l a r i z a t i o n expected  field  Axen (Ax65) has of s i n g l y  i o n i z e d ^Ee atoms f o r equal f i e l d s i n the i o n i z i n g and targe.t  regions  His r e s u l t s are shown i n F i g . 3.  3  6  9  H (kilogauss) Fig.  3  Nuclear P o l a r i z a t i o n of S i n g l y I o n i z e d 3^ Atoms f o r E q u a l F i e l d s i n the I o n i z i n g and Target Regions. e  For zero f i e l d  i n the two r e g i o n s a p o l a r i z a t i o n o f 50% i s  a c h i e v e d and the p o l a r i z a t i o n i n c r e a s e s u n t i l i t reaches almost  100$ w i t h a f i e l d  by i o n i z i n g and p l a c i n g  of about 9 KG i n both r e g i o n s .  the t a r g e t i n a r e g i o n o f h i g h but not  t e c h n i c a l l y e x c e s s i v e magnetic f i e l d  i t i s p o s s i b l e to o b t a i n a  beam o f near 100$ n u c l e a r p o l a r i z a t i o n . p o l a r i z a t i o n which makes the atomic polarized  ^He  experiments.  +  Thus  I t i s t h i s v e r y high  beam method o f producing  ions so p o t e n t i a l l y a t t r a c t i v e i n n u c l e a r p h y s i c  13 CHAPTER I I I THE A.  PRODUCTION OF MOLECULAR B E A M S  M o t i v a t i o n f o r Development o f M o l e c u l a r Beams. Atomic beams have been i n s t r u m e n t a l i n the advancement  of many f i e l d s o f p h y s i c s . Maxwellian  v e l o c i t y d i s t r i b u t i o n helped e s t a b l i s h the K i n e t i c  theory o f gases. two  E a r l y experiments v e r i f y i n g the  The c l a s s i c s p l i t t i n g o f a s i l v e r beam i n t o  beams as i t passed  through  an inhomogeneous magnetic  field  was an e a r l y r e s u l t e x p l a i n a b l e by s p a t i a l q u a n t i z a t i o n , a r e s u l t of quantum  theory. Molecular  opening  flow beams, beams where flow through the  i s c o l l i s i o n l e s s , can be f i n e l y c o l l i m a t e d but the  i n t e n s i t y a v a i l a b l e i s v e r y low. higher i n t e n s i t y K a n t r o w i t z  F o r experiments r e q u i r i n g  and Grey (Ka51) i n  1951 proposed  a  system which h o p e f u l l y would r e s u l t i n c o n s i d e r a b l e improvements of beam i n t e n s i t i e s and v e l o c i t y  spread.  T h e i r p r o p o s a l employing a s u p e r s o n i c L a v a l n o z z l e appeared to p r o v i d e a means o f i n c r e a s i n g beam i n t e n s i t i e s by a t l e a s t one order of magnitude and to a l l o w  significant  r e d u c t i o n s i n the v e l o c i t y spread o f the beam. o r i g i n a l l y proposed as a technique  Although  f o r the study of other  p h y s i c a l phenomena, the n o z z l e beams r a p i d l y became the s u b j e c t of i n t e n s e s t u d y . most p r o t o t y p e  This study came about due to the f a i l u r e o f  sources  to perform  i n the p r e d i c t e d f a s h i o n .  Subsequent i n v e s t i g a t i o n s have r e v e a l e d much o f the true behaviour  of these n o z z l e sources and now the expected  Ik  behaviour  of a g i v e n n o z z l e system can be p r e d i c t e d w i t h  reasonable  confidence.  The d i s c u s s i o n o f theory and r e s u l t s  to  be p r e s e n t e d  w i l l be d i r e c t e d  of  the o p e r a t i o n o f the n o z z l e source used i n the p r o d u c t i o n of  a polarized 3 H e ion  i o n beam.  +  towards a b e t t e r  The p r o d u c t i o n of t h i s  polarized  beam has been the main m o t i v a t i n g f o r c e f o r the development  work which has gone i n t o beam s o u r c e .  The l a s t  e x i s t i n g work on l i q u i d  the d e s i g n o f a low v e l o c i t y  s e c t i o n i n t h i s chapter w i l l  atomic  summarize  helium c o o l e d n o z z l e sources and  d i s c u s s p o s s i b l e uses f o r low temperature n o z z l e B.  understanding  sources.  P r o p e r t i e s o f the M o l e c u l a r Flow Beam. Before d i s c u s s i n g the n o z z l e source  p r o p e r t i e s o f the molecular f r e e molecular Molecular  flow i m p l i e s that the mean f r e e path A o f the gas i s considerably larger  d and l e n g t h o f the o r i f i c e  molecular  flow beam i . e . a beam formed by  flow through an o r i f i c e w i l l be d e s c r i b e d .  p a r t i c l e s i n the source  Kn = V d  the b a s i c  than the diameter  t h a t i s , the Knudsen number  i s much g r e a t e r than u n i t y .  The o p e r a t i o n o f a  flow beam has been d i s c u s s e d (Sm55"} Ra5&) but w i l l be  summarized below f o r completeness. The  f a t e N a t which molecules  of  area A i s equal  of  the w a l l per second, and i s g i v e n by  to the number o f molecules  N = invA  and  v =  QkT TTTn  i  S  hitting  molecules/sec  where n i s the number o f molecules  1  pass through  an a p e r t u r e that area  (1)  per u n i t volume i n the source  the average speed, K i s Boltzman's  constant,  15 T the oven temperature  (°K), and m the mass of the gas  The i n t e n s i t y I a t a d i s t a n c e r from  - i Tiv A  T  the oven source i s g i v e n by  molecules /cm*-Sec  cos O  (2)  T l "  where 8 i s the angle between the r a d i u s v e c t o r r and  the normal  Eq. 2 can be r e w r i t t e n f o r the case of  to the a p e r t u r e .  intensity i e . 0 =  centerline  molecule.  0 i n terms of the t o t a l p a r t i c l e  gas flow through the o r i f i c e N as  The number o f p a r t i c l e s p a s s i n g through the opening w i t h a g i v e n v e l o c i t y V f o l l o w s from Maxwells law and i s g i v e n by T f \ J\t -  X(v)dV  -  ?T  / V \  tto(z)  where «L- J ~ ^ ' i s  5  p ~  V  /  ^  L  6  dV £  the most probable  ci-l-oms/cm  - Sec  velocity.  The above equations r e p r e s e n t the p h y s i c a l providing A »  (If)  situation  d h o l d s ; however, as the oven pressure i s r a i s e d  there i s a g r a d u a l t r a n s i t i o n from f r e e molecular to v i s c o u s flow.  I n t h i s t r a n s i t i o n r e g i o n the i n t e n s i t y i s l i m i t e d  l a c k of c o l l i m a t i o n beam which r e s u l t s  due  to c o l l i s i o n s between molecules i n the  i n a low I/N r a t i o and consequently r e q u i r e s  e x c e s s i v e pumping c a p a c i t y to remove the background useful C.  by  gas f o r the  i n t e n s i t y obtained.  P r o p e r t i e s of the Nozzle Beam. K a n t r o w i t z and Grey  (Ka5l) proposed  a supersonic  n o z z l e source f o r the p r o d u c t i o n of molecular beams as shown i n F i g . k.  16  ///////  h77/  nozzle  Fig. k  The  Schematic  R e p r e s e n t a t i o n o f Nozzle Beam  Source.  c r o s s s e c t i o n o f t h e i r n o z z l e was shaped to produce a flow  w i t h a predetermined  Mach number M, equal  to the r a t i o o f the  v e l o c i t y o f mass motion W to the l o c a l v e l o c i t y o f sound a . core o f the beam so produced  The  would be e x t r a c t e d w i t h a s u i t a b l y  shaped skimmer and c o l l i m a t o r system w i t h no a n t i c i p a t e d i n t e r a c t i o n between the skimming a p e r t u r e s and the beam.  The  obvious advantages o f such a system were the l a r g e i n c r e a s e i n i n t e n s i t y and c o n s i d e r a b l e r e d u c t i o n i n v e l o c i t y spread o f the beam produced  when compared to an oven beam.  The l a r g e  i n t e n s i t y i n c r e a s e a r i s e s because o f the high gas d e n s i t i e s i n n o z z l e flows compared flows.  to the low gas d e n s i t i e s i n molecular beam  The attainment of beams w i t h a v e l o c i t y o f mass motion  i n excess o f the l o c a l s o n i c v e l o c i t y r e s u l t s i n a v e l o c i t y d i s t r i b u t i o n c o n s i d e r a b l y narrower than that achieved w i t h oven beams.  I t was soon d i s c o v e r e d , however, that i t was not p o s s i b l e  17 to produce a beam of c o n t r o l l e d p r o p e r t i e s , that i s a gas c h a r a c t e r i z e d by a predetermined  Mach number using  t h e o r e t i c a l l y shaped n o z z l e nor was  flow  the  i t p o s s i b l e to e x t r a c t the  beam produced without i n t e r f e r e n c e between the skimming elements and  the background gas.  The nature of the beam a c t u a l l y  produced i s d i s c u s s e d i n the f o l l o w i n g s e c t i o n s . (1)  Gas  Flow Through a N o z z l e .  The mass gas flow, G,  through a n o z z l e f o r  one-  d i m e n s i o n a l , f r i c t i o n l e s s a d i a b a t i c flow i s g i v e n by (Sh53)s  where A  = e f f e c t i v e c r o s s s e c t i o n a l area of the n o z z l e . = r a t i o of s p e c i f i c  po and  heats,  To are the s t a g n a t i o n p r e s s u r e and  upstream of the n o z z l e entrance, temperature  temperatures  that i s the p r e s s u r e  and  of the gas i n the r e g i o n where the flow i s  e s s e n t i a l l y completely random.  "One  d i m e n s i o n a l flow" means  t h a t the flow p r o p e r t i e s are assumed to be c o n s t a n t i n any plane p e r p e n d i c u l a r to the d i r e c t i o n o f flow and hence a p p l i e s to the case of a gas f l o w i n g through a n o z z l e of v a r y i n g c r o s s s e c t i o n a l area. The  e f f e c t i v e c r o s s s e c t i o n a l area of the n o z z l e i s  under c e r t a i n c o n d i t i o n s l e s s because of v i s c o u s e f f e c t s .  than the a c t u a l g e o m e t r i c a l area The r a t i o of e f f e c t i v e area to  a c t u a l g e o m e t r i c a l area i s known as the d i s c h a r g e Govers, Le Roy  and Deckers (G069)  coefficient.  g i v e experimental  values of  18  t h i s c o e f f i c i e n t f o r helium gas p a s s i n g through diameter  R  P  -  a nozzle of  d as a f u n c t i o n of n o z z l e Reynolds number,  A-m N —;—  , based  on e x p e r i m e n t a l flow N and v i s c o s i t y ri a t  stagnation conditions.  T h e i r r e s u l t s f o r Helium  F i g . 5 a t s t a g n a t i o n temperatures  between 2 9 5 ° K and  u s i n g a n o z z l e w i t h d = 0.266 mm. c o l l a p s e onto a s i n g l e l i n e  are shown i n  Although  120H-°K  the r e s u l t s do  not  they do show what f r a c t i o n of the  t h e o r e t i c a l l y c a l c u l a t e d flow w i l l  be a c h i e v e d under  e x p e r i m e n t a l c o n d i t i o n s c h a r a c t e r i z e d by a g i v e n Reynolds number a t temperatures are a v a i l a b l e operate.  of 2 9 5 ° K and 120 f°K.  U n f o r t u n a t e l y no  l  f o r temperatures  near 7 ° K where our n o z z l e w i l l  I n s p i t e of the f a c t our n o z z l e w i l l operate a t  Reynolds numbers i n excess of 600 d i s c h a r g e c o e f f i c i e n t may however p r e s e n t s no (2)  i t appears  Expansion.  w i t h a near vacuum on one  t h a t slows  such an opening  can be  molecular  flow.  t r e a t e d by continuum on  that s i d e .  the Mach d i s k .  gas  flow  The Mach d i s k  the boundary between continuum and  In t h i s "zone of s i l e n c e "  i s e n t r o p i c a l l y u n a f f e c t e d by the presence outside  The  the j e t boundary and can be  continuum gas dynamics.  high  (As66) forms a j e t as shown i n F i g . 6  d e f i n e d by a b a r r e l shock and b a r r e l shock form  d as shown i n F i g . 6  s i d e and a p r e s s u r e s u f f i c i e n t l y  dynamics techniques, t h a t i s A ^ d ,  and  This  problems.  The Free J e t  on the o t h e r s i d e  p o s s i b l e t h a t the  be c o n s i d e r a b l y below u n i t y .  C o n s i d e r an o r i f i c e of diameter  through  results  free  the f l o w expands of background  gas  t r e a t e d by methods of  This expansion  has been d e s c r i b e d  19  0  200  400 TT  Fig. 5  600  D 72.  Discharge C o e f f i c i e n t v s . Reynolds Number based on E x p e r i m e n t a l Flow and V i s c o s i t y a t S t a g n a t i o n C o n d i t i o n ;  20  = l.h  theoretically for  by Owen and T h o r n h i l l  (0w52) u s i n g the  method o f c h a r a c t e r i s t i c s and confirmed e x p e r i m e n t a l l y by Reiss  (Fe63)  and Sherman ( S h 6 3 ) .  jet boundary  Fig. 6  Their  Schematic R e p r e s e n t a t i o n o f Flow from an O r i f i c e i n t o an Evacuated Region.  solution i s applicable  external  to any j e t f l o w i n g  p r e s s u r e i n that r e g i o n  f i r s t wavefront which r e g i s t e r s  bounded by the o r i f i c e and the the e x i s t a n c e o f an e x t e r n a l  p r e s s u r e o u t s i d e the j e t . Askenas Owen and T h o r n h i l l s  1  and Sherman (As66) extended  s o l u t i o n to gases with7f= I . 6 7 ( e g . H e l i u m ) .  They suggest the f o l l o w i n g number o f a f r e e j e t :  i n t o any  formula- f o r the c e n t e r l i n e Mach  24 -^1.67  •  K 18 UJ CQ < «s5£  z x  u  12  <  K = i.4  6  o •  Fig. 7  -  —  1  0  " 4  1  i  i  S6 12 8 DISTANCE FROM NOZZLE EXIT  D i s t r i b u t i o n o f Mach Number Along the  20 24 (nozzle diameters)  Axis of Symmetry of the Expanding J e t .  22 where x = d i s t a n c e from o r i f i c e along X  Q  such that f o r Y  are c o n s t a n t s  and  £2,  0.075.  =  This three  the c e n t e r l i n e j B , C  = 1.6?;  B = 3.26,  term formula  0.31  C =  i s accurate  and  for X ^ d  w i t h maximum d e v i a t i o n s from the c h a r a c t e r i s t i c data o f ^ - g ^ of M.  The  c a l c u l a t e d values  is interesting the n o z z l e  to note  are shown g r a p h i c a l l y i n F i g . 7.  It  that these r e s u l t s are independent of  temperature and  pressure.  For a d i a b a t i c flow w i t h d e n s i t i e s . s u f f i c i e n t l y t h a t methods o f continuum gas  dynamics may  high  be a p p l i e d , the  local  pressure  and  temperature p^ and  pressure  and  temperature measured i n a r e f e r e n c e frame moving  with  T j of a beam, t h a t i s the  the v e l o c i t y of mass motion W as  a n o z z l e , may  be expressed  c o n d i t i o n s and  the beam expands through  i n terms o f the n o z z l e  the l o c a l Mach number (Em58).  This  stagnation treatment  gives T ,  =  .  (7) T o  and  Pi  -  The  l o c a l sound v e l o c i t y  Q  and  the v e l o c i t y of mass motion  W  I n the i n e r t i a e x p a n s i o n Askenas and decreases  (9)  =  - M  dominated r e g i o n of the f r e e j e t  Sherman (As66) have shown that the d e n s i t y  along each s t r e a m l i n e  i n p r o p o r t i o n to the i n v e r s e  square of d i s t a n c e from an apparent source stream from the a c t u a l o r i f i c e . c a l c u l a t e d angular  (10)  a distance x  They a l s o show that  dependence of the d e n s i t y f i e l d  0  the  can  be  down-  23 r e p r e s e n t e d by the simple formula  (11)  w i t h an a c c u r a c y o f about 3>% of n ( r , o ) .  That i s , t h e i r data  from a method of c h a r a c t e r i s t i c s s o l u t i o n d i f f e r s l e s s  1% from  the r e s u l t s o b t a i n e d using Eq. 1 1 .  depends on the s p e c i f i c  The c o n s t a n t (j>  heat r a t i o f o r the gas used;  The d i s t a n c e from  than  thus f o r  the o r i f i c e  to the Mach  d i s k XJJJ i s g i v e n by Askenas and Sherman (As66), as a f u n c t i o n of  the p r e s s u r e r a t i o Po/Pbg a c r o s s the o r i f i c e ,  by:  (12) where Pbg  i s the background  p r e s s u r e i n the n o z z l e exhaust r e g i o n .  T h i s formula g i v e s reasonable agreement to experimental r e s u l t s independent (3)  of the v a l u e of Y,  £  i n the r e g i o n 15  0//  Pba~ 1 7 , 0 0 0 .  The F r e e z i n g S u r f a c e . The f r e e expansion d i s c u s s e d e a r l i e r  t r a n s f e r s energy from the i n t e r n a l degrees molecules  to d i r e c t e d mass motion.  beam molecules  essentially  of freedom  Thus we may  of the  c o n s i d e r the  to be c h a r a c t e r i z e d by some l o c a l  temperature  T,  i n a l o c a l r e f e r e n c e frame moving w i t h the v e l o c i t y of mass motion.  A c e r t a i n c o l l i s i o n frequency between the molecules of  the beam i s r e q u i r e d  to support t h i s continuous r e d u c t i o n i n the  randomness of the motion o f the molecules w i t h r e s p e c t to the l o c a l r e f e r e n c e frame. low and  When the gas d e n s i t y gets  sufficiently  t h i s minimum c o l l i s i o n frequency i s not maintained,  the  expansion  to higher Mach number ceases and  a t a g i v e n temperature.  the system " f r e e z e s "  Once t h i s f r e e z i n g r e g i o n i s reached  the gas  continues  as  but w i t h no f u r t h e r change i n temperature.  be noted  to expand r a d i a l l y ,  the i n t e n s i t y d e c r e a s i n g I t should  that the l o c a t i o n of t h i s f r e e z i n g s u r f a c e i s not  c o i n c i d e n t w i t h the Mach d i s k l o c a t i o n . E m p i r i c a l d e t e r m i n a t i o n of the t e r m i n a l Mach number Mj. a t which t r a n s l a t i o n a l f r e e z i n g occurs based s t a g n a t i o n c o n d i t i o n s , has y i e l d e d M  t  =  T h i s r e s u l t was  l.-'B  on n o z z l e  the r e s u l t (An65).  ( K r O ^ )  ( 1 3 )  o b t a i n e d f o r Argon beams a t room  temperature;  subsequent i n v e s t i g a t i o n has shown t h a t i t a l s o holds f o r other However, Abuaf e t a l (Ab66) have shown that experimental  gases.  v a l u e s f o r helium f a l l below the r e s u l t s p r e d i c t e d using e q u a t i o n ; h i s r e s u l t s are shown i n F i g . 8 . calculated  Knuth (Kn6 +) l  the l o c a t i o n o f the f r e e z i n g planes u s i n g the  r e l a x a t i o n times f o r the c o l l i s i o n p r o c e s s e s i n v o l v e d . found  this  He  f o r a monatomic g a s , V = 5 / 3 t h a t  where K n  0  = the Knudsen number based  on s t a g n a t i o n c o n d i t i o n s .  Knuth's r e s u l t s are a l s o shown on F i g . 8 .  The agreement w i t h  e x p e r i m e n t a l r e s u l t s f o r Argon i s pdor f o r low Knudsen numbers but improves f o r l a r g e r K n • Q  N a t u r a l l y the t r a n s i t i o n between  the continuum to t r a n s i t i o n and  then f r e e molecular flow i s  not a sudden process so t h a t the above formula and on which they are based  only  represents a f i r s t  the model  approximation  , to the r e a l s i t u a t i o n which i s p r o p e r l y d e s c r i b e d o n l y by a •  S t a g n a t i o n C o n d i t i o n s a t the  Nozzle.  26 complete s o l u t i o n (*+)  Velocity  o f the k i n e t i c  equations.  Distribution  of P a r t i c l e s  i n the Beam.  P a r t i c l e s . i n an expanding j e t from a m i n i a t u r e s u p e r s o n i c n o z z l e c a n be c o n s i d e r e d  to move w i t h r e s p e c t  to a  l o c a l r e f e r e n c e frame which i s moving r a d i a l l y outwards from the n o z z l e w i t h the v e l o c i t y o f mass motion. illustrated surface.  i n F i g . 9 includes  For s i m p l i c i t y  the presence o f the f r e e z i n g  the r e s u l t s  presented i n t h i s arri the  next s e c t i o n w i l l assume the f r e e z i n g w i t h the skimmer opening.  This behaviour  surface i s coincident  Because the r a d i a l d e n s i t y  is  the same on both s i d e s of the f r e e z i n g  of  the f r e e z i n g  s u r f a c e , the i n c l u s i o n  s u r f a c e upstream o f the skimmer w i l l  e f f e c t oh the r e s u l t s  obtained.  The p a r t i c l e s  moving frame have a M a x w e l l i a n v e l o c i t y  variation  have no  as seen i n the  distribution  c h a r a c t e r i z e d by some l o c a l temperature.  In fact,  careful  s t u d i e s o f the v e l o c i t y d i s t r i b u t i o n o f n o z z l e beams that c o n s i d e r both the r a d i a l and angular dependence o f the v e l o c i t y d i s t r i b u t i o n f i n d that the Maxwellian d i s t r i b u t i o n i s c h a r a c t e r i z e d by one temperature T// and  another Tj_ i n the u  o r i f i c e T„  and u^ d i r e c t i o n s  = Tj_ but due to d i f f e r e n c e s  translational different  2  i n the r a d i a l d i r e c t i o n u^  relaxation  (Fi67).  A t the  i n the r a t e s f o r  the two temperatures p r o g r e s s  to the  t e r m i n a l values achieved when the expansion s t o p s .  Thus the v e l o c i t y d i s t r i b u t i o n f u n c t i o n can be w r i t t e n  Fig. 9  Schematic R e p r e s e n t a t i o n o f R a d i a l l y Expanding Flow a Skimmer to a D e t e c t o r .  throug  28 •f ( U i ^ - ( - ( W i )  -T(u ) d u , clui  d"-  N  3  (15)  ex  2ir kT„  This f u n c t i o n r e p r e s e n t s the f r a c t i o n a l number o f p a r t i c l e s i n the beam w i t h v e l o c i t i e s u^, U £ j  i n some range d u j , du2, du^,  I f v e l o c i t y d i s t r i b u t i o n measurements are made o n l y along the beam a x i s i t i s n o t p o s s i b l e to determine it  i s common to s e t T n = T j_ = T  ;  simplified  velocity  both T,  and T  (  , thus r e s u l t i n g  x  and  i n the  distribution  -PO,) f ( u O - f (u 5 ) d u , d u d u s  = (^Ty* *P[z^, fa-"'? e  x  r  U  *  3  }]  d M  '  (16)  The above equations give the v e l o c i t y d i s t r i b u t i o n o f p a r t i c l e s a t some p o i n t i n the beam.  The f r a c t i o n a l i n t e n s i t y o r  d i f f e r e n t i a l i n t e n s i t y d i s t r i b u t i o n function, I(u) - d i  ?  0  f  p a r t i c l e s w i t h a g i v e n v e l o c i t y a r r i v i n g a t a d e t e c t o r depends on the r e s t r a i n t s  imposed by the geometry o f the complete n o z z l e  system i n summing over a l l p o s s i b l e v e l o c i t i e s  to o b t a i n the  t o t a l i n t e n s i t y o f p a r t i c l e s a t the d e t e c t o r .  I f p a r a l l e l flow  at  the entrance  to the skimmer i s assumed (one o f K a n t r o w i t z and  Grey's o r i g i n a l assumption) Eq.B8 o f Appendix B g i v e s  (B18)  3 where  ^(u)  :  ^  - ^ > - w )  2  (B19)  e  and l i s i s the c e n t e r l i n e  isentropic  from a f r e e  u n a f f e c t e d by the presence  j e t expansion  beam i n t e n s i t y  skimmer as d i s c u s s e d i n S e c t i o n 3C a n d £ \  s  I  expected  the h a l f  s  of a angle  subtended by the skimmer w i t h r e s p e c t to the n o z z l e e x i t as shown i n F i g . 4-8.  Now i f the r a d i a l flow divergence  the skimmer i s i n c l u d e d i n c a l c u l a t i n g  o f the beam a t  the i n t e n s i t y a t the  d e t e c t o r Eq. B8 o f Appendix B g i v e s  (^~\'  (B20)  Q(u)  k  where g(u) i s as before and  ^p[-( 1^yi- ^0D] 2  •;GrM^{i?i4^J  now  ^  ^ M  to  thus  2  when the skimmer subtends a very s m a l l h a l f  2^M Then —  du  2  1  Sir\*(^?)  2*rV  Q-(u)  ^ ( f )  S A P [-ZW J thus m o d i f i n g  *  PC  angle  ^ r=  eoftS-fa.A +  the flow at. skimmer i s  When the skimmer subtends a l a r g e h a l f y>\  a  sin ^) ^ 0  2  ^  and  «* 3(11) as i n E q . B18 where  assumed p a r a l l e l .  ( B 2 D  n  angle  d  2  a  n  d  the v e l o c i t y dependence o f E q . B8 to  9 ( u V ( ^ M  =  ^ expL~^ Z  ( U - \ N ¥  ]  ( i  7  )  when the r a d i a l dependence o f the flow i s c o n s i d e r e d f o r flows w i t h a p p r o p r i a t e Mach number and skimmer r a d i u s .  This i s the  form o f the d i f f e r e n t i a l i n t e n s i t y d i s t r i b u t i o n f u n c t i o n recommended  30  by Hagena and Morton (Ha67) (5)  I n t e n s i t y A v a i l a b l e From Nozzle Beams. (i) The  F r e e l y Expanding J e t . case of the f r e e l y expanding j e t without a skimmer  or c o l l i m a t o r using Eq. 11 the beam a x i s has  to r e p r e s e n t the d e n s i t y f i e l d  been c o n s i d e r e d .  As shown i n a  c a l c u l a t i o n g i v e n i n Appendix A the expected on  simple  flux density I  the beam a x i s i s I = 0.6N  where N = G/m The  about  atoms/steradian  = particle  - sec  flow through  the n o z z l e g i v e n from Eq. 5»  e q u i v a l e n t e x p r e s s i o n f o r molecular N/TT  I =  (A5)  atoms/steradian  flow beam i s  - sec  (3)  ( i i ) Beam I n t e n s i t y Downstream from the Skimmer. The  t h e o r e t i c a l l y expected  gas  has passed  Two  cases are c o n s i d e r e d :  Kantrowitz  and while  through  beam i n t e n s i t y a f t e r  the  a skimmer i s d i s c u s s e d i n Appendix B. One  assumes the c o n d i t i o n s of  and Grey model (Ka5l),  the  namely:  (1)  i s e n t r o p i c flow upstream o f the skimmer  (2)  p a r a l l e l flow a t the skimmer  (3)  c o l l i s i o n l e s s flow downstream of the skimmer,  the o t h e r c o n s i d e r s  the case as suggested  Morton ( H a 6 7 ) where c r i t e r i o n model i s m o d i f i e d  (2)  i n the Kantrowitz and  to take i n t o account  the flow a t the skimmer.  by Hagena and Grey  the d i v e r g e n t nature  of  31 The r e s u l t o f t h i s a n a l y s i s i s (1)  P a r a l l e l flow a t skimmer - 1,5  I  (2)  Sif)V  ( !  s  entrance.  Ar Vf)  '  R a d i a l l y d i v e r g i n g flow a t skimmer  I - I ^ C i - c o s V . e ^  S m  (Bl?)  entrance.  * ) s  ( B 1 2 )  Both E q s . B12 and B17 are f o r the case of the detector-skimmer s e p a r a t i o n %77 / of  s  , the nozzle-skimmer s e p a r a t i o n ,  the s i m p l i f i c a t i o n s a f f o r d e d  and make use  by assuming M > 3.  Eq. B17 based on the Kantrowitz-Grey model p r e d i c t s an i n t e n s i t y p r o p o r t i o n a l  to the skimmer area  but i t i s c l e a r  that i t p r e d i c t s unreasonably h i g h i n t e n s i t i e s I > I i s skimmer i s so l a r g e  that  ^  ) Sin V  y  s  |  .  i f the  This  u n p h y s i c a l l y h i g h i n t e n s i t y i s due to the n e g l e c t o f the divergent  nature of the flow approaching  the d i v e r g e n t Eq. B12. increase  the skimmer.  Including  nature o f the flow i n the c a l c u l a t i o n r e s u l t s i n  T h i s second e q u a t i o n no longer  shows an u n l i m i t e d  of I w i t h e i t h e r M or sinc<s but p r e d i c t s an i n t e n s i t y  approaching I^g, the i n t e n s i t y one would expect i f no skimmer had  been p r e s e n t (6)  at a l l .  Deviations  From I d e a l Behaviour.  E x p e r i m e n t a l i n v e s t i g a t i o n s have shown that the i n t e n s i t i e s p r e d i c t e d i n the p r e v i o u s achieved  i n practice.  s e c t i o n are not always  This d i s c r e p a n c y  between theory and  experiment i s caused a t l e a s t i n p a r t by the assumption i n the t h e o r e t i c a l c a l c u l a t i o n that  (1)  the beam i n u n a f f e c t e d by the presence o f the skimmer  and  (2)  the beam i s u n a f f e c t e d by the presence o f background gas  The e f f e c t o f these i d e a l i z a t i o n s i s o f t e n a severe r e d u c t i o n o f beam i n t e n s i t y below that expected from the previous  analysis. The presence of a shock wave a t the skimmer entrance  was expected to cause a r e d u c t i o n o f the beam i n t e n s i t y due to the  presence o f the skimmer but the electron-beam f l o w -  v i s u a l i z a t i o n photographs failed of  o f McMichael and French (McM66)  to d e t e c t any l o c a l b u i l d up o f gas molecules  the skimmer.  upstream  The skimmer i n t e r f e r e n c e i s now p o s t u l a t e d to  occur downstream o f the skimmer entrance i e . i n s i d e the skimmer, and  to be caused by a c l o u d of low v e l o c i t y molecules whose  c r e a t i o n i s caused by molecules r e f l e c t e d o f f the i n s i d e o f the skimmer. placing  The skimmer d e g r a d a t i o n o f the beam can be avoided by ^ I'  the skimmer i n a r e g i o n where  (An66).  This  M c r i t e r i a g e n e r a l l y r e s u l t s i n l a r g e nozzle-skimmer S c a t t e r i n g o f the beam by background  separations.  gas o c c u r s i n  a l l r e g i o n s o f the apparatus i f the p r e s s u r e s a r e s u f f i c i e n t l y high.  The b e a m - i n t e n s i t y a t a d i s t a n c e / from the source can be  c a l c u l a t e d using  r  _ \  2 > I o where I and I  0  \  n  -no-dX  e  (is)  are the a t t e n u a t e d and unattenuated beam  i n t e n s i t i e s , n the l o c a l gas d e n s i t y and cr the s c a t t e r i n g section.  S c a t t e r i n g o f the beam i n the nozzle-skimmer  cross  region i s  33  a s p e c i a l case, as the presence o f the b a r r e l shock p a r t i a l l y prevents  the beam from s c a t t e r i n g i n the r e g i o n between the  n o z z l e and the Mach d i s k l o c a t i o n . occurs downstream conditions Thus  S c a t t e r i n g o f the beam  o f the Mach d i s k and occurs under  to a l e s s e r e x t e n t upstream as w e l l  certain  ( B r 6 6 , An65b).  to reduce s c a t t e r i n g i n the nozzle-skimmer r e g i o n to a  minimum the skimmer should be upstream o f the Mach d i s k l o c a t i o n which can be p r e d i c t e d using Eq. 12.  This  condition  u s u a l l y c o n f l i c t s w i t h the s e p a r a t i o n f o r minimum skimmer i n t e r f e r e n c e and hence a compromise  s i t u a t i o n develops.  T y p i c a l e x p e r i m e n t a l i n t e n s i t y p r o f i l e s obtained as a f u n c t i o n o f nozzle-skimmer s e p a r a t i o n are shown i n F i g . 30. The i n t e n s i t y maximum i s the p h y s i c a l r e a l i z a t i o n o f t h i s compromise  between background gas s c a t t e r i n g and skimmer  interference.  Downstream o f the maximum, background  scattering  dominates w h i l e upstream, skimmer i n t e r f e r e n c e dominates. s m a l l n o z z l e skimmer s e p a r a t i o n s  At  the r e l a t i v e l y high beam  i n t e n s i t y i s caused by the f r e e j e t "popping" through the skimmer and expanding towards the c o l l i m a t o r which now a c t s as a skimmer.  With i n c r e a s e d s e p a r a t i o n the j e t s l o w l y r e t u r n s to  i t s normal l o c a t i o n and skimmer i n t e r f e r e n c e i s a t i t s maximum hence the minimum i n beam i n t e n s i t y a t fo ~ 5. L  (7)  Low Temperature Nozzle Sources and t h e i r uses. Few e x p e r i m e n t a l r e s u l t s e x i s t d e s c r i b i n g  o f h e l i u m beams formed by n o z z l e s c o o l e d temperatures.  the nature  to l i q u i d helium  Becker, K l i n g e l h o f e r and Lohse ( B e 6 l ,  Be62)  r e p o r t o b s e r v i n g a condensed helium beam w i t h an i n t e n s i t y o f  3  l 2 x l 0 9 atoms/sr-sec, 1  0  a v e l o c i t y of 165  m/sec and a v e l o c i t y  to a Mach number of about 80.  FWHM c o r r e s p o n d i n g  were o b t a i n e d w i t h a 0.15  mm  k  These r e s u l t s  diameter nozzle operated a t 7*K> T o r r .  They r e p o r t no o b s e r v a t i o n s of an uncondensed beam a t l i q u i d helium i n t e n s i t i e s . recently  Zapata, B a l l a r d  made some measurements of i n t e n s i t y and  d i s t r i b u t i o n of ^ e nozzle source.  beams produced  n o z z l e temperature mm  (Za69) have velocity  by a c r y o g e n i c a l l y  cooled  They r e p o r t a peak i n t e n s i t y of 6x10^  s r - s e c and a beam v e l o c i t y o f 320  0.11  and Cabrera  o f 10°K.  m/sec.  This corresponds  to a  These r e s u l t s obtained w i t h a  diameter n o z z l e operated a t p r e s s u r e s up  to 200  are i n r e a s o n a b l e agreement w i t h corresponding r e s u l t s l a t e r i n t h i s work.  atoms/  Torr presented  No work has a p p a r e n t l y been done w i t h  n o z z l e beams c o o l e d to l i q u i d helium  ^Ee  temperature.  The study o f condensation fragments  i n low  temperature  Argon beams has been c a r r i e d out by M i l n e and Greene (Mi67) u s i n g mass spectrometer using e l e c t r o n were i n t e r e s t e d  techniques and A u d i t and Rouault  d i f f r a c t i o n techniques.  Both  experimenters  i n s t u d y i n g the i n t e r m o l e c u l a r p o t e n t i a l  between groups of Argon atoms.  M i l n e used  these  measurements to t e s t t h e o r e t i c a l c a l c u l a t i o n s c o n c e n t r a t i o n o f dimers, beam.  these  (Au69)  acting  experimental  f o r the  t r i m e r s e t c . i n a p a r t i a l l y condensed  H o p e f u l l y s t u d i e s w i t h helium beams s i m i l a r  to those  made w i t h argon beams w i l l show r e s u l t s a t t r i b u t a l to quantum e f f e c t s which would be p r e s e n t w i t h helium a t low  temperatures  but which would not have p l a y e d a n o t i c e a b l e r o l e i n the case o f Argon.  The  use o f both % e  and ^He  may  result i n interesting  35 d i f f e r e n c e s because  of the F e r m i - D i r a c and Bose E n s t e i n  S t a t i s t i c s obeyed by the two  gases.  Be56, B e 6 l , Be62)  Becker e t a l ( B e 5 , L  o r i g i n a l work w i t h low  temperature  n o z z l e beams were i n t e r e s t e d  i n s t u d y i n g c o n d e n s a t i o n phenomena. formed  i n their  P a r t i a l l y condensed  from a mixture of the i s o t o p e s , ^>Ee and ^He,  be used  to p r e f e r e n t i a l l y e n r i c h  of the i s o t o p e s .  might  the r e s u l t i n g beam w i t h  Such a technique a t higher  one  temperatures  c o u l d p o s s i b l e be used i n the s e p a r a t i o n of l i g h t and water vapour,  beams  a p r o c e s s of c o n s i d e r a b l e commercial  heavy  interest.  I s o t o p e s can be e n r i c h e d i n the f r e e j e t expansion w i t h o u t c o n d e n s a t i o n because  of the dependence of the v e l o c i t y components  on the mass o f the p a r t i c l e s . Knuth and F i s h e r from room temperature temperatures  (Kn68)  to measure v i s c o s i t y c r o s s s e c t i o n s a t  as low as 10°K.  S i m i l a r s t u d i e s c o u l d be  out w i t h helium beams s t a r t i n g liquid  helium temperatures.  both ^He  and Sfe  have used Argon beams expanded  from room, l i q u i d n i t r o g e n or  A g a i n the a v a i l a b i l i t y of beams of  a l l o w s comparison  their different s t a t i s t i c s .  carried  between the e f f e c t s due  As w i l l be mentioned  to  later i n this k  •5  work, the d i f f e r e n c e i n s c a t t e r i n g c r o s s s e c t i o n f o r He J  and  He  has been observed f o r j e t s expanded from a l i q u i d helium c o o l e d nozzle. The a v a i l a b i l i t y of a low energy helium beam i s of i n t e r e s t i n the study o f g a s - s u r f a c e i n t e r a c t i o n . B a l l a r d and Cabrera  (Za69)  Zapata,  have c o n s t r u c t e d a l i q u i d  helium  c o o l e d n o z z l e source to a l l o w the study of the s u r f a c e phonon  36 spectrum o f a c r y s t a l by s c a t t e r i n g p a r t i c l e s o f f a pure, i s o t r o p i c  an aerodynamic  beam o f  crystal.  A low temperature helium beam may be o f use i n the study of the f r e e  j e t expansion i t s e l f ,  nature o f the t r a n s l a t i o n a l  relaxation  i n particular  i n the  e f f e c t s which even f o r  helium beams expanded from room temperature show a behaviour different  from that o f most other gases.  37 CHAPTER IV THE POLARIZED H e 3  A.  +  BEAM SOURCE  The Low Temperature Atomic Beam Source. (1)  G e n e r a l d e s c r i p t i o n o f Atomic Beam Source. Fig.  10 shows the f u l l  atomic beam apparatus.  gas p r e c o o l e d to l i q u i d n i t r o g e n temperature passes cryostat f i l l e d  with l i q u i d  through a  helium and subsequently flows  through a n o z z l e , skimmer and c o l l i m a t o r system -the  ^He  thus forming  atomic beam. The copper c r y o s t a t weighing 10 kg i s supported a t the  top  by a s i n g l e s t a i n l e s s s t e e l tube.  entering  the c r y o s t a t passes  through the c e n t e r o f t h i s inside the  The l i q u i d  helium  through a t r a n s f e r l i n e  inserted  tube; the e v a p o r a t i n g gas passes up  the support tube through a heat exchanger  used  to p r e c o o l  incoming ^He gas and then back to the helium r e c o v e r y system.  The bottom o f the c r y o s t a t i s connected to the l i q u i d  nitrogen  c o o l e d s h i e l d by a t h i n s t a i n l e s s s t e e l b e l l o w s , a c t i n g as a d i f f e r e n t i a l pumping  bulkhead.  The d e s i g n o f the c r y o s t a t , i t s supports and c o n n e c t i o n s along w i t h the q u a l i t y o f the vacuum s u r r o u n d i n g the chamber, determines the of  the heat l e a k to the l i q u i d  evaporation rate.  The c a l c u l a t e d and measured heat l e a k s  the v a r i o u s components of the c r y o g e n i c system i n d i f f e r e n t  .stages o f assembly are summarized i n Table 1. was determined by measuring the  helium and hence  cryostat.  The heat l e a k  the r a t e o f helium gas b o i l o f f  The r e d u c t i o n o f the r a d i a t i o n heat l o a d  from  from-  38  TO  H  He  RECOVERY  SYSTEM  He  —  INLET  -2  mitt"" 7Z  TL  TRANSFER TUBE HEAT SHIELD  NOZZLE  HEXAPOLE ET  ASSEMBLY  EJECTOR  LIQUID NITROGEN  rzzo DIFFUSION F i g . 10  The Low  PUMP  r  Temperature ^>Ue Atomic Beam Source,  Table 1 D e t a i l e d Summary o f Heat Leaks i n t o  the C r y o s t a t o f the Low Temperature Atomic Beam Source.  Measured heat leak (watts)  System C o n d i t i o n  .  Expected heat leak (watts)  Finally reduced to (watts)  S t r i p p e d c r y o s t a t (no bellow; s o l i d p l a t e s over a l l openings)  0.25  0.3*+  0.2  Bellows between k°K c r y o s t a t and copper heat s h i e l d  0.16  0.16  0.16  R a d i a t i o n over 10" d i f f u s i o n pump (pump n o t o p e r a t i n g )  0.3  0.0  R a d i a t i o n b a f f l e on Cu heat  0.76  O o O  0 0.16  Pumping to Leybold pump  0.63  0.06  0.009  O p e r a t i o n o f l a r g e d i f f pump  0.2  0.0  0.06  Pumping p o r t s on Cu heat  shield  0.25  0.0  0  Total  2.55  0.56  shield  C67  ho 300°K s u r f a c e s  by p a i n t i n g 77°K b a f f l e s w i t h  high  eraissivity  aqua dag was e s s e n t i a l to the s u c c e s f u l o p e r a t i o n o f the cryostat.  The heat l o a d on the system was a c t u a l l y reduced  by about 10$ when gas flow T h i s confirms  through the n o z z l e was  introduced.  the expected high e f f i c i e n c y i n excess o f 98$  o f the heat exchanger system and a l s o i n d i c a t e s that the c o l d gas  flowing  i n the channel to the Leybold  E j e c t o r pump acted  as a s i n k f o r a f r a c t i o n o f the heat l e a k coming through the metal bellows  there.  The t o t a l measured heat l e a k f o r the  system was 0.6 w a t t s . 6 liters  of l i q u i d  fillings.  With a c r y o s t a t capable o f h o l d i n g  helium t h i s allowed  7 hours o p e r a t i o n between  T y p i c a l c o o l down and i n i t i a l f i l l i n g o f the c r y o s t a t  r e q u i r e d 19 l i t e r s  of l i q u i d  helium.  P r e c o o l i n g o f the system  to 77°K f o r 8 hours r e q u i r e d about 80 l i t e r s while  the continued  of l i q u i d  nitrogen  o p e r a t i o n o f the system r e q u i r e d 8 l i t e r s /  hour. The One  vacuum pumping system was separated  i n t o four p a r t s .  s e c t i o n was used to pump the nozzle-skimmer r e g i o n ; one to  pump the skimmer-collimator r e g i o n ; one to pump the r e g i o n surrounding  the c r y o s t a t and magnet, and a f o u r t h to pump the  i o n i z e r chamber.  The pumping system f o r the nozzle-skimmer  r e g i o n c o n s i s t e d o f a Leybold  Hg h5 mercury e j e c t o r pump w i t h  a pumping speed o f 4-5 l i t e r s / s e c a t a p r e s s u r e and  20 l i t e r s / s e c a t 10"^ T o r r .  operating  o f 10"^  Torr  This pump was capable o f  i n t o a backpressure o f 30 Torr f o r a c l o s e d  r e c i r c u l a t i n g ^He gas system but was n o r m a l l y Welch l*+02 pump.  provided  with a  The skimmer-collimator r e g i o n was. pumped  hi  10"  w i t h a CVC  o i l d i f f u s i o n pump having a pumping speed  kOOO l i t e r s / s e c a t p r e s s u r e s below 10"3 pumped w i t h 2 Heraeus 6"  r e g i o n was  having pumping speeds of 1500 was  pumped w i t h a CVC  o f 1HO0  liters/seco  6"  Torr.  The  of  surrounding  d i f f u s i o n pumps each  liters/sec.  The i o n i z e r chamber  d i f f u s i o n pump having a pumping  The 10" and  three - 6"  speed  d i f f u s i o n pumps  were backed w i t h a Stokes *+0 cfm r o t a r y backing pump to m a i n t a i n the n e c e s s a r y f o r e p r e s s u r e . 6"  CVC  10"  and  two  Heraeus  pumps were p r o v i d e d w i t h water c o o l e d b a f f l e s ,  the  Leybold  pump was 6"  The  p r o v i d e d w i t h a l i q u i d n i t r o g e n c o o l e d trap and  pump was  provided with a freon cooled b a f f l e .  Pressure measurements i n the nozzle-skimmer skimmer-collimator attached diameters passed  r e g i o n s were made by means of P i r a n i gauges  of 2„5 + mm 1  and 2.h  mm  respectively.  the a p p r o p r i a t e r e g i o n through  and vacuum bulkheads S i n c e one  and  to the end of l o n g s t a i n l e s s s t e e l tubes w i t h  from  the  These  the r e q u i r e d  thermal  n o r m a l l y a t room temperature  the o t h e r a t e i t h e r 77°K or h.2°K  These c o r r e c t i o n s w i l l  d i s c u s s e d i n d e t a i l i n the next s e c t i o n of t h i s The p r e s s u r e i n the main system was I t was  and  c o r r e c t i o n s f o r thermal  t r a n s p i r a t i o n e f f e c t s were n e c e s s a r y .  gauge c o n t r o l box  tubes  to the o u t s i d e of the main vacuum chamber.  end of the tube was  an i o n i z a t i o n gauge.  inside  be  chapter.  monitored  with  p o s s i b l e to i n t e r l o c k the i o n  t r i p out c i r c u i t  to a r e l a y c o n t r o l l i n g  the  d i f f u s i o n pump power to prevent damage to the d i f f u s i o n pumps should  the p r e s s u r e i n the system become e x c e s s i v e .  d i f f u s i o n pumps used Dow proved  Corning 705  Silicone  The o i l  f l u i d which  to be a v e r y r e l i a b l e and r o b u s t pump f l u i d  withstanding,  '2 k  without  damage, many a c c i d e n t a l exposures to atmospheric  pressure. Nozzle  i n p u t and  nozzle  measured w i t h 2 W a l l a c e - T i e r n a n o t h e r 0- +00 T o r r range.  than 3$  gauges; one  v/ere  0-760 Tori* and  For n o z z l e p r e s s u r e s  1  1 T o r r the  stagnation pressures  the  i n excess of  t h e r m a l . t r a n s p i r a t i o n c o r r e c t i o n s r e q u i r e d were l e s s  and were hence  ignored.  D e t a i l s of the n o z z l e , skimmer, and c o l l i m a t o r system i s shown i n F i g . 11. be a d j u s t e d  nozzle-skimmer d i s t a n c e c o u l d  by r e v o l v i n g the skimmer-collimator  screw thread assembly.  The  (26  The  threads  gear on  per i n c h ) c u t on  the end  of the  c a r r i a g e on a  the main n o z z l e  skimmer-collimator  c a r r i a g e c o u l d be connected by a gear c h a i n system to a rod passing  through the vacuum chamber w a l l .  allowed  the r o d  One  to be r o t a t e d from o u t s i d e  An O-ring  seal  the vacuum system.  complete r e v o l u t i o n o f t h i s rod correcponded to 1 / 8  r e v o l u t i o n o f the skimmer-collimator or decreased  c a r r i a g e which i n c r e a s e d  the nozzle-skimmer s e p a r a t i o n by 0 . 0 0 ^ 8 i n c h e s .  This e x t e r n a l l y a d j u s t a b l e system f u n c t i o n e d o n l y w i t h n o z z l e a t room temperature as n i t r o g e n temperature and  t h i s framework.  the 0 - r i n g s  below.  collimators of'appropriate  Nozzles,  s i z e and  w i t h a telescope as  freeze at  liquid  skimmers,  and  observing  achieved  by mounting  the v a r i o u s  the n o z z l e system was  apertures  rotated.  Thermal T r a n s p i r a t i o n C o r r e c t i o n s to > Measurements.  the  shape c o u l d be i n s t a l l e d  P r e c i s e alignment was  the framework i n a l a t h e and  (2)  of a  Pressure  on  © o-ring  n  7J  ^moin nozile ossemoty /•skimmer-collimofor carnage 6 4 cog g ear  F i g . 11  The A j u s t a b l e Nozzle-Skimmer  Assembly.  ,-r  kk  When one end o f a p r e s s u r e s e n s i n g d e v i c e i s a t a temperature d i f f e r e n t from the o t h e r end i t i s n e c e s s a r y to correct  the measured p r e s s u r e f o r thermal t r a n s p i r a t i o n  F i g . 12  C o n d i t i o n s f o r Thermal  Transpiration Effect,  A t y p i c a l s i t u a t i o n i s shown i n F i g . 12 i n which and V  2  a t temperatures  diameter d.  and T  2  effects.  two volumes  are connected by a tube o f A >~? d  I f the d e n s i t y i n the' volume i s such that  then the gas f l o w through any opening a c c o r d i n g to Eq. 1 i s JL  p r o p o r t i o n a l to n T . 2  The steady s t a t e i s e s t a b l i s h e d when  (19) now  Ii  - I iiV  / z  When c o l l i s i o n s between molecules predominate against i  s  P]_  =  over  collisions  the w a l l s , ie.A<^d, then the c o n d i t i o n f o r e q u i l i b r i u m P » 2  Numerical v a l u e s f o r 'the r a t i o P j / p  are p r e s e n t e d by Roberts and S y d o r i a k  (Ro56)  2  where T j < T  2  f o r 3 j f e and ^ e .  T h e i r r e s u l t s are g i v e n as a f u n c t i o n o f the p r o d u c t p d which 2  a l l o w s the n e c e s s a r y c o r r e c t i o n f o r tubes o f v a r y i n g s i z e s to  h5 be e a s i l y determined. into  The l e n g t h of the tube does not e n t e r  these c o n s i d e r a t i o n s .  work r e l a t i n g  The a p p r o p r i a t e r e s u l t s from  their  to the measurement of p r e s s u r e i n the n o z z l e -  skimmer and skimmer-collimator r e g i o n s are shown i n F i g . 13. A t the low p r e s s u r e end the dependence approaches p, /T \^ i P  = / 1 \  the  r e l a t i o n s h i p expected from f r e e molecular flow  I V  2  c o n s i d e r a t i o n s w h i l e a t the higher p r e s s u r e end  the dependence  approaches  continuum  the p-^ = p  2  dependence expected from  considerations. (3)  Carbon R e s i s t o r Temperature The  apparatus was  Measurement.  temperature of the n o z z l e i n the atomic beam measured w i t h a 33-CL A l l e n B r a d l e y r e s i s t o r i n  one arm of a A.C. Wheats tone b r i d g e operated a t 1 K c y c l e as shown s c h e m a t i c a l l y i n F i g . l k b r i d g e to - 1 a t  liquid  0  I t was  possible  to n u l l the  helium temperatures.  The  null  r e s i s t a n c e a t near l i q u i d helium temperature as a f u n c t i o n of o s c i l l a t o r i n p u t v o l t a g e i s shown i n F i g . 15. of the b r i d g e was  Normal o p e r a t i o n  i n the p l a t e a u r e g i o n of t h i s curve where the  power d i s i p a t e d i n the r e s i s t o r was  so s m a l l that i t d i d not  i n f l u e n c e the r e s i s t a n c e o f the carbon r e s i s t o r .  The  calibration  of t h i s r e s i s t o r a t room 295°K, l i q u i d n i t r o g e n 77°K, and helium *t.2°K temperature i s shown i n F i g . 16.  liquid  The r e s i s t a n c e R  o f such a r e s i s t o r as a f u n c t i o n o f temperature T n o r m a l l y can be expressed by the r e l a t i o n s h i p  -  a ^ R  (C152)  -f-b  (  20)  h6  nozzle-skimmer pressure correction skimmer-collimator pressure correction  2°K Pw • 300°K  1 200 P  F i g . 13  w  300  (millitorr)  Thermal T r a n s p i r a t i o n C o r r e c t i o n s to Measurements o f Nozzle-Skimmer and SkimmerCollimator Pressure.  180  170  —  O  ©-^  —  160 (  • i  ;  150 '  -  ;  ^  »  140  C  . !  °  <  -  £  '20  UJ  cr 110  100  —  90 0  F i g . 15  :  ;  r •  10 20 AMPLITUDE  H !  ?  -  . ]..:„_ L ' J  30 40 50 60 S E T T I N G on hp oscJIIotor  70  80  90  Input Power Induced Heating o f Carbon R e s i s t o r Thermometer R e s i s t o r a t Near L i q u i d Temperature.  100  with  -r  1+8  k9  where a and  b are s u i t a b l e f i t t i n g  d o t t e d l i n e i n F i g . 16 p o i n t s w i t h a = 0.4-5  constants,,  i s a l e a s t squares  The  straight  f i t to the  experimental  and b = - 2 . 1 7 .  nrrrx  I 1  1  impedonce  transformer  scope  Fig.  B.  The  Ik  A.C. Bridge Used to Monitor R e s i s t o r Thermometer.  Hexapole Magnet. The  separate of  ^He  R e s i s t a n c e of Carbon ,  tapered hexapole magnet, 50  cm l o n g , used to  the p a r t i c l e s i n the two p o s s i b l e n u c l e a r s p i n s u b s t a t e s  i s shown i n F i g . 17.  by Axen ( A x 6 5 )  T h i s magnet was  to produce a near 100%  originally  s e p a r a t i o n of n u c l e a r s p i n  s t a t e s f o r a Mach k n o z z l e source o p e r a t i n g a t 2 . 2 ° K . measured f i e l d  designed  The  s t r e n g t h i n the r e g i o n of the p o l e t i p s as a  f u n c t i o n of the e l e c t r i c a l c u r r e n t through measured value of  the magnetic f i e l d  the c o i l s , and  the  s t r e n g t h as a f u n c t i o n o f  the r a d i a l d i s t a n c e from the c e n t r a l a x i s are shown i n F i g s .  .18  50 cms.  Figure 17-  .  :  J  _J «_  2-54 cms.  Dimension of the Components of the Hexapole Magnet  51  to CO  bO O H •H  W  a •H  Pole  •H  Pieces  O •H +5  CU  a to  P o s i t i o n o f Probe  20  0  Current  Increasing  •  Current  Decreasing  TO  E l e c t r i c a l Current F i g u r e 18.  oO  "50  i n Amperes  Magnetic F i e l d S t r e n g t h i n the Region o f t h e P o l e T i p s as a F u n c t i o n o f the E l e c t r i c a l C u r r e n t Through Coils.  ? and  19 r e s p e c t ! v e l y .  r = 2.5tor  The  average f i e l d g r a d i e n t i n the r e g i o n  = 3 n i m i s 7 0 , 0 0 0 gauss/cm while  f i e l d a t the p o l e Ce  The  t i p s Ho  2  the measured  i s 9000 gauss.  E l e c t r o n Bombardment I o n i z e r . The  i o n i z e r used i n t h i s experiment was  bombardment type i o n i z e r s i m i l a r  to one  b u i l t by Weiss (We6l)  but employing s i d e i n s t e a d of a x i a l e x t r a c t i o n . of the p r o t o t y p e  an e l e c t r o n  The  i o n i z e r i s d e s c r i b e d by Vermette  development  (V^^f).  Vermette used f i l a m e n t s w i t h r e c t a n g u l a r c r o s s s e c t i o n while the p r e s e n t  i o n i z e r ' s f i l a m e n t s are c i r c u l a r i n c r o s s s e c t i o n .  A schematic end  view of the i o n i z e r used i n t h i s experiment i s  shown i n F i g . 20.  The  diameter tungsten w i r e . rectangular of ^ . 7 5 " . biased)  f i l a m e n t s c o n s i s t of 5 lengths of 0 . 0 1 0 " The  a c t i v e i o n i z a t i o n volume has a  cross s e c t i o n 0.25" The  wide by 0.22"  high and  a length  i o n c u r r e n t i s c o l l e c t e d on a p l a t e ( n e g a t i v e l y  immediately a t the s i d e of the i o n i z e r and was  measured  using a Hewlett Packard Model *+25A DC microvolt-ammeter. e l e c t r o n i c s used are shown i n F i g . 2 0 A . was  The* above  The  technique  s u i t a b l e f o r measuring i o n c u r r e n t y i e l d s by i n t r o d u c i n g  c a l i b r a t i o n gases a t known p r e s s u r e s  i n t o the i o n i z e r chamber.  Measurement o f . i o n y i e l d s from the a c t u a l atomic beam complicated  by  the n e c e s s i t y to separate  the r e s i d u a l background gas separating  ion yield.  was  the i o n beam y i e l d The  from  l a c k of a bulkhead  the i o n i z e r r e g i o n from the magnet vacuum chamber  and  also excessive  was  mainly r e s p o n s i b l e f o r t h i s c o n d i t i o n .  were overcome by  outgassing  of the. i o n i z e r d u r i n g  operation  These two  difficulties  the i n s t a l l a t i o n of a beam chopper between the  Magnetic F i e l d i n Kilogauss  o  Radial Distance from Central Axis i n  Figure  19  o o  MMS.  Measured Value of' Magnetic F i e l d Strength as a Function of the Radial Distance from Central Axis.  grid - plot e separation ~ 0 2 2 filament widths = 0.25" f i l a m e n t terfgth =4.75"  plate  grid i  O  +200v  hp AI-V ammeter  <+)—%  4 O  ion collector  O  (  0 . 4 7 jjf  filament  F i g . 20  scope  signal  Schematic R e p r e s e n t a t i o n of I o n i z e r and Ion Measurement Apparatus. (A) D.C. C u r r e n t Measurement (B) Chopped C u r r e n t Measurement  F i g . 21  Two  slit  Chopper  55 end of the magnet and the entrance to the i o n i z e r .  The  motor  and r e f e r e n c e s i g n a l c i r c u i t used are i d e n t i c a l to those d e s c r i b e d i n chapter 5 f o r the t i m e - o f - f l i g h t  velocity-  measuring a p p a r a t u s . . The chopper used i n the i o n y i e l d measurement was  the same as that shown i n F i g . 21  essentially  except that the two s l o t s have been widened lengthened  to h cm.  The e l e c t r o n i c s  to 0.8  cm and  used i n making  the i o n  beam c u r r e n t measurement employing the chopper system i s shown in Fig.  20B. The i o n i z a t i o n e f f i c i e n c y o f the i o n i z e r  gas was  determined by s l o w l y r a i s i n g  the background p r e s s u r e  i n the i o n i z e r chamber and measuring the r e s u l t i n g The r e s u l t s are shown i n F i g . 22.  f o r hydrogen  ion yield.  The p r e s s u r e measurements  were made w i t h a B a y a r d - A l p e r t type i o n i z a t i o n gauge and were i n c r e a s e d by a f a c t o r o f 2.2  to a l l o w f o r the r e l a t i v e  s e n s i t i v i t y o f the gauge to hydrogen and n i t r o g e n , the gas f o r which the gauge i s c a l i b r a t e d . the  i o n i z e r during  The o p e r a t i n g c o n d i t i o n s o f  t h i s measurement are summarized  P l a t e and g r i d v o l t a g e  260  V  Plate + grid current  600  mA  The r e s u l t i n g  below.  i o n i z a t i o n e f f i c i e n c y o f the i o n i z e r  f o r hydrogen gas a t room temperature i s 6.5 y i e l d shown as a dashed l i n e on F i g . 22  A/Torr.  This  compares f a v o u r a b l y  w i t h the 6 A / T o r r r e p o r t e d by G l a v l s h (G168) of Auckland University  f o r a strong f i e l d  B r i t i s h Columbia i o n i z e r while  The University  has an i o n i z a t i o n volume o f k.2  the Auckland i o n i z e r  These volumes  axial ionizer.  has an e f f e c t i v e volume of 3«5  of  cm^ cm^.  are r e l e v a n t i n comparing i o n i z a t i o n y i e l d s o f the  56  57 background gas but are n o t the r e l e v a n t volume when c o n s i d e r i n g actual  beam i o n i z a t i o n e f f i c i e n c i e s .  depends more on the a c t i v e beam p a s s e s .  The l a t t e r  efficiency-  volume through which the atomic  The l e n g t h o f the i o n i z a t i o n  zone, Ik cm f o r the  Auckland i o n i z e r and 12 cm f o r the U.B.C. i o n i z e r , g i v e s a b e t t e r i n d i c a t i o n o f the i o n i z i n g a b i l i t y . ' ionizers  the two  appear r o u g h l y comparable but the Auckland i o n i z e r i s  much s u p e r i o r i n a t l e a s t field  On the s u r f a c e ,  rather  two - r e s p e c t s , f i r s t i t i s a strong  then weak f i e l d  higher p o l a r i z a t i o n  ionizer  thus a l l o w i n g  substantially  values and second i t s a x i a l d e s i g n  i n beam emittances much s u p e r i o r  to the s i d e  extraction  results ionizer.  58  CHAPTER V TECHNIQUES FOR MEASUREMENT OF ATOMIC BEAM INTENSITY AND A.  VELOCITY  Measurement of Atomic Beam I n t e n s i t y . Measurements of atomic beam i n t e n s i t y were a c h i e v e d  using a d i f f e r e n t i a l P i r a n i d e t e c t o r .  This detector, described  by J a s s b y ( J a 6 * + ) , has a s e n s i t i v i t y of 1 . 0 ^ 0 . 1 x l O ^ atoms/ 1  If sr  - sec -y&t-volt s i g n a l measured w i t h a  J a s s b y shows t h a t the r e l a t i v e f o r ^He  and ^He  He oven source beam.  s e n s i t i v i t y S of the d e t e c t o r  depends on the r a t i o o f s p e c i f i c  heats C  accomodation c o e f f i c i e n t s o£ o f the two gases a c c o r d i n g following  and  to the  relation  Se  „  C  Se  v  4  W c  Cv3  At room temperature identical;  y  °^ 4Ue  H e  <*- 3  the s p e c i f i c  (2D H  e  heats of the two gases are  thus the r a t i o reduces to  V  _  Thomas, Krueger-and H a r r i s the r a t i o cX^^ / c< ^ 3  e  tungsten a t 3 0 8 ° K as  ^He  (Th69)  ( 2 2 )  g i v e an e x p e r i m e n t a l value f o r  of accomodation c o e f f i c i e n t s on c l e a n  1.088i.029.  It i s unlikely  that the  tungsten f i l a m e n t s used i n our d e t e c t o r o p e r a t i n g a t 5 6 0 ° K w i l l be p a r t i c u l a r l y c l e a n ; n e v e r t h e l e s s  t h i s number i n d i c a t e s  approximate d i f f e r e n c e i n s e n s i t i v i t y of the gauge f o r ^Ee He  t h a t should be expected.  the and  59 Bo  The  T i m e - o f - F l i g h t Measuring Apparatus. The  a  v e l o c i t y of  time-of-flight  this  F i g . 23  system.  inside  of a 1*+  wide and  the  shows the main components of  diameter d i s k 0.8  cm  2 cm  long.  A  phototransistor  cm  i n the  displayed  chopper to the 2.5  i n diameter and  cm  the  shown i n F i g . 25.  on a T e k t r o n i x 56h  oscilliscope;  the  to e l i m i n a t e  57°^  was  chopper r o t a t i n g  S(t)  the  i s shown to be r e l a t e d  d i s t r i b u t i o n function  I(v)  the  The  the  signal  being  the  directions  triggered The then  beam.  time-of-flight  to the d i f f e r e n t i a l f o r the  was  the  the measured f l i g h t p a t h are  shape of  high  reference  chopped.  the most probable v e l o c i t y of  I n Appendix D  low  to i n a c c u r a t e mechanical  the atomic, beam was  to c a l c u l a t e  The  i n both c l o c k w i s e  s l i g h t l y before or a f t e r  used  cm.  Measurements i n both  e r r o r s due  times and  ionization  t r i g g e r and  i n the p h o t o t r a n s i s t o r  two  the  removed by  alignment which r e s u l t e d  the  the l e n g t h of  used to t r i g g e r the  at  The  o s c i l l i s c o p e screen.  counterclockwise d i r e c t i o n s .  average of  located  high frequency s i g n a l  time s e p a r a t i o n of  measured w i t h the  were r e q u i r e d  long was  slots  the d i s k  center of  s i g n a l was  The  s i g n a l from the p h o t o t r a n s i s t o r  p u l s e was  r e v e r s i b l e motor  c i r c u i t shown i n F i g . 2h,  f r e q u e n c y e l e c t r o n i c n o i s e on pass f i l t e r  21  thick with 2  t r i g g e r r e f e r e n c e s i g n a l i s p r o v i d e d by  f l i g h t p a t h from the  gauge 2.5  The  mm  vacuum chamber i s capable of r e v o l v i n g  3 0 , 0 0 0 rpm.  and  measured u s i n g  chopper used i n t h i s system i s shown i n F i g .  consists  each 2 mm  the  atomic beam was  system. The  and  the  signal  intensity  case of an i n f i n i t e l y  short  60  chopper  disk  motor 2.5  beam axis  2 . 5 cm  0 ^ p h o t o transistor ion  gauge  F i g , 23  Schematic R e p r e s e n t a t i o n o f T i m e - o f - F l i g h t V e l o c i t y Measurement Equipment.  -o 7.5 volts I M  1.5 K ^ output  F P T - 100  F i g . 2*+  Photo t r a n s i s tor Reference S i g n a l  Circuit.  shutter  f u n c t i o n and d e t e c t o r  S(-t)  -  Cor\s+an+  LoKere  V -  '  _L  l e n g t h by the r e l a t i o n s h i p X (V)  (  D  1  )  t  For a g i v e n I ( v ) the f u l l width a t h a l f maximum FWHM o f the s i g n a l S ( t ) i s used to o b t a i n the Mach number M o f the beam.  a ion gouge signal b r e f e r e n c e signal |  1  I  1000 pf '  ion gouge I detector i  500K textronix 5 6 4 ~, . storage -Oinpufa scope Q in put b friggg  L  high pass filter  Q  _____  D  light photo transistor Fig.  25  Schematic o f I o n Gauge S i g n a l C i r c u i t , Reference S i g n a l and O s c i l l i s c o p e D i s p l a y .  The e f f e c t a f i n i t e w i d t h r e c t a n g u l a r  shutter  f u n c t i o n and d e t e c t o r l e n g t h has on the s i g n a l shape S ( t ) are a l s o c o n s i d e r e d the F ¥ H M A t  Q  i n Appendix D.  The r e l a t i o n s h i p between  o f the s i g n a l S ( t ) w i t h an i n f i n i t e l y  f u n c t i o n and the FWHM A t f o r a r e c t a n g u l a r  thin shutter  shutter function  o f f i n i t e w i d t h T i s shown i n F i g . 26. The c a l c u l a t i o n o f _ t  J .1  F i g . 26  1  I .3  M i l .6  11! 1  \\  I  I 3  I I I 6  1 111 \ 10  Broadening of Experimental S i g n a l due to F i n i t e Width S h u t t e r F u n c t i o n . Nozzle Beam Curve Includes C o r r e c t i o n f o r a 2.5 cm D e t e c t o r Length.  ON  63 was  done f o r a d e t e c t o r l e n g t h o f 2.5 * cm.  Thus w i t h the a i d  1  of  F i g . 26 the FWHM o f the experimental  to  the t h e o r e t i c a l s i g n a l A t  s i g n a l A t was r e l a t e d  and hence to a Mach number M o f  the d i f f e r e n t i a l i n t e n s i t y d i s t r i b u t i o n f u n c t i o n I ( v ) ,  Also  shown on t h i s f i g u r e are some s i m i l a r r e s u l t s obtained by Becker and Henkes (Be56b) f o r a d i f f e r e n t i a l  intensity  d i s t r i b u t i o n f u n c t i o n a r i s i n g from an oven beam w i t h a Maxwellian in  velocity distribution.  I n the c a l c u l a t i o n g i v e n  Appendix D the s h u t t e r f u n c t i o n i s assumed r e c t a n g u l a r .  Although  the r e a l s h u t t e r f u n c t i o n i s c o n s i d e r a b l y more  complicated,  the consequence o f the approximations  resulting  in  the assumption o f a r e c t a n g u l a r s h u t t e r f u n c t i o n are shown  to  be s m a l l .  With the time o f f l i g h t geometry shown i n F i g . 23  the i n t e n s i t y d i s t r i b u t i o n as a f u n c t i o n o f time o f a group o f p a r t i c l e s p a s s i n g through  the chopper s l i t  i n t e n s i t y p r o f i l e o f the atomic s o l i d angle of  depends mainly on the  beam a t the chopper and the  subtended by the i o n gauge.  The speed o f r o t a t i o n  the chopper, the chopper s l i t width and other  parameters are a l s o c o n s i d e r e d i n determining  geometrical  the r e a l s h u t t e r  function. From the geometry o f the experimental p a r t i c l e s eminating  arrangement o n l y  from the n o z z l e w i t h i n a cone subtended by  the e x t r e m i t i e s o f the i o n gauge d e t e c t o r enter the d e t e c t o r . Hence, a t the chopper l o c a t i o n , e f f e c t i v e diameter  o f 5.3 mm.  the beam has a t most an As i s shown i n F i g . 38 the  a c t u a l measured beam p r o f i l e a t the chopper l o c a t i o n had a FWHM o f 7 mm.  The i n t e n s i t y i n the c e n t r e 5.3 mm wide  v a r i e d about ± \ % f  r 0  m  strip  the average o f i t s value a t the s i d e  6k of  t h i s r e g i o n and  intensity profile assumption Implies  the peak value  a t the c e n t r e .  Thus the beam  can be assumed to be r e c t a n g u l a r . that the beam c r o s s s e c t i o n i s not  but i s i n f a c t square.  Hagena, S c o t t , and  This circular  Varma (Ha67b) have  shown f o r the case o f a s h u t t e r width equal to the w i d t h of the beam that t h i s approximation had of  the s h u t t e r  function.  of p a r t i c l e s p a s s i n g i s shown i n F i g .  e f f e c t on  With these assumptions and  t a n g e n t i a l chopper v e l o c i t y ' o f 35 experimental c o n d i t i o n s ,  little  the shape an average  m/sec, c o r r e s p o n d i n g to  our  the c a l c u l a t e d i n t e n s i t y d i s t r i b u t i o n  through the chopper as a f u n c t i o n of  time  27.  _  ( l d i v . = 0 . 0 2 8 ms) F i g . 27  Assumed I n t e n s i t y P r o f i l e of P a r t i c l e s Passing through the Chopper Opening (Shutter F u n c t i o n ) . T r a n g e n t i a l Chopper V e l o c i t y = 35 m/sec.  To a p p l y p r o p e r l y  the r e s u l t s o f Appendix D t h i s i n t e n s i t y  d i s t r i b u t i o n must a l s o be assumed approximately r e c t a n g u l a r . i n shape.  As w i l l be d e s c r i b e d  i n s e c t i o n 6B,  the e x p e r i m e n t a l s i g n a l as a r e s u l t of  the c o r r e c t i o n to  the f i n i t e  w i d t h i s s u f f i c i e n t l y s m a l l , l e s s than 5%,  that  chopper  the  65 approximations made i n d e r i v i n g produce any s i g n i f i c a n t  errors.  the c o r r e c t i o n formula do not  66 CHAPTER VI RESULTS OF STUDIES OF THE A.  ATOMIC BEAM  The Atomic Beam I n t e n s i t y . The atomic  beam source p r e v i o u s l y d e s c r i b e d has  t e s t e d under many v a r y i n g c o n d i t i o n s . n o z z l e diameter  such as  d, skimmer diameter, nozzle-skimmer  Xs, s t a g n a t i o n p r e s s u r e p been v a r i e d and  Parameters  the  separation  and s t a g n a t i o n temperature  0  been  T  0  have  the r e s u l t i n g beam i n t e n s i t y I measured.  T y p i c a l data are p r e s e n t e d f o r . 0 . 2 mm  and 0.025 mm  diameter  nozzles. Beam i n t e n s i t i e s  f o r a 0.2  mm  diameter n o z z l e as a  f u n c t i o n of n o z z l e p r e s s u r e f o r p a r t i c u l a r s e p a r a t i o n s and Fig.  28.  diameter was  15  The  the n o z z l e a t room temperature  skimmer and c o l l i m a t o r were 0.6  r e s p e c t i v e l y while  cm.  nozzle-skimmer are shown i n mm  the skimmer-detector  and 1 mm  in  separation  The i n t e r p r e t a t i o n of these contours i n the manner  d e s c r i b e d i n Chapter  III  i s most c l e a r l y seen by c o n s i d e r i n g  c r o s s s e c t i o n s o b t a i n e d a t f i x e d s t a g n a t i o n p r e s s u r e s and varying  the nozzle-skimmer  i s p r e s e n t e d i n F i g . 29 Fig.  28.  separation.  Such a s e t of curves  f o r the room temperature  data of  With the e x c e p t i o n of one or two p o i n t s the data  p o i n t s were f i t t e d w i t h a smooth c u r v e .  The d i f f i c u l t y i n  p r o d u c i n g completely c o n s i s t e n t data can be a t t r i b u t e d l a c k o f p r o f i l e s a t a s u f f i c i e n t number of separations,  the d i f f i c u l t y of keeping  to the  nozzle-skimmer  the d e t e c t o r alignment  e x a c t l y .the same between runs when the system was  disassembled  NOZZLE-SKIMMER F i g . 29  SEPARATION (nozzle d i a m e t e r s )  Room Temperature Beam I n t e n s i t y P r o f i l e s as a F u n c t i o n o f Nozzle-Skimmer  Separation.  69 and  reassembled  to vary the nozzle-skimmer s e p a r a t i o n , and the  a c c i d e n t a l l y enforced  use of a d i f f e r e n t n o z z l e f o r the  measurements a t a s e p a r a t i o n of 5 n o z z l e diameters.  The room  temperature data shown i n F i g . 30 was obtained w i t h the a d j u s t a b l e nozzle-skimmer apparatus. of  the d e t e c t o r remained f i x e d  The p h y s i c a l  throughout  alignment  the measurement and  the nozzle-skimmer s e p a r a t i o n was a d j u s t e d from o u t s i d e the vacuum system.  The l a r g e number o f data p o i n t s can be  w i t h v e r y smooth c u r v e s .  Although  the n o z z l e and skimmer used  i n o b t a i n i n g the data o f F i g . 30 were approximately diameter as those  fitted  the same  used i n o b t a i n i n g the data o f F i g . 2 9 ,  a r e not the same n o z z l e and skimmer.  This accounts  they  f o r the  d i f f e r e n c e s i n a b s o l u t e I n t e n s i t i e s and nozzle-skimmer s e p a r a t i o n s r e p o r t e d f o r the peaks and v a l l e y s , however, the g e n e r a l shape of the p r o f i l e s remains the same. The r e s u l t s shown i n these  two f i g u r e s i l l u s t r a t e the  t y p i c a l dependence of beam i n t e n s i t y on nozzle-skimmer  separation  o b t a i n e d w i t h s u p e r s o n i c n o z z l e systems, namely, the l a r g e beam i n t e n s i t y a t v e r y s h o r t nozzle-skimmer s e p a r a t i o n s f o l l o w e d by a r e d u c t i o n i n i n t e n s i t y to a minimum f o l l o w e d by a f u r t h e r i n c r e a s e i n i n t e n s i t y to a maximum and subsequent a t t e n u a t i o n . T h i s behaviour- i s due to the e f f e c t s d e s c r i b e d i n Chapter I I I . For v e r y s m a l l nozzle-skimmer s e p a r a t i o n s  the beam passes  through the skimmer w i t h no i n t e r a c t i o n and then expands as a f r e e j e t downstream o f the skimmer. increased  As the s e p a r a t i o n i s  the beam i s i n f l u e n c e d by the skimmer and e v e n t u a l l y  the "skimmer i n t e r a c t i o n " d e s c r i b e d p r e v i o u s l y takes i t s maximum e f f e c t .  F u r t h e r s e p a r a t i o n o f the n o z z l e and skimmer  NOZZLE PRESSURE P T = 7 7 'K. T = 295°K • ! 0 TORR A 34 A O 83 140 O c  o 0 ^  5  o x O xx ****  —x  oo^* Po o Co.-  o O  O  A t  0  0  3  <3»  A A  PAAA  o  0<  AA  A* O Ox ^O *A*6cP A  A  :  A  O V A O * 2 ' 4  AA&  t3 • • • • •  A  D^d  •  •  o&  0  :  4  :  °o •  6  E  0 F i g . . 30  5 10 15 20 25 30 NOZZLE-SKIMMER SEPARATION  35  L/D  Continuous Beam P r o f i l e Taken w i t h A d j u s t a b l e Nozzle-Skimmer Assembly,  71 r e s u l t s i n a r e d u c t i o n of the gas d e n s i t y a t the entrance.  skimmer  Reduced gas d e n s i t y a t the.skimmer i m p l i e s reduced  skimmer i n t e r a c t i o n so that the beam i n t e n s i t y i n c r e a s e s .  As  the s e p a r a t i o n gets even l a r g e r the skimmer becomes downstream o f the Mach d i s k and  background gas  s c a t t e r i n g becomes more  and more s i g n i f i c a n t , e v e n t u a l l y overwhelming any beam i n t e n s i t y due The  to reduced skimmer  appearance of the  by Campargue (Ca66)  then reaches a maximum and A similar data  'maximum maximorum' d e s c r i b e d  e x a m i n a t i o n of the data  the peak i n t e n s i t y grows s l o w l y thereafter f a l l s o f f .  shows a behaviour s i m i l a r  to the room  c o n s i d e r a b l y lower than i n  This "compression o f contours"  is  the higher gas d e n s i t i e s , hence much s m a l l e r mean  f r e e paths and  greater s c a t t e r i n g f o r a given nozzle  the lower temperature.  skimmer i n c r e a s e starts  An  though with much l e s s prominent maxima, f o r  the room temperature case.  at  temperature  the p r o f i l e s shown i n F i g . 3 2 .  a s e t of n o z z l e s t a g n a t i o n p r e s s u r e s  caused by  30 where f o r  treatment of the l i q u i d n i t r o g e n  shown i n F i g , 3 1 g i v e s  temperature d a t a ,  interaction.  i s seen i n both F i g s . 29 and  i n c r e a s i n g nozzle pressures  increase i n  Also  the higher gas d e n s i t i e s a t  the skimmer i n t e r a c t i o n .  openings.  the  Another e f f e c t which  to become e v i d e n t a t higher p r e s s u r e s  temperatures i s beam f o r m a t i o n  pressure  and  lower  from the skimmer or c o l l i m a t o r  T h i s e f f e c t causes i n c r e a s e d beam i n t e n s i t y f o r  increased stagnation pressures separations. the l i q u i d  a t l a r g e nozzle-skimmer  More w i l l be s a i d about t h i s w h i l e d i s c u s s i n g  helium  c o o l e d beams i n the next paragraph.  A s i m i l a r p l o t of i n t e n s i t y as a- f u n c t i o n of n o z z l e -  NOZZLE - SKIMMER  SEPARATION (nozzle  diameters)  F i g . 3 2 L i q u i d N i t r o g e n Temperature Beam I n t e n s i t y P r o f i l e s as a F u n c t i o n o f Nozzle-Skimmer S e p a r a t i o n .  skimmer s e p a r a t i o n u s i n g the n o z z l e s t a g n a t i o n p r e s s u r e as a parameter i s shown i n F i g . 33 f o r the data d i s p l a y e d i n F i g . 3*+. liquid due  This data was obtained w i t h  helium  temperature.  to the g r e a t compression  the n o z z l e c o o l e d to  The l a r g e s c a t t e r o f p o i n t s i s o f the peaks and v a l l e y s i n t o a  n o z z l e p r e s s u r e range o f o n l y a few Torr and the dominant r o l e p l a y e d by the f o r m a t i o n o f s u b s i d i a r y beams from the skimmer and  c o l l i m a t o r . With e x p e r i m e n t a l  r e s u l t s f o r so few n o z z l e -  skimmer s e p a r a t i o n s and because o f the s c a t t e r o f the observed points  the c o n s i s t e n t trends do n o t appear as i n the data  p o i n t s o b t a i n e d a t higher n o z z l e  temperatures.  The g r a d u a l  r i s e i n i n t e n s i t y a t l a r g e nozzle-skimmer s e p a r a t i o n s i s c o n s i s t e n t w i t h a r e d u c t i o n o f the gas flow p a s t the skimmer and  hence a r e s u l t i n g r e d u c t i o n o f p r e s s u r e i n the skimmer-  c o l l i m a t o r r e g i o n and downstream o f the c o l l i m a t o r . improved background p r e s s u r e r e s u l t s i n improved of  The  transmission  s u b s i d i a r y beams from the skimmer and c o l l i m a t o r and the  r e s i d u a l n o z z l e beam.  The a c t u a l beam i n t e n s i t y versus  nozzle  p r e s s u r e p r o f i l e s measured a t a f i x e d nozzle-skimmer s e p a r a t i o n are o f c o n s i d e r a b l y more i n t e r e s t i n t h i s case.  For the  profile  a t a s e p a r a t i o n o f 19«5 n o z z l e diameters  shown i n  Fig. 3  the beam i n t e n s i t y i n the r e g i o n up to the f i r s t  L  maximum which occurs a t a n o z z l e p r e s s u r e o f 1 Torr i s attributed  to a true n o z z l e beam.. The r e d u c t i o n o f beam  i n t e n s i t y f o r higher n o z z l e p r e s s u r e s i s a t t r i b u t e d  to the  dominance o f background gas s c a t t e r i n g i n the nozzle-skimmer region.  The subsequent i n c r e a s e i n beam i n t e n s i t y i s caused  by the combined e f f e c t o f a s m a l l r e s i d u a l nozzle beam along  nozzle pressure X I torr 0 2 torr EI 10 t o r r A 2 0 torr j 5 0 torr  A  o 5  o  O  "5  O  C/)  _ _  0  1 10  20  NOZZLE-SKIMMER Fig.  33  30  1  S E P A R A T I O N (nozzle-diameters)  Beam I n t e n s i t y P r o f i l e s as a F u n c t i o n o f Nozzle-Skimmer w i t h the Nozzle a t L i q u i d Helium Temperature.  Separation  .  77  w i t h a s u b s i d i a r y beam from the skimmer and c o l l i m a t o r openings. In data o b t a i n e d  w i t h a s m a l l e r n o z z l e , d e s c r i b e d i n the next  paragraph, the p r e s s u r e is  range over which the f i r s t peak occurs  expanded c o n s i d e r a b l y and the a c t u a l behaviour o f the n o z z l e  beam i s much e a s i l y determined. predictions w i l l Fig.  Comparison with  theoretical  be d e s c r i b e d i n d e t a i l i n that s e c t i o n .  35 shows r e s u l t s obtained with a 0 . 0 2 5 mm  diameter n o z z l e a t room, l i q u i d A 0.57  temperatures.  n i t r o g e n , and l i q u i d  helium  mm diameter skimmer and a 1 mm  c o l l i m a t o r were used f o r these measurements.  diameter  The n o z z l e -  skimmer s e p a r a t i o n was s e t a t 0.28 cm and the skimmer d i s t a n c e a t 16 cm. results  F i g . 36 shows i n g r e a t e r d e t a i l the  using both ^Ee and ^ e  l i q u i d helium  temperature.  beams w i t h  i s due to background gas  i n the nozzle-skimmer r e g i o n .  by assuming the beam i n t e n s i t y I should to  the n o z z l e p r e s s u r e  p  \~p~ )  v  0  with p I  0  = I e D  s  Po*  T  ^  e  This can be checked be l i n e a r l y p r o p o r t i o n a l  and the s c a t t e r i n g p r e s s u r e  0  be l i n e a r l y p r o p o r t i o n a l to p log  the n o z z l e c o o l e d to  I n both - f i g u r e s the d e v i a t i o n from  a l i n e a r r e l a t i o n with pressure scattering  detector  0  also.  should  F i g . 37 shows a p l o t of  observed l i n e a r decrease of i n t e n s i t y .  i s c o n s i s t e n t w i t h s c a t t e r i n g of the beam a c c o r d i n g to (18)  where I , the beam i n t e n s i t y with no 0  s c a t t e r i n g , and n, the gas d e n s i t y i n the nozzle-skimmer are both assumed  to be p r o p o r t i o n a l to the n o z z l e p r e s s u r e  or i s the e f f e c t i v e s c a t t e r i n g c r o s s s e c t i o n and along  region,  the beam a x i s .  X  p ? 0  the d i s t a n c e  The d i f f e r e n c e i n the slopes f o r 3 j j  e  a  He i n F i g . 37 i n d i c a t e s that the e f f e c t i v e s c a t t e r i n g c r o s s  n  d  o <u  v> 4 . 4 I  4.2 tn E 4.0 o 3.8  O 3.6 >-  _ _  3.4 3.2 3.0  I  G)  I  2.8 2.6 < UJ CQ  /  /A  ' 0  2.4 2.2  A  2.0  0  1.8 1.6  -  /  i  i  /A  /  /  1.4 1.2 /  1.0  A  /A  •  0.8  4  He  ROOM  a  4  He  LN T  O  4  He  LHeT  © He  LHeT  A  3  ©  0.6  a  TEMP,  2  / A  0.4 0.2 0  V. i/  0  100  200  300  400  5,00  600  700  NOZZLE  800 PRESSURE  (TORR)  Fig.  35  P  0  0  10  20  30  40  50  60 P  Fig. 36  0  70  80  (TORR)  Beam I n t e n s i t i e s f o r ^Ee and ^He Beams a t L i q u i d Helium Temperature Before and A f t e r Correction f o r Scattering. Only the u n c o r r e c t e d experimental p o i n t s are shown when the c o r r e c t i o n i s s m a l l .  90  F i g . 37  The U n c o r r e c t e d Data of F i g . 36 D i v i d e d by the Nozzle Pressure to V e r i f y E x i s t a n c e of S c a t t e r i n g .  81 is.1.7  s e c t i o n f o r ^He  times l a r g e r  than that of - % .  e x p e r i m e n t a l v i s c o s i t y measurements and  quantum mechanical  c a l c u l a t i o n s a l s o i n d i c a t e a l a r g e r cross The  d i f f e r e n c e i n cross  state  i n the 3He The  H e  a n d  system  2  s  e  n  c  e  o f  a  to the d i f f e r e n t n  e  a  stationary  r  are  predicted  and a 3ne  the ^ e  The  s 1.9  The  : 9.5..  slopes  of  5 and  Eqs.  The  0  A5 p r e d i c t  3.3°K.  82 and  measurements, d i s c u s s e d  liquid  to pass in  the  the i n t e n s i t y should pressure the  p  Q  nozzle  s t r a i g h t l i n e s confirm  dependence; t h e i r slopes  temperatures 295,  these l i n e s are  to the square r o o t o f  temperature T .  0  and  to the n o z z l e s t a g n a t i o n  inversely proportional  The  data, s i m i l a r l y  dashed l i n e s are r e q u i r e d  be d i r e c t l y p r o p o r t i o n a l  stagnation  using  beam.  f o r s c a t t e r i n g a t room, l i q u i d n i t r o g e n  through the o r i g i n .  linear p  b  = 6.7°K, D = 0.025 mm  0  helium temperatures.  and  a  ^He.  (Bo51).  dashed l i n e s shown i n F i g . 35  ratio 1  t h Q  s t r a i g h t l i n e i n F i g . 36 was  Eq. A5 assuming T  corrected  section for  section is attributed  by 3  s t a t i s t i c s followed  Both  e  would correspond  the  to  However, v e l o c i t y  later, indicate  temperatures  of  i  295,  77  and  7°K  so  that the  appear to break do\^n Eqs. be  5 and  larger for 3  H e  that  A5 p r e d i c t  the -'He  than the ^ e A  N  D  H^Q  L  9$ lower d e t e c t o r  N  I  G  dependence would  temperatures.  that  to the  the beam i n t e n s i t y should  square r o o t of  the  i n t e n s i t y should be a f a c t o r  intensity. F  Q  a t v e r y low  inversely proportional  mass, so  theoretical T ^  >  26  The  e q u a l i t y of the  is p a r t i a l l y attributable  s e n s i t i v i t y expected f o r 3ne,  as  atomic 3  J  slopes to  the  discussed  in  S e c t i o n 5A.  There remains, however, a 6% d i s c r e p a n c y  which c o u l d be due e i t h e r  to a s t i l l  larger difference i n  s e n s i t i v i t y f o r ^Ee and ^He, or to an e f f e c t i n the n o z z l e system not taken account of i n the simple theory. A ^e  beam v e r t i c a l p r o f i l e  skimmer i s shown i n F i g . 38.  I t has a. f u l l width a t h a l f  7 mm (2.5°) and  maximum (FWHM) o f  taken 16 cm from the  a f u l l width of Ih  mm.  p r o f i l e was  taken w i t h a n o z z l e s t a g n a t i o n temperature  pressure of  77°K  and  L  20 Torr  Gas flow through the  0.025 mm  diameter n o z z l e i s  c c / s e c (STP) f o r ^He gas a t p  and l i q u i d  temperatures.  B.  and  respectively.  e s t i m a t e d a t 0.17 helium  The  0  = 50 Torr  The Beam V e l o c i t y . A t i m e - o f - f l i g h t measuring  apparatus was used to  measure the most probable v e l o c i t y and v e l o c i t y d i s t r i b u t i o n of  ^He and ^He beams produced u s i n g the c r y o s t a t a t room,  l i q u i d n i t r o g e n and l i q u i d these temperatures  helium temperatures.  For Sle  at  the measured most probable v e l o c i t i e s were  1660, 850 and 270 m/sec  r e s p e c t i v e l y , using the  0.025  mm  diameter n o z z l e and the t i m e - o f - f l i g h t geometry d i s c u s s e d i n section 5B.  Using the form of t h e . d i f f e r e n t i a l  d i s t r i b u t i o n g i v e n by Eq. 17, v e l o c i t y determined  liquid  to the most probable  the temperature  77 and 7°K w h i l e s t i l l At  fits  intensity  of the n o z z l e to be  295,  a l l o w i n g a wide range of Mach numbers.  helium temperatures  probable v e l o c i t y of 310  the ^Ee beam had a measured most  meters/sec.  The $Ee and ^He  >-  i  1  T  i  CO  0  LU i-  ©  i  r  r  \  .0  \  /  Q  bJ N  9  _!  <  DI  \  O  o J  o / 0. J _ _ _  J_  '  -7 -6 -5 -4 -3 - 2 - 1  '  0  '  1 2  '  '  3 4  5  6  7  V E R T I C A L DISPLACEMENT F i g . 38  (mm)  Normalized i n t e n s i t y P r o f i l e v s . V e r t i c a l Displacement from Beam A x i s S t a g n a t i o n Pressure Po = *f20 Torr S t a g n a t i o n Temperature To = 77°K  CO  v e l o c i t i e s s h o u l d d i f f e r o n l y be a f a c t o r p r o p o r t i o n a l to the square r o o t o f t h e i r masses eg. | lUi^ ^  =  f 4" '  = 0.865.  E x p e r i m e n t a l l y a r a t i o o f 270/310 = 0.87 was o b t a i n e d i n good agreement w i t h the expected dependence. The d i f f e r e n c e between 7 ° K and H-.2°K, the temperature of the l i q u i d  helium, i s a t t r i b u t e d  td poor  thermal c o n t a c t  between the n o z z l e and the c r y o s t a t and a thermal g r a d i e n t due  to the heat l e a k to the n o z z l e assembly.  A temperature o f  7 ° K i s c o n s i s t e n t w i t h carbon r e s i s t o r measurements of the nozzle  temperature which i n d i c a t e d a temperature on the o u t s i d e  of the n o z z l e o f 8 . 5 ° K .  The measurement o f the temperature  using a carbon r e s i s t o r i s d i s c u s s e d i n S e c t i o n H A 3 . A  t y p i c a l 3He t i m e - o f - f l i g h t spectrum o b t a i n e d w i t h  a chopper speed o f 11,000 rpm i s shown i n F i g . 3 9 .  In this  measurement the n o z z l e temperature was reduced s l i g h t l y by pumping on the helium r e s e r v o i r .  A v e l o c i t y spectrum d e r i v e d  from the time spectrum i s shown i n F i g . ho.  The experimental  s i g n a l w i t h a FWHM o f 53 m/sec i s f i t t e d q u i t e w e l l by the dashed  t h e o r e t i c a l curve o b t a i n e d from Eq. 17 w i t h the same  FWHM and most probable v e l o c i t y using a s t a g n a t i o n T  = 0  5 . 9 ° K and a Mach number M = 1 0 .  The chopper  temperature  distribution  f u n c t i o n shown' i n F i g . 27 has a FWHM T = 0.1^3 ms and the FWHM of the e x p e r i m e n t a l s i g n a l i s resolution R =  = 2.6.  broadening o f A t - A t  0  A t = 0.37 ms; thus the  From F i g . 26 t h i s corresponds to a  = k% where  At  0  i s the width o f the  A to  i d e a l d i s t r i b u t i o n which would have been o b t a i n e d had the shutter s l i t  and the d e t e c t o r width been i n f i n i t e l y  thin.  The  ail.  . 1  :  F i g . 39  ?  I  .  i l l  1  .. i  L  6  :  ist.  '  '., •'-•|  =  ,./\  Typical 3 T i m e - o f - F l i g h t Spectrum f o r L i q u i d Helium Cooled Nozzle. Stagnation Pressure i s 36 T o r r . H o r i z o n t a l Time Scale i s 0.5 m s e c / d i v . The Upper Trace shows the Time Reference L i g h t P u l s e . H E  #  1  98  w  •  Fig.  is.  • :  as  T y p i c a l I o n i z e r S i g n a l s from Chopped Atomic Beam w i t h Hexapole Magnet Turned On and Off, H o r i z o n t a l Scale 0.5 ms/dlv. V e r t i c a l Scale 0.5 mv/div.  1.0 /  £ 0.9 co  o^e  0.8  5  /  G  i  To= 5 . 9 ° K , M-10 FWHM=53 m/sec  0 7 [  NI  experimental results FWHM = 5 3 m / s e c  \  0.6  O  o z 0.5  \  o  0.4  o  0.2  I  o.ih  :  0_L 200  250  300 VELOCITY  F i g . 40  350  400  ( M/ SEC)  R e s u l t s of F i g . 3 9 Converted i n t o a V e l o c i t y Spectrum. The curve shown i s a f i t o f Eq. 1 7 to the e x p e r i m e n t a l spectrum.  co ON  87 approximations  made here should not s i g n i f i c a n t l y i n c r e a s e  t h i s v a l u e o f h%. correction  Because o f the s m a l l s i z e o f the r e s u l t i n g  i t w i l l be n e g l e c t e d .  The  experimental r e s u l t s  shown i n F i g . ko were  o b t a i n e d w i t h a n o z z l e s t a g n a t i o n p r e s s u r e of 36 T o r r . t h i s p r e s s u r e and a s t a g n a t i o n temperature  of 5.9°K the  c o r r e s p o n d i n g n o z z l e s t a g n a t i o n Knudsen number i s 1,8 Using Eq. 13  the t e r m i n a l Mach number i s c a l c u l a t e d  x  10"^.  to be 15  the e x p e r i m e n t a l data shown i n F i g . 8 i n d i c a t e s  while  For  that f o r  He a t t h i s Knudsen number the t e r m i n a l Mach number would be 12,  T h i s i s i n good agreement w i t h  the experimental  d e t e r m i n a t i o n o f M = 10 c o n s i d e r i n g that the r e a l width o f the measured d i s t r i b u t i o n i s a c t u a l l y result  s l i g h t l y narrower and as a  the Mach number w i l l be s l i g h t l y h i g h e r . I t should be noted  that no i n d i c a t i o n  f r a c t i o n of the beam was observed That i s , no second  i n the v e l o c i t y measurements.  peak a t a lower v e l o c i t y corresponding to  a condensed f r a c t i o n o f the beam appeared spectrum.  beam f o r m a t i o n .  later)  i n the  time-of-flight  The appearance o f a second peak has been d e s c r i b e d  by Becker, B i e r  expected  of a condensed  and Henkes (Be56) as being t y p i c a l o f condensed The good agreement between the measured and  polarization  of the ^He beam (as w i l l be mentioned  i s c o n f i r m a t i o n that a t most a very s m a l l f r a c t i o n o f  the beam was condensed.  88  CHAPTER V I I POLARIZATION AND IONIZATION OF THE H e BEAM 3  Ac  The T r a j e c t o r i e s o f Atoms through  the Hexapole Magnet.  The development o f the e q u a t i o n s d e s c r i b i n g the trajectories of p a r t i c l e s  through  the hexapole  magnet has  been d e s c r i b e d by Axen (Ax65) and i s summarized i n Appendix C. The p o s i t i o n and s l o p e o f a f o c u s s e d p a r t i c l e i n the tapered s e c t i o n o f the magnet i s g i v e n by E q s . C32 and C3*+ as a f u n c t i o n o f the r a d i a l p o s i t i o n o f the p a r t i c l e a t the magnet entrance.  The r a d i a l p o s i t i o n and d i v e r g e n c e  p a r t i c l e i s g i v e n by E q s . C36 and C 3 7 .  o f the d e f o c u s s e d  The p o s i t i o n and s l o p e  o f the p a r t i c l e s i n the p a r a l l e l s e c t i o n o f the magnet were c a l c u l a t e d u s i n g E q s . C 2 5 and C26 i n the case o f the f o c u s s e d p a r t i c l e and E q . C27 i n the case o f the d e f o c u s s e d  particle.  The i n i t i a l p o s i t i o n and s l o p e o f the p a r t i c l e as i t e n t e r s the p a r a l l e l s e c t i o n i s d e t e r m i n e d  from the s o l u t i o n o f the  t r a j e c t o r i e s a t the end o f the t a p e r e d s e c t i o n s . The hexapole most p r o b a b l e  magnet was d e s i g n e d  v e l o c i t y o f 175 m e t e r s / s e c .  d i s c u s s e d i n the p r e c e e d i n g  f o r a beam w i t h a As has been  s e c t i o n the beam produced had a  c o n s i d e r a b l y higher v e l o c i t y .  T h e - c a l c u l a t i o n s o f the p o s i t i o n  and s l o p e s o f p a r t i c l e s a t c e r t a i n l o c a t i o n s i n the magnet f o r v a r y i n g r a d i a l d e f l e c t i o n s a t the magnet e n t r a n c e and v a r y i n g s e p a r a t i o n o f the magnet from the n o z z l e source a r e summarized i n Table 2.  I n these c a l c u l a t i o n s the f i e l d H  t i p s o f the magnet was 9000 g a u s s .  Q  a t the p o l e  Typical trajectories of.the  Table 2 S e l e c t e d T r a j e c t o r i e s of Focussed and Defocussed •^He Atoms Passing Through the Tapered Hexapole Magnet FOCUSSED  TRAJECTORIES  R = radial deflection S = slooe Particle Velocity (m/sec)  R a d i a l Deflection) 5 cm At End of At End of a t entrance to magnet (cm) Taper Magnet 0.025 0.05 0.075  245  SOURCE-MAGNET SEPARATION  .  0.1717 0.0003 0.3433 0.0007  R=0.o44 S=0.00095 0.087 0.0019 0.13 0.0029. 0.17 0.0038 0.22 0.0047  0.055 -0.0004 0.109 -0.0007 0.1644 -0.0011 0.215 -0.0014  0.0425 0.0009 0.0847 '0.0017 0.1274 0.0026 0.1698 0.0035 0.212  O.0523 -o.ooo4 0.1016 -0.0008 0.1539 -0.0012 0.2061 -0.0016 0.255  0.0946 0.0043 0.1892 0.0086  0.2070 0.0018 0.4l4l 0.0037  0.046 0.0012 0.092 0.0024 0.138 O0OO36 0.185 0.00486  0.072 0.0002 0.1445 0.0005 0.2168 0.0007 0.29 0.001  0.0447 0.0011 0.0893 0.0022 0.1340 0.0034 0.1787 0.0045  0.0681 0.0002 0.1316 o.ooo4 0.2074 0.0006 0.2756 0.0008  0.125  0.05 0.075 310 D S F O C U i3SED  16 cm At End o f At End o f Taper Magne t  R= 0 . 0 9 1 4 S= 0.0039 i 0.1828 0.0078  0,1  0.025  15 cm At End of At End o f Taper Magnet  0.1  •  TRAJECTORIES  245  0.025 0.05 0.075  R=0.91  R=0.l8 0.36 0.54  310  0.025 0.05 0.075  0.79  0.15  8-4  0.16 0.33 0.50 ' 0.14 0.28 0.42  90 f o c u s s e d and defocussed atoms f o r the case of a s e p a r a t i o n of 16  cm are shown i n F i g . kl.  As can be seen,  magnet proves i n c a p a b l e of b r i n g i n g p a r t i c l e s  the  to a focus on  the magnet a x i s i f they have a v e l o c i t y of 310 of  nozzle-magnet  m/sec  irrespective  the r a d i a l d i s t a n c e from the a x i s a t which they enter the  magnet except f o r a s m a l l number of p a r t i c l e s v e r y c l o s e to the magnet a x i s . trajectories 1 mm  from  The magnet does succeed however i n keeping of p a r t i c l e s which e n t e r the magnet l e s s  are s t i l l  These t r a j e c t o r i e s  d i v e r g i n g when they leave the magnet.  should be a good approximation to the paths  the 3jje atoms produced  B.  than  the a x i s w i t h i n the p o l e t i p s although the  trajectories  through  the  from  the n o z z l e source w i l l  take  the a c t u a l magnet.  The C a l c u l a t e d P o l a r i z a t i o n  of the Atomic' Beam.  The r e l a t i v e numbers of f o c u s s e d and defocussed p a r t i c l e s p a s s i n g through pass  the hexapole magnet which subsequently  through some s p e c i f i e d  ionization  volume downstream of  the magnet e x i t i s needed i n order to c a l c u l a t e polarization  o f the beam.  be o b t a i n e d from previous section. trajectories  the atomic  the expected  This i n f o r m a t i o n c o u l d i n p r i n c i p l e trajectories  presented i n the  This would i n v o l v e c a l c u l a t i n g  the  f o r p a r t i c l e s w i t h many d i f f e r e n t v e l o c i t i e s  and  i n i t i a l c o n d i t i o n s then d e c i d i n g whether or not a g i v e n trajectory  passes  through the magnet and i n t o  the  ionizer.  Then the r e s u l t would have to be a p p r o p r i a t e l y weighted  for  the e f f e c t of the v e l o c i t y d i s t r i b u t i o n of the p a r t i c l e s  i n the  beam and  the s o l i d angle of p a r t i c l e s  of a g i v e n v e l o c i t y  F i g . kl  T y p i c a l T r a j e c t o r i e s of Focussed and Defocussed ~>He Atoms p a s s i n g through the Hexapole Magnet.-..The Source-Magnet S e p a r a t i o n i s 15 cm and the F i e l d a t the Magnet P o l e T i p s i s taken as 9000 Gauss.  92 which would c o n t r i b u t e  to the  final  G l a v i s h (GI67, G168) which does t h i s . possible  His  has  intensity. w r i t t e n a computer program  program takes i n t o account a l l the  trajectories  the  atoms can  d i s t r i b u t i o n of atoms i n the  the  velocity  This program was  initially  focussed p r o t o n  states  f o r a beam w i t h a Maxwellian v e l o c i t y d i s t r i b u t i o n .  These  used f o r c a l c u l a t i o n s  calculations  involving  of Auckland.  to c a l c u l a t e states  the  were used f o r o p t i m i z i n g  parameters f o r a p o l a r i z e d University  beam.  take and  the  the  p r o t o n i o n source developed a t  The  program was  beam w i t h  H  the  the  m o d i f i e d a t U.B.C.  t r a j e c t o r i e s of both the  of an atomic 3 e  v a r i o u s system  focussed and  velocity  defocussed  distribution  c h a r a c t e r i s t i c of a n o z z l e beam. The inside Figs,  an  r e l a t i v e i n t e n s i t y and  H-2 and. 43  as  entrance from the nozzle. of 0,  10,  a p e r t u r e 1.0  ionizer  a function  20  polarization  of  obtained  i n diameter are  shown i n  the  n o z z l e source and  Calculations and  cm  polarization  the  No  change i n the  the 0.5  cm  these three s e p a r a t i o n s .  these r e s u l t s  i n Chapter V I I I .  namely, n o z z l e and  the  temperature = 7°K,  the  r a t i o of  i o n i z e r aperture with  the  separations  and  More w i l l  be  said  magnet was  Mach number of beam =  a magnet-source s e p a r a t i o n = 15  the  intensity  c o n d i t i o n s under which the  been used to c a l c u l a t e into  temperature of  r a d i u s i o n i z a t i o n volume i s  predicted for  For  the magnet  were done f o r magnet-ionizer  cm.  inside  d i s t a n c e of  of  operated 10  cm,  G l a v i s h ' s program  the  t o t a l f l u x of atoms  the magnetic f i e l d on  to  has  the  93  He  3  T ' 4.2°  K  M-10  175 |facu&&e4150  125  "  — —  —  -  co  2  c  I 100 °?  P  ^ '  Oi  O  INTENSITY 1 (ari POLARIZATION P  "  —  25 - •  0 0  1 5  1 10  S O U R C E - M A G N E T SEPARATION  F i g . k2  I 15 (cm)  E f f e c t o f Source-Magnet S e p a r a t i o n on I n t e n s i t y and P o l a r i z a t i o n o f Atomic Beam. Nozzle a t 4-.2°K.  He  6  T=7°K  M=I0  Ionizer diameter = lcm 100-  Jfocussed CL  75-  tS Oz 50.  UJ  V o -  25-  Cu  5 SOURCE-MAGNET  10 SEPARATION  15 (cm)  F i g . **3 E f f e c t o f Source-Magnet S e p a r a t i o n on I n t e n s i t y and P o l a r i z a t i o n o f Atomic Beam. Nozzle a t 7°K.  t o t a l f l u x of atoms i n t o field  off.  the i o n i z e r aperture w i t h  This r a t i o ( R ) i s equal to 1.33.  The  the magnetic polarization  p r e d i c t e d f o r the c o n d i t i o n s mentioned above i s 62$. C.  The P o l a r i z a t i o n Measurement and Ion Beam Y i e l d . Two d e t e c t i o n methods were used i n determining the  p o l a r i z a t i o n of the 3 e n u c l e i H  hexapole magnet.  a f t e r passing  through the  The f i r s t method, u s i n g the d i f f e r e n t i a l  P i r a n i gauge d e t e c t o r , measured the change i n n e u t r a l i n t e n s i t y w i t h the magnet turned on and o f f , while  beam  the second  method measured the change i n i o n i z e d  beam under s i m i l a r  c i r c u m s t a n c e s w i t h the magnetic f i e l d  on and o f f .  mognet  0.6  nozzle  _L_  -3- -  . . ionizer  T -15-  •50  b  [056  I d i f f erentioi f Pironi d e t e c t o r  fo708 cm  T 12 -20  Fig.  kh  Schematic Diagram I n d i c a t i n g R e l a t i v e L o c a t i o n o f Components Used i n Atomic Beam P o l a r i z a t i o n Measurement. Dimensions i n cm.  The l o c a t i o n o f the d i f f e r e n t i a l P i r a n i d e t e c t o r and the i o n i z e r r e l a t i v e to the magnet w h i l e these measurements were made i s shown i n F i g . Typical Fig.  45 where  off  i s shown.  M+.  results  o f the f i r s t method are shown i n  the e f f e c t o f the magnetic f i e l d  being on and  The i n c r e a s e of approximately 50% i n n e u t r a l  beam i n t e n s i t y i s i n t e r p r e t e d  to i n d i c a t e  an e f f e c t i v e  96 3ffe  p o l a r i z a t i o n of the  n u c l e i passing  although i t i s d i f f i c u l t the a b s o l u t e  value  of  through the magnet  to quote any.degree of accuracy  the  increase.  T y p i c a l r e s u l t s obtained  using  the i o n i z e r to  measure the change i n beam i n t e n s i t y w i t h o f f are shown i n F i g . ^6.  on and  the magnetic  In t h i s  field  experimental  i n beam i n t e n s i t y of $0% was  measurement an i n c r e a s e  to  observed.  Because of the s m a l l number o f ions produced from the atomic beam as compared background gas The  similar  magnet o f f of R =  1.32-0.1.  The  increased.  of R reaching  This value  The  r a t i o R increased This data  The  s l o w l y as  i s not i n c o n s i s t e n t w i t h  begins to  measured i o n c u r r e n t was c u r r e n t a t 750  mA  the estimated  to the magnet was  0A5  x 10  18  3jje  12  nA w i t h  and  the magnet  a plate voltage  atomic beam at the  310  amps. 18  saturate.  atoms ( s r - sec)  p r o b a b l e v e l o c i t y of the beam was  the  shown i n F i g .  c o n d i t i o n s under whic h t h i s measurement was  were such that  the  the magnet  a p l a t e a u a t a magnet c u r r e n t of 70  the i o n i z e r e m i s s i o n  the  i n c r e a s e of i o n i z e d beam  o f c u r r e n t corresponds to the value  The  V.  y i e l d e d a r a t i o R of  the magnet e x c i t a t i o n c u r r e n t i s  a t which the magnetic f i e l d  350  measurements,  the magnet on to the i o n c u r r e n t w i t h  as a f u n c t i o n of  c u r r e n t was  r e s u l t s from 18 y  shown i n F i g . *+7.  value  The  shown i n F i g . k6  to the one  modulated.  a s s o c i a t e d d e t e c t i o n e l e c t r o n i c s were  i n S e c t i o n *+B.  current with  obtained  the  (lslOOO) the incoming atomic beam was  chopping system and  described  ion  to the l a r g e number produced from  m/sec.  —1  and  on, of  made  entrance the most  Assuming 50$  of  TIME Fig.  Change i n D i f f e r e n t i a l P i r a n i D e t e c t o r S i g n a l when Hexapole Magnet i s Turned On and O f f . ^3  98 the  atoms e n t e r i n g  the  12  the magnet pass  through the i o n i z e r  nA i o n c u r r e n t corresponds to an i o n i z a t i o n  then  efficiency  of 0.15#. A Run a Ei Run b O Run c  1.4 a:  2 < K  0  1.3  ^6•Q  I 2 h  I.I 1.0  •  h  L  J  0  20  40  60  MAGNET CURRENT Fig.  h?  80  (amps)  Enhancement R a t i o o f I o n i z e d Beam as a F u n c t i o n of Magnet E x c i t a t i o n Current.  The e x p e r i m e n t a l r a t i o R = 1.32-0.1 o b t a i n e d by measuring  the i o n y i e l d from the i o n i z e r  i s i n good agreement  w i t h the t h e o r e t i c a l l y expected r a t i o R = 1.33 G l a v i s h ' s program.  This r a t i o i s e q u i v a l e n t to a  p o l a r i z a t i o n o f the atomic beam of 62%. polarization magnetic  polarization  s t r e n g t h i n the i o n i z e r .  of the i o n i z e d  s t r e n g t h assuming is  The  of the s i n g l y i o n i z e d '^He w i l l  field  calculated  The  calculated  actual depend on the expected  beam as a f u n c t i o n of  field  the p o l a r i z a t i o n o f the atomic beam i s  shown i n F i g . 3«  using  100  CHAPTER V I I I CONCLUSIONS A.  Comparison w i t h other Sources o f P o l a r i z e d ^He  +  Ions.  Three methods are p r e s e n t l y used f o r the p r o d u c t i o n of p o l a r i z e d ^He secondary through  +  ions.  The p r o d u c t i o n o f a p o l a r i z e d  beam f o l l o w i n g a n u c l e a r r e a c t i o n has been d i s c u s s e d  the example o f e l a s t i c  by ^He i n Chapter  I.  s c a t t e r i n g o f u n p o l a r i z e d ^He  The R i c e U n i v e r s i t y p o l a r i z e d i o n beam  i  o b t a i n e d by o p t i c a l pumping techniques S e c t i o n 2A. techniques  has been d i s c u s s e d i n  The U.B.C. p o l a r i z e d beam o b t a i n e d by atomic i s the s u b j e c t o f t h i s  beam  t h e s i s where t h e ' r e s u l t s o f  a v a i l a b l e p o l a r i z a t i o n and i o n c u r r e n t measurements a r e discussed i n Section 7C  A comparitive  summary o f the  p o l a r i z a t i o n and i o n c u r r e n t a v a i l a b l e from these techniques  i s presented  i n Table 3»  three  The time r e q u i r e d i n an  e x p e r i m e n t a l measurement to o b t a i n a d e s i r e d f r a c t i o n a l e r r o r  p in  the measurement i s i n v e r s e l y p r o p o r t i o n a l to P I .  This  f i g u r e o f m e r i t P I g i v e n i n Table 3 demonstrates the advantage of the i o n source i n producing  technique  over  the secondary  a u s e f u l beam o f p o l a r i z e d ^He.  beam  technique  The f i g u r e o f  m e r i t i s a t l e a s t 3 o r d e r s of magnitude higher f o r the i o n source  techniques.  Both the R i c e U n i v e r s i t y and U.B.C. i o n  p sources  have s i m i l a r P I values but are c h a r a c t e r i z e d by low  p o l a r i z a t i o n and high i o n c u r r e n t i n the case o f the R i c e U n i v e r s i t y source and high p o l a r i z a t i o n and low c u r r e n t i n the case o f the U.B.C. s o u r c e .  Both the beam p o l a r i z a t i o n and •  Table 3 Comparison o f d i f f e r e n t Methods o f Producing  Method of P r o d u c t i o n  $ Polarization P  Beam  P o l a r i z e d 3jj e +  Current I  i  O p t i c a l Pumping Rice U n i v e r s i t y Ion Source Atomic Beam U.B.C. Ion Source  100$  5$  65% Potentially  100$  .001 - .Olnf\  n  s  .  Figure of Merit P I 2  Secondary Beam eg. ^ e ^ R - e ^ H e ^ e  o  IO"  6  3/xA  .007  12 nA  .005  extracted i o n y i e l d  c a n be p o t e n t i a l l y i n c r e a s e d i n both the  R i c e and U.B.C. s o u r c e s .  The p o l a r i z a t i o n of the Rice source  might be i n c r e a s e d as high as 60% and the U.B.C. source polarization  to 100$.  Improved atomic beam f o r m a t i o n and  i o n i z a t i o n e f f i c i e n c y may r e s u l t i n an order o f magnitude i n c r e a s e i n the U.B.C. i o n c u r r e n t . B.  Measurement o f the ^>Ee Beam P o l a r i z a t i o n by the +  DC^He.P^He R e a c t i o n . The  measurement o f the atomic beam p o l a r i z a t i o n i s  d i s c u s s e d i n Chapter V I I and the t h e o r e t i c a l  relationship  between the atomic beam p o l a r i z a t i o n and the i o n i z e d p o l a r i z a t i o n as a f u n c t i o n the  i o n i z e r and t a r g e t  o f the magnetic f i e l d  beam  strength i n  r e g i o n s i s i l l u s t r a t e d i n F i g . 3»  spite of this theoretical relationship d e t e r m i n a t i o n o f the i o n i z e d  In  an experimental  beam p o l a r i z a t i o n would be  desirable. the p o l a r i z a t i o n o f the 3fj.e beam  Although i n p r i n c i p l e  c o u l d be determined by measuring the asymmetry i n the ^He(3He,  3He)Ste r e a c t i o n ; the energy r e q u i r e d  s i g n i f i c a n t amount o f P wave s c a t t e r i n g v a n i s h i n g L«S s p i n - o r b i t  force  i o n source development work. an e x o e r g i c n u c l e a r r e a c t i o n  for a  i n order to have a non-  i s inconvenient  f  o  preliminary  r  A more s u i t a b l e method i s to use to produce p o l a r i z e d  spin £  p a r t i c l e s o f s u f f i c i e n t energy to make p o l a r i z a t i o n by e l a s t i c DC^HejP^He by  scattering ( Q = 18.36  possible. MeV).  An a p p r o p r i a t e r e a c t i o n i s  I f this reaction  S waves and assumed to proceed  analysis  is initiated  through the J = 3/2  +  resonance i n L i ^  then a simple r e l a t i o n s h i p e x i s t s 3 e  the p o l a r i z a t i o n of the incoming  H  between  beam PC^He) and the  p o l a r i z a t i o n P(p) o f the protons which are emitted a t an angle o f 90° w i t h r e s p e c t to the d i r e c t i o n o f the a x i s o f p o l a r i z a t i o n o f the incoming  PCp>=  -(  2 /  ^He p a r t i c l e s  3)  P  (Fi67)  (23)  ( »e) J  To measure the p o l a r i z a t i o n o f the Rice U n i v e r s i t y p o l a r i z e d ^He * i o n source 4  through  the p o l a r i z a t i o n of the protons was measured  the l e f t - r i g h t asymmetry A o f t h e i r e l a s t i c  scattering  i n a h i g h - p r e s s u r e (35 atmospheres) helium f i l l e d p o l a r i m e t e r . D e t a i l s o f the e x p e r i m e n t a l apparatus Findley ( F i 6 7 ) .  where N  L  used are d i s c u s s e d by  The asymmetry A i s d e f i n e d as  i s the number o f protons s c a t t e r e d  the beam i n the p o l a r i m e t e r and r i g h t and N  L  + N  R  to the l e f t s i d e o f  the number s c a t t e r e d  = N, the t o t a l number o f events.  p o l a r i m e t e r had an a n a l y z i n g power o f - 0 . 6 .  to the  The  Thus the measured  e x p e r i m e n t a l asymmetry A o f the protons i s r e l a t e d  to the  p o l a r i z a t i o n o f the ^Ee beam P(3R"e) by  /AM The f r a c t i o n a l e r r o r  / —j^- j i n the measured asymmetry i s e q u a l to  where N i s the t o t a l number o f observed  events.  The asymmetry i n the case o f the R i c e p o l a r i z a t i o n measurement was determined  to be 0.0227^0.0033 (Ba68).  This  103 value of  i s an averaged asymmetry obtained  the beam p o l a r i z a t i o n every  to d e t e c t o r  5 minutes to c a n c e l e r r o r s due  s o l i d angle and e f f i c i e n c y asymmetries i n the  polarimeter.  To o b t a i n  r e q u i r e d a t o t a l of 3-4jik  by r e v e r s i n g the s i g n  this accuracy  90,000 counts.  F o r a ^He beam c u r r e n t o f  on a deuterium i c e t a r g e t a t 300  a counting  r a t e i n the p o l a r i m e t e r  KeV F i n d l e y r e p o r t s  o f 2 events per second.  take approximately 13  Thus t h e i r measurement should  however, they r e p o r t a p p r o x i m a t e l y 18-24 t a k i n g was r e q u i r e d  to Eq. 25  according  hours;  hours of a c t i v e data  to o b t a i n adequate s t a t i s t i c s .  The  d i f f e r e n c e i n the two times may be the r e s u l t o f background runs. , The time r e q u i r e d  to determine the p o l a r i z a t i o n o f the  U.B.C. i o n source can e a s i l y be estimated R i c e group's e x p e r i m e n t a l  count r a t e .  p o l a r i z a t i o n o f 0 . 6 5 , A = 0.26  from Eq. 25 and the  3g  For a  e  D e a m  ( T h i s assumes s t r o n g  field  I f a ±20% measurement o f the beam p o l a r i z a t i o n  ionization).  AA i s d e s i r e d -j~ For weak f i e l d  0.2  and Eq. 25  shows 350  counts are r e q u i r e d .  i o n i z a t i o n the p o l a r i z a t i o n i s reduced by one-  h a l f and the number o f counts r e q u i r e d i n c r e a s e d If  the 3  H  e  w  e  r  e  a c c e l e r a t e d to  increases  1+  the 300  KeV i n the Rice  the c r o s s s e c t i o n f o r p r o t o n  production  by a f a c t o r o f 4 and the experimental  the p o l a r i m e t e r  1500,  600 KeV where the D(3He,P) He  c r o s s s e c t i o n i s a maximum i n s t e a d , o f U n i v e r s i t y case,  to about  thus i n c r e a s e s by a f a c t o r o f 4.  count r a t e i n However, the  U.B.C. i o n c u r r e n t i s a p p r o x i m a t e l y 10 nA as compared to the Rice  source 3-4  nA.  Combining  the i n c r e a s e  i n count r a t e  because o f the higher  ^Ee energy and the decrease due to  lower beam c u r r e n t the expected count r a t e i s 2/100 per second. -20f  0  accuracy  The measurement o f the beam p o l a r i z a t i o n to using, t h i s count r a t e and strong f i e l d  would r e q u i r e approximately o f l8-2k  counts  5 hours or using  ionization  the quoted  time  hours f o r the R i c e measurement our measurement would  r e q u i r e 7-9 hours.  Weak f i e l d  i o n i z a t i o n would i n c r e a s e the  time r e q u i r e d f o r these measurements by a f a c t o r o f C.  P o s s i b l e Improvements of the P o l a r i z e d 3ne (1)  Improvements I n c r e a s i n g One  +  Beam.  the Atomic Beam I n t e n s i t y .  o f the most e f f e c t i v e ways o f i n c r e a s i n g the  u l t i m a t e i o n y i e l d o f the beam apparatus i s to i n c r e a s e the From the data shown i n F i g . 37  n e u t r a l atomic beam i n t e n s i t y .  i t appears as i f c o n s i d e r a b l e i n c r e a s e s i n i n t e n s i t y can be achieved  by r e d u c i n g  the s c a t t e r i n g i n the nozzle-skimmer  region.  Reduced s c a t t e r i n g i s a c h i e v e d  pumping speed and hence r e d u c i n g  by i n c r e a s i n g the  the background gas p r e s s u r e  in  this region.  The pumping speed a t the n o z z l e  by  the long pumping channel from the n o z z l e  i s limited  to the Leybold  pump and the r e s t r i c t i v e geometry i n the nozzle-skimmer r e g i o n . A p o s s i b l e s o l u t i o n to these combined problems i s to remove the p r e s e n t nozzle-skimmer pumping system and to pump the nozzle-skimmer r e g i o n w i t h  the 10" d i f f u s i o n pump p r e s e n t l y  pumping the skimmer-collimator  region.  The p r e s e n t  skimmer-  c o l l i m a t o r r e g i o n might be pumped e i t h e r by the 10" pump a l s o or by the pumps which p r e s e n t l y pump the r e g i o n downstream o f the e x i s t i n g c o l l i m a t o r .  The d i s c u s s i o n o f the p r o p e r t i e s of  105 the n o z z l e o p e r a t i o n g i v e n i n S e c t i o n 3C shows that the c o l l i m a t o r might best be The  u l t i m a t e improvement achieved  pumping speed may and  eliminated.  be l i m i t e d by  skimmer a p e r t u r e s .  by i n c r e a s e d  the s m a l l s i z e of the nozzle  However, i t does not appear  unreasonable to expect  an i n c r e a s e i n beam i n t e n s i t y of a  f a c t o r 2 w i t h r e l a t i v e l y simple m o d i f i c a t i o n s to the apparatus, (2)  existing  perhaps even more w i t h e x t e n s i v e m o d i f i c a t i o n s .  Improvements to Reduce the Atomic Beam V e l o c i t y . The  r e d u c t i o n of the v e l o c i t y to that  corresponding  to a s t a g n a t i o n temperature of H-.2°K, the temperature o f liquid  helium  thermal  i n the c r y o s t a t , i s expected  attachment of the n o z z l e  a t t a c h e d by a brass bar has proved to p r o v i d e evidenced resistance proposed  The  present  the l i q u i d but i s  to the bottom of the c r y o s t a t .  inadequate  thermal  This  c o n t a c t as  by v e l o c i t y measurements o f the beam and  carbon  thermometer measurements of the n o z z l e .  It is  that a new  c r y o s t a t would be designed  a c t u a l l y surrounded by the c o o l a n t . nozzle  with a b e t t e r  to the c r y o s t a t .  n o z z l e i s not i n d i r e c t c o n t a c t w i t h  the  temperature to H-.2°K.  with  the n o z z l e  This should reduce  the  In f a c t r e c e n t work, subsequent  to the measurements mentioned i n t h i s  t h e s i s , with a m o d i f i e d  c r y o s t a t has produced an atomic beam w i t h a v e l o c i t y corresponding  to +.2°K. l  measured p r e v i o u s l y was the n o z z l e  This confirms  velocity  caused by poor thermal attachment of  to the c r y o s t a t .  n o z z l e i s now  that the high  In the m o d i f i e d c r y o s t a t the  almost completely  surrounded by l i q u i d  helium  thus e n s u r i n g adequate thermal c o n t a c t . temperature of  n o z z l e from 7 K  the  Lowering  the  to nearer +.2°K w i l l l  C  improve the p o l a r i z a t i o n .  The  improvement expected i n  calculated  the  lower temperature p a r t i c l e s  t r a j e c t o r i e s of  seen i n F i g . ^1  can  be  310  m/sec (7°K)  As  and  where the  2k5  focussed  to a p o i n t  p a r t i c l e s are  on  m/sec ( f . 2 K ) p a r t i c l e s are  shown.  the 2h^  be  the  s t i l l diverging *+3  and  i n c r e a s e from 62%  w i t h the 7°K  m/sec p a r t i c l e s can  at the  indicate  magnet e x i t .  that  The  results  the p o l a r i z a t i o n  beam to 8k%  d e s i r a b i l i t y of c o o l i n g  m/sec  the  will  w i t h the >+.2 K beam. 0  to 2 . 2 ° K  beam f u r t h e r  o r i g i n a l l y proposed (Wa63) i s very e v i d e n t from  as was point  0  beam a x i s whereas-the 310  shown i n F i g s . h2  The  t r a j e c t o r i e s f o r both  L  shown i n t h i s f i g u r e  the  of view of i n c r e a s e d s e p a r a t i o n of  the  the  spin states  i n c r e a s e d i o n i z a t i o n e f f i c i e n c y both of which depend on v e l o c i t y of (3)  the  and the  atoms.  Improvements i n I o n i z a t i o n  E f f i c i e n c y and  Ion  Extraction. The the  s i d e of  difficulties the  a u s e f u l i o n beam from  i o n i z e r , as must be done w i t h the  i o n i z e r , have not sensible  i n extracting  yet  been f u l l y c o n s i d e r e d .  into a useful a new  I t w i l l be most  to r e c o n s i d e r an a x i a l i o n i z e r because of  c o n s i d e r a b l y i n c r e a s e d ease w i t h which the beam a f t e r  they l e a v e the  i o n i z e r care must be  present  the  ions may  ionizer.  be In  focussed constructing  taken to i n s u r e minimum outgasing  from the  constituent  components of  the  i o n i z e r when the  electron  e m i s s i n c u r r e n t bombards the p l a t e  and  high  causes g e n e r a l  107 h e a t i n g o f the apparatus. 0.15$  c o u l d be improved both by reduced  improved i o n i z e r d e s i g n . the  The p r e s e n t i o n i z a t i o n e f f i c i e n c y o f  time  atomic  Reducing the atomic  v e l o c i t y and v e l o c i t y increases  the atoms s t a y i n the i o n i z a t i o n r e g i o n thus i n c r e a s i n g  the i o n i z a t i o n e f f i c i e n c y .  Improved i o n i z e r d e s i g n would  a l l o w higher e l e c t r o n bombardment c u r r e n t s hence higher ionization efficiency. field  type i n order  A new i o n i z e r should be of the strong  to take advantage o f the s i g n i f i c a n t  enhancement o f the u l t i m a t e n u c l e a r p o l a r i z a t i o n o f the i o n i z e d beam as shown i n F i g . 3»  (h)  O v e r a l l System Improvement P o s s i b i l i t i e s  by Changing  the Geometry. Some i n c r e a s e i n beam i n t e n s i t y s h o u l d , a t f i r s t be o b t a i n e d by moving the source entrance  to the magnet  as the i n t e n s i t y of p a r t i c l e s e n t e r i n g the magnet i s  p r o p o r t i o n a l to 1/r . in  of atoms c l o s e r  glance,  This would a l s o produce a r e a l i n c r e a s e  i o n c u r r e n t i f the magnet were i n f a c t able to focus the  i n c r e a s e d number o f p a r t i c l e s e n t e r i n g the magnet a p e r t u r e . The d i f f i c u l t y i s t h a t the p a r t i c l e s can be c o n s i d e r e d as coming from a p o i n t s o u r c e ; thus enter such  the a d d i t i o n a l p a r t i c l e s  the magnet w i t h an i n i t i a l divergence  and r a d i a l  location  that the p r e s e n t magnet i s i n c a p a b l e o f f o c u s s i n g the  e x t r a atoms i n t o a u s e f u l beam.  This e f f e c t i s evident i n  Table 2 where the t r a j e c t o r i e s o f atoms w i t h v a r y i n g r a d i a l displacements  a t the magnet entrance  magnet s e p a r a t i o n s o f 5 and 15 cm.  are t a b u l a t e d f o r n o z z l e For the increment  size  (0.025 cm) o f the r a d i a l displacement used i n these c a l c u l a t i o n s  5  p a r t i c l e s w i t h a r a d i a l displacement entrance  up to  0.075  cm a t the  to the magnet pass through the magnet when the  source-magnet s e p a r a t i o n i s 15  cm.  However, when the source-  magnet s e p a r a t i o n i s reduced to 5 cm o n l y atoms which enter the magnet w i t h a r a d i a l displacement the  0.025  pieces.  from the a x i s o f l e s s  cm pass through the magnet without  hitting  the p o l e  Hence moving the magnet c l o s e r to the source  r e s u l t i n a l l the a d d i t i o n a l p a r t i c l e s being u s e f u l beam.  focussed  into a  The comparison between v a r y i n g source-magnet  s e p a r a t i o n i s shown more q u a n t i t a t i v e l y i n F i g . k2. i n t e n s i t y I o f focussed annulus v a r i e s l e s s  atoms p a s s i n g  The  through the i o n i z e r  than 3% when the source-magnet s e p a r a t i o n  i s v a r i e d from 5 to 15  cm.  p o l a r i z a t i o n P or r e l a t i v e  A l s o shown on t h i s f i g u r e i s the amounts o f focussed  atoms as d e f i n e d e a r l i e r which enter The  w i l l not  and  defocussed  the i o n i z e r annulus.  p o l a r i z a t i o n i n c r e a s e s from a value o f 73$  for a  source-  magnet s e p a r a t i o n of 5 cm to 84$ f o r a source-magnet 2 s e p a r a t i o n o f 15  cm.  The parameter P I i s of g r e a t e r  interest  to the e x p e r i m e n t a l i s t as t h i s f i g u r e i s i n v e r s e l y r e l a t e d to the l e n g t h of time needed to o b t a i n the same s t a t i s t i c s f o r a p a r t i c u l a r experiment w i t h beams o f v a r y i n g i n t e n s i t y and p o l a r i z a t i o n . - The value  o f t h i s parameter i s 20$  source-magnet s e p a r a t i o n s o f 15 As  larger for  cm than f o r the 5 cm s e p a r a t i o n .  a r e s u l t o f the above there appears to be no advantage i n  moving the magnet c l o s e r to the source  as any s l i g h t g a i n i n  i n t e n s i t y through the i o n i z e r annulus i s l o s t because of a l a r g e r r e d u c t i o n i n the p o l a r i z a t i o n of the atoms.  109 (5)  Improvements i n Vacuum System Reducing Background I o n Yieldo The maximum a c c e p t a b l e p r e s s u r e i n a g i v e n s e c t i o n of  the  atomic beam apparatus i s determined by the c r i t e r i o n  the  beam should not s u f f e r a s i g n i f i c a n t l o s s of i n t e n s i t y by  s c a t t e r i n g as i t passes through the r e g i o n o f i n t e r e s t . room temperature i t i s n o t too d i f f i c u l t to  10%,  This means that the mean f r e e p a t h o f the gas must be  the  the beam must  Thus i f the chamber were 100 cm long a p r e s s u r e o f 10  T o r r would At  At  to keep beam l o s s e s  10 times the s c a t t e r i n g l e n g t h through which pass.  that  be adequate  to keep beam l o s s e s  to l e s s  lower temperatures, i n p a r t i c u l a r a t l i q u i d s i t u a t i o n i s c o n s i d e r a b l y more d i f f i c u l t  than 10$.  helium temperatures,  as the mean f r e e  p a t h a t a g i v e n p r e s s u r e i s a p p r o x i m a t e l y 100 times s m a l l e r than a t room  temperature.  The p r e s s u r e requirement i n the i o n i z i n g chamber i s set  by the r a t i o of the number o f p o l a r i z e d 3jje  ions produced  +  from the atomic beam to the number o f i o n s formed background  gas i n the i o n i z i n g r e g i o n .  s h o u l d be as l a r g e as p o s s i b l e ; c o m p o s i t i o n o f . t h e background to  Naturally this  gas ions as i t may be p o s s i b l e  separate the u s e f u l p o l a r i z e d ^Ee  about 15 nA o f p o l a r i z e d 3 H e +  l  o  n  gas i o n s i s n a t u r a l l y i n t o l e r a b l e . required  ratio  the exact s i z e depends on the  ±  +  o n s  gas ions by means o f momentum a n a l y s i s . of  from the  s  a  n  f  r  o  the background  m  The p r e s e n t s i t u a t i o n d  1  0  ^  o  f  background  Momentum a n a l y s i s i s  to reduce contaminants i n the beam to a minimum so  u n d e s i r e d lons would  be e l i m i n a t e d .  The atomic beam d e n s i t y  110  i n the i o n i z e r r e g i o n corresponds  to a p r e s s u r e of  approximately  10~7 T o r r ; the background gas p r e s s u r e should be brought w e l l below t h i s as the volume of background gas a v a i l a b l e f o r ionization i s larger To improve bulkhead chamber.  than the volume o f beam p a r t i c l e s . the p r e s s u r e  i n the i o n i z a t i o n r e g i o n a  should be i n s t a l l e d between the magnet and the i o n i z e r This d i v i d i n g  bulkhead  would have o n l y a s m a l l h o l e ,  the s i z e o f the magnet e x i t , l o c a t e d on the beam a x i s to a l l o w the beam to pass through  to the i o n i z e r .  Such a system  would reduce the flow of u n p o l a r i z e d -^Ee atoms from the magnet r e g i o n and would a l l o w e f f o r t s concentrated the i o n i z e r stainless wires  to improve the vacuum to be  i n one s p e c i f i c a r e a .  Reduction  can be achieved by r e b u i l d i n g  of outgassing of  the i o n i z e r  with  s t e e l p a r t s and by a r e d u c t i o n i n the number o f  and other m a t e r i a l s which are s u b j e c t to e x c e s s i v e  o u t g a s s i n g upon e l e c t r o n bombardment. Although are l e s s severe  the vacuum requirements  i n the magnet r e g i o n  than i n the i o n i z a t i o n r e g i o n , 10"^ Torr  would be s a t i s f a c t o r y ,  a pump should be p r o v i d e d on the magnet  chamber to ensure low background gas p r e s s u r e s around t i p s o f the magnet.  the p o l e  APPENDIX A INTENSITY FROM A FREELY EXPANDING JET The angular dependence o f the I n t e n s i t y from a f r e e l y expanding n o z z l e j e t i s g i v e n by Eq. 1 1 as  1(e)  =K « s ^ ( § ^ )  ui)  where 0 i s the angle between the r a d i u s v e c t o r to any p o i n t and  the normal to the a p e r t u r e and (j> i s a c o n s t a n t ,  (f> =  1.365  Y = 1.67  for  The t o t a l i n t e g r a t e d i n t e n s i t y over a l l angles must equal the t o t a l molecular  gas flow N through  the n o z z l e g i v e n by E q . 5  e-W  ie.  x(e)  Total flux = N =  (A2)  dn(e)  where  dJn(Q)  - ITT sm 0 J ©  Thus  N Performing  or K =  =  a  9  d e  (A3)  the i n t e g r a t i o n r e s u l t s i n N = _ K TX ( O . Z 6 5 )  N / C2TT ( 0 . 2 6 5 ) ] . = 0 . 6 N 1(9)=:  Therefore  COSHES)-n: "  0.6 N  CO-'(fj)  the c e n t e r l i n e i n t e n s i t y (0 = 0)  " ( A » f )  can be w r i t t e n  112  center fine  r  N  dloms  (s+ J, fi-sec)" era  A  (A5)  113 APPENDIX B INTENSITY AND VELOCITY DISTRIBUTION OF PARTICLES IN JET AFTER PASSING THROUGH SKIMMING ORIFICE The  i n t e n s i t y and v e l o c i t y d i s t r i b u t i o n o f atoms  arriving at a location  on the beam a x i s downstream from the  skimmer can be c a l c u l a t e d  w i t h r e f e r e n c e to F i g . 4 8 .  Assuming r a d i a l flow o r i g i n a t i n g  a t the n o z z l e w i t h the v e l o c i t y  of mass motion w i n the r a d i a l d i r e c t i o n and a uniform atomic d e n s i t y over that r e g i o n c u t out by the skimmer, the number o f 2 p a r t i c l e s passing  through some s m a l l r e c t a n g u l a r area (da)  l o c a t e d a d i s t a n c e i ^ / ' X 5 along the a x i s can be found by summing  the c o n t r i b u t i o n s  to the f l u x from a l l elemental areas  dA = 2TT X$ sir\ov doC on the s p h e r i c a l the  s u r f a c e which c h a r a c t e r i z e s  t r a n s i t i o n from continuum to f r e e molecular f l o w .  of p a r t i c l e s p a s s i n g  through t h i s area i s g i v e n by: u, da 3  The f l u x (Bl)  where T\ i s the number d e n s i t y o f p a r t i c l e s on the s p h e r i c a l s u r f a c e and u Is t h e i r v e l o c i t y . and  The o r i e n t a t i o n  of  U2  UT i s shown i n F i g . 48 and  (B2)  As  the area  close  (da)  i s very  s m a l l , o n l y atoms w i t h v e l o c i t y very  to u" where u" i s the v e l o c i t y v e c t o r  from the p o i n t i n  2  question  to the c e n t e r  w i l l contribute  F i g . H-9  to the  (da)  as shown i n F i g . 49  flux.  D e f i n i t i o n of C e r t a i n V a r i a b l e s used i n C a l c u l a t i o n of Flow through Nozzle-Skimmer System.  Thus the v a l u e s and  of the area  of U]_, u ,  and  2  u^ may  be w r i t t e n , d e f i n i n g  &  <f> as i n F i g . 4-9, U]  Since i  1  =  U COS  s  as  O  u  2  = U  Sin 0  u  3  = u  sine  0 and  ^ X,  be w r i t t e n  _  Cos  <f>  (B3)  sinf,  the s m a l l increment i n u^, u^ and  u^  may  116 where u i s allowed to take on a l l values from 0 toe<?Eq. B l can be w r i t t e n a s :  fl u  \  ' '  1  %  now  2.  and  i  •n  also  Thus E q . Bk  *  r  C  Xs  =  \  ^T/s / w  (B5)  becomes  (B6)  ?  01 =  co  Integrating  over angles  (B7) .i  ^,x-4 %Xt^ 2  *  i ^ - c - ^  now i n t e g r a t i n g over v e l o c i t i e s  u and r e c a l l i n g  *  (B8>  117  2  &  °  5  D - e r K - ^ ^ C o s ^ ) ]  £  where  -  2 f e T  -  7-  f o r Mach numbers rV\>3 rf 9  limit  0  and  is  for  vito  +  may  be r e p l a c e d by i t s assymptotic  w) and er-ff-J^Twcos CK<,) may be r e p l a c e d by  er^C-^P  limit - 1 .  t h e i r assymptotic  (BIO)  E q . BIO thus s i m p l i f i e s sin*  'W  " ^  M>3  + C  ° ^^ 5  to  (B11)  I  and E q . B l l becomes  However, i f i n E q . B4 the r a d i a l divergence o f the flow a t the skimmer had been n e g l e c t e d ( i e . the flow i s assumed p a r a l l e l at  the skimmer entrance)  and E q . Bh becomes  as b e f o r e  X  r  .  (Mf  X  then  Q =  0  jdf\  ~  f\$KiMMziz  118 fl -7) H  and  c  Thus r  X ; . TT  IT / s -= -X -/s  W W  s  S"M  sm'" oi,  J  V< / m  V/z  „~  /vv (u-w)' /„..,.AI  u  w  Performing  (B15)  UTTKTJ  the i n t e g r a t i o n over u i n Eq. B l 4 r e s u l t s i n ^M z  for  A  /  z  1  fav^  _^M 2.  2  (B16)  -[NA > 3  Thus r e d u c i n g Eq. B l 6 to  x"= x  /s  $/AV  S  a2 *x*n  (B17)  Eq. B15 can be w r i t t e n  d2E —  =  J  i'TT*n'*  s  /m  y/z  ^  ( B 1 8 )  where  ^  u  ?  e - ^ ^  w  ^  ( B 1 9 )  E q . B8 can be c a s t i n t o a s i m i l a r dT  =  /J2___y^  q ( u )  where  U  and q(u)  i s as g i v e n by Eq.  B19  form  CT(U)  (B20)  120 APPENDIX C TRAJECTORIES OF PARTICLES PASSING THROUGH A HEXAPOLE MAGNET 1.  E q u a t i o n o f M o t i o n o f a Magnetic  Dipole i n a A x i a l l y  Symmetric M u l t i p o l e F i e l d . The  energy o f i n t e r a c t i o n ^ / between a magnetic  H and a magnetic d i p o l e M i s /ty = - M « H . W f o l l o w s from  The c l a s s i c a l  field  energy  this W =  -//f///./ c o s9  (Cl)  \tfhere M has been r e p l a c e d by the magnetic m o m e n t w h i c h i s a t an angle 6? w i t h r e s p e c t to the magnetic f i e l d  H .  L e t t i n g the  component o f the magnetic moment i n the d i r e c t i o n o f the applied f i e l d  be e q u a l tcyC-eff we can w r i t e Eq. C l  W =  The  yUeff  Two  W , ,  (  field  50.  C  3  )  gradlHl  p o l e s o f a r a d i a l l y symmetric m u l t i p o l e f i e l d  Fig.  in  C ( 2)  f o r c e on a d i p o l e o f c o n s t a n t s t r e n g t h i s g i v e n by F = -grad  ie.  I HI  -yO<e«  are shown i n  The z a x i s i s taken as the a x i s o f symmetry and the  i s assumed to be c o n s t a n t i n t h i s = 0 .  direction,  The d e t e r m i n a t i o n o£ the magnetic f i e l d  the plane p e r p e n d i c u l a r to t h i s a x i s i s then a two  d i m e n s i o n a l problem.  strength  121  entrance aperture  source  F i g . 50  Schematic Diagram Showing Two Poles of a R a d i a l l y Symmetric Magnet.  The p e r t i n e n t Maxwell Equations a r e : V -  B =  O  i n f r e e space j = D = M = 0 and the f i r s t •V-H  VxH  =  two equations become: (c*o  O  = 0  "  (C5)  Hence H can be d e s c r i b e d as the g r a d i e n t o f a s c a l a r magnetic potential  (j) as  using Eq. Ck  H = -grad <j>  v <p ~ o 2  ( C 6 )  (C7)  which i s Laplace's e q u a t i o n . equation suitable  A general s o l u t i o n  f o r two d i m e n s i o n a l  F(V) =  o f Laplace's  geometry i s  <p  (G8)  X f 1%  (C9)  where V •=  A general property of this s o l u t i o n  i s that l i n e s of c o n s t a n t  (p are p e r p e n d i c u l a r to l i n e s of constant IjJ . the l i n e s of c o n s t a n t magnetic p o t e n t i a l , (JJ r e p r e s e n t the l i n e s of  As  <f> r e p r e s e n t s  the l i n e s o f c o n s t a n t  force.  W r i t i n g Eq. C6 i n v e c t o r form as  where i and J, are u n i t v e c t o r s i n the x and y d i r e c t i o n ,  the  square o f the magnitude o f H i s  |Hl' =  3x  >1  u s i n g the Cauchy-Riemann  S I  equations  _ ^  =  the above e x p r e s s i o n becomes  11  IH  1  which u s i n g Eq. C8 can be w r i t t e n as  H  2  lb  FCv)  ax  ^  (CIO)  and  H  ax  (Cll)  Any p o l y n o m i a l  i n V i s a s o l u t i o n o f Laplace's  equation.  the g e n e r a l s o l u t i o n g i v e n by Eq. C8 can be expressed  FM = f  d  n  as  V"  (oi2)  Each p o s s i b l e m u l t i p o l e f i e l d one term o f t h i s p o l y n o m i a l  F „ M=  Thus  c o n f i g u r a t i o n can be expressed  by  as  d  V "  n  (ci3)  I n c y l i n d r i c a l c o o r d i n a t e s , ! and Q , the v e c t o r V = X +ly can be w r i t t e n as  V  r (cos e  -  4-  i < \ ^  6)  and Eq. C12 may be w r i t t e n  F(v) = £ | ^ | e thus  ,  now and i  H = -grad  r e  .  <^  *  grad =  where Thus  £  £  +  S*^  from Eq. C6  i n c y l i n d r i c a l coordinates  S  £  h-  +  the e x p r e s s i o n f o r the g r a d i e n t © J_  and 6 are u n i t v e c t o r s .  r  2e —j  For a s i n g l e m u l t i p o l e f i e l d we may drop the summation and the relative H  n  azimuthal  i s r a d i a l where  In any case a n d  . H  term S  n  .  7) 6 f Srx  Jrcos(ne4 ^ r  r  "~'  K V  - P ,  TT  y  2TT  Y  3> TT^  )-Dsin(ri©+S )| = | n  c c l 5 )  In terms of Eq. £  and  and  Eq.  Cl5  -n(-n-i)  ^y(J<*K  the drs  f o r c e on r  -  mn  -n(-n-)) d  Those d i p o l e s  6  )  (017)  A Z  the d i p o l e  and  t i s time.  which have a n e g a t i v e component of the a p p l i e d  towards the c e n t r a l a x i s of  field H  away from the  Trajectories  central  the  are  the r a d i a l f i e l d ,  those w i t h a p o s i t i v e component i n t h i s d i r e c t i o n  deflected  l  e q u a t i o n of motion  r"  n  magnetic moment i n the d i r e c t i o n of  while  The  c  y_r  where m i s the mass of  2.  (  be  ^ ' MeU  accelerated  is  i s then F  Sid  the d i p o l e  A_2  i s always i n the d i r e c t i o n of r .  of the d i p o l e  0 r  C3  are  axis.  of a Magnetic D i p o l e i n a P a r a l l e l Hexapole  Magnet. The of Eq.  hexapole f i e l d  the  g e n e r a l term  C12  F(v)-= u s i n g Eqs.  f(y)  i s r e p r e s e n t e d by  C8  and  ol V  C9 and  ~ cp t- 1 (p = J  (C18)  3  3  3  changing to c y l i n d r i c a l c o o r d i n a t e s  r  ?  (cos  1®  f <- <^  5a)  thus the l i n e s of c o n s t a n t magnetic p o t e n t i a l <p and of f o r c e 1^ are g i v e n  0 -  d r  1  5  the  lines  by c o s  3e  (019)  and  y  = d  3  r  3  sin  30  (C20)  125 ' The parameters used to d e s c r i b e the hexapole magnet are shown i n F i g , 50, to  where a i s the d i s t a n c e from the source  the magnet entrance, r  particle  i s the r a d i a l p o s i t i o n  0  a t the magnet entrance, r  m  of the  i s the r a d i a l d i s t a n c e to  the p o l e t i p s , Ho i s the s t r e n g t h o f the magnetic f i e l d p o l e t i p s , and r and H denote the p o s i t i o n the magnet.  a t the  of the p a r t i c l e i n  I n terms o f these parameters, the magnitude o f  the magnetic f i e l d  s t r e n g t h a t any r a d i a l p o s i t i o n ,  as g i v e n  by Eq. C15 i s  l"l= The  CrJ  H  o  (021)  e q u a t i o n o f motion o f the d i p o l e i n the hexapole f i e l d as  g i v e n by Eq. C17 i s dV  +  r  2/6e  t f  Ho r  '771 TrX  dt " 7  letting 7 (C22) V the t r a j e c t o r y  of the focussed p a r t i c l e s  component o f / X e f f i n the d i r e c t i o n  r = A Sin b.rjusing  and  z - ut  f  (those w i t h a n e g a t i v e  o f H) i s  B cos b,-fc  t h i s e q u a t i o n becomes  the slope o f the t r a j e c t o r y i s  If  the p a r t i c l e s  and r a d i u s r  su  enter the p a r a l l e l magnet w i t h divergence S  then the a r b i t r a r y c o n s t a n t s are B = r  s  s  and  I n terms o f these constants E q s . C23 and G2h ;, \ ' ,L. ->\  A = . become r  s u sin(^) f r cos( jl)  =  The  describing  (C25)  b  s  s o l u t i o n o f the d i f f e r e n t i a l  equation  the t r a j e c t o r i e s o f the defocussed b,t „ ~b,t  .r = A, e  particles i s  e  B,  which using £ = u t can be w r i t t e n as  r ^ A, If  —  + B,  the p a r t i c l e s  {(r,  3.  e  b. *  e  have s l o p e S  f _ii)e u  u  4-  d  ^ and p o s i t i o n r ^ a t 2-= 0  ^ ( r  d  - < £ ^ )  e  then  (027)  ~ - ^  T r a j e c t o r i e s o f a Magnetic D i p o l e i n a Tapered Hexapole Magnet. The g e o m e t r i c a l parameters, d e s c r i b i n g the tapered  hexapole magnet are shown i n F i g . 5lo  The magnetic  field  s t r e n g t h , Ho, a t the p o l e t i p s i s assumed to be c o n s t a n t the l e n g t h o f the magnet as should be approximately the magnet i r o n i s s a t u r a t e d i n t h i s r e g i o n . to be a ,good approximation  i n practice.  along  true i f  This turns out  127  Z| —  Fig.  J >  2  51  ~  Schematic Diagram Showing the Parameters used d e s c r i b e the Tapered Hexapole Magnet.  By s i m i l a r  triangles  i n F i g . 51,  the p o l e  to  t i p radius r  as a m  f u n c t i o n of Z i s given r  ^~_  L±  A t any p o s i t i o n 2 , to  ^  (C28)  the f i e l d  s t r e n g t h i n a plane  the d i r e c t i o n 2 i s g i v e n by Eqs. C. 21  1 HI = The  by  rlii  c a l c u l a t i o n o f the  1  and C.  perpendicular 28.  Ho trajectories is limited  f o r which the v a r i a t i o n of the magnetic f i e l d  to those  cases  s t r e n g t h i n the  2 d i r e c t i o n i s s u f f i c i e n t l y s m a l l .so that the component of grad lfjI  i n t h i s d i r e c t i o n can be n e g l e c t e d .  of  the tapered  hexapole f i e l d ,  of  the d i p o l e as g i v e n by Eq. C17  Thus f o r the  case  the g e n e r a l e q u a t i o n o f motion becomes  128  \  where  u  TV)  the change o f v a r i a b l e ~£ = ut has been made.  Letting  ^ •  a  the  _  Ho  Z/de-f-C  (C29)  above e x p r e s s i o n becomes  ^  = t b:  r  3 ^  where and  x  (C30) ?  t  the p o s i t i v e and n e g a t i v e signs  focussed portions  o f the beam r e s p e c t i v e l y .  W i t h i n the above s t a t e d of  r e f e r to the defocussed  l i m i t a t i o n s , the s o l u t i o n  t h i s e q u a t i o n should not d i f f e r s i g n i f i c a n t l y from the  s o l u t i o n f o r the case o f the p a r a l l e l magnet. the n e g a t i v e p a r t  r--DZ CoS k  The s o l u t i o n of  of Eq. C30 can be shown (Ax65)  2  [JbfJJ^  ^  to be  }  (C31)  The two a r b i t r a r y c o n s t a n t s D and £ , determined by the boundary c o n d i t i o n s  and  6-  that r = r  R  - tan''  j  _ X f "^J _ J  2,  Q  and  =  at Z  z  £,  are  129 u s i n g these  two  constants  the r a d i a l p o s i t i o n s of the d i p o l e  i n the tapered hexapole magnet a t a p o s i t i o n 2 , as g i v e n by Eq. C31  r  as  z.  2r  0  Cz "0  1  [~k>l + \ 4bl -/ -±J  cos  (C33)  _ -fan"' }  By d i f f e r e n t i a t i n g Eq. C32 w i t h r e s p e c t to 2 , the s l o p e of  the  trajectory i s  k  •+ ^ ( ^  \  c o s  ^_  s/n  (  4bi-l  the t r a j e c t o r y of the defocussed l+ Hbi  The  +i'  a r b i t r a r y constants,  particles is i ->f4bi  and C^., as determined  by  boundary c o n d i t i o n s are  3  =  (  r.  2-,  2, 2*  J~4b\  (C34)  j  s o l u t i o n of the p o s i t i v e p a r t of Eq. C30, corresponding  The  C  ?  1 +xMfe'jH,  the  to  Substituting position  these  two equations  r o f the defocussed  i n Eq. C 3 5 the r a d i a l  particles at position  "2 i n the  hexapole magnet i s  (C36)  By d i f f e r e n t i a t i n g t h i s e x p r e s s i o n w i t h r e s p e c t to of  the t r a j e c t o r y o f the defocussed  in  the hexapole magnet i s  b+$^}{ f 2  the slope  particles at position  Z  - 0 f a \  4-Zr,  (C37)  Thus the t r a j e c t o r i e s o f the p a r t i c l e s  through a  combined tapered and p a r a l l e l hexapole magnet are o b t a i n e d f o r the case o f the focussed p a r t i c l e s as f o l l o w s .  F i r s t the  p o s i t i o n and s l o p e o f the p a r t i c l e s a t the end o f the tapered section  are o b t a i n e d using E q s . C32 and C3*+.  The p o s i t i o n and  slope o f the p a r t i c l e s i n the p a r a l l e l r e g i o n are then calculated  using Eqs. C 2 5 and C 2 6 .  the defocussed  A s i m i l a r proceedure f o r  p a r t i c l e s uses Eqs. C36 and C37 to c a l c u l a t e the  p o s i t i o n and s l o p e a t the end o f the tapered s e c t i o n  and uses  C27  to c a l c u l a t e  the p o s i t i o n i n the p a r a l l e l  region.  132 APPENDIX D CALCULATION OF SIGNAL SHAPE FROM TIME-OF-FLIGHT APPARATUS If of p a r t i c l e s  the chopper allows o n l y an i n f i n i t e l y s h o r t b u r s t to s t a r t on the way to the d e t e c t o r and i f the  d e t e c t o r i s i n f i n i t e l y s h o r t then the s i g n a l S (t) observed a t the d e t e c t o r can be d i r e c t l y r e l a t e d  to the d i f f e r e n t i a l  intensity distribution function K v j the i n i t i a l  j - o f the p a r t i c l e s i n  beam  •s(t)=A"r(v)  w h e r e  V  r  t  ( D 1 )  V and since  the d e t e c t o r  D-—of  signal  the p a r t i c l e s  A" =  constant  i s p r o p o r t i o n a l to the d e n s i t y  a t the d e t e c t o r separated  by a d i s t a n c e  L from the s o u r c e . Unfortunately time to pass a c r o s s  the chopper takes  the atomic beam p r o f i l e and as a r e s u l t  a group o f p a r t i c l e s w i t h a f i n i t e past  the chopper.  a f i n i t e length of  Also  time spread  i s allowed  the d e t e c t o r has a f i n i t e l e n g t h so  t h a t the s i g n a l r e c e i v e d w i l l be a sum o f c o n t r i b u t i o n s from all  s e c t i o n s o f the d e t e c t o r . Consider  burst of p a r t i c l e s  the case where the chopper allows a r e c t a n g u l a r such as shown i n F i g . 52 to enter  This d i s t r i b u t i o n w i l l  be c a l l e d  the s h u t t e r f u n c t i o n .  assume the d e t e c t o r has a l e n g t h s e c t i o n s of i t are e q u a l ,  the system.  V  and the response from a l l  that i s we have a r e c t a n g u l a r  response f u n c t i o n shown i n F i g . 53• system i s now as shown i n F i g . 54.  Also  detector  The geometry o f the Consider  some p o i n t  Jl i n  133  FWHM= T  F i g . 52  Rectangular  r  time t  Chopper S h u t t e r F u n c t i o n .  i'/v  F i g . 53  Rectangular  D e t e c t o r Response  Function.  DETECTOR  CHOPPER  £'•  F i g . 5\  Geometry o f T i m e - o f - F l i g h t  Apparatus.  13>  the d e t e c t o r at  at  some  time  t;  the s i g n a l a r i s i n g from p a r t i c l e s  t h i s p o s i t i o n i n s p a c e and t i m e S C t , / )  S(tj)  =.  >  •  V  since  J  /)"  f  n  ' • V  =  given  V  g i v e n by  =  Summing o v e r  2  ,  (D3) =  -t/fc-'t)  provided  -fr>T  c o n t r i b u t i o n s from a l l elements  S(t) = J c U  of  the  detector  S(t,X)  set) = [ u j Taking  X (V) d v  JU  1  V  by;  (D2)  V  an increment i n i n t e n s i t y i s  where  is  the f o r m o f  A" I M av  the d i f f e r e n t i a l  <"*>•  intensity distribution  f u n c t i o n recommended b y Hagena a n d M o r t o n (Ha67) (17)  where  we  A' -  con$4anV  have  (D5) v  where A = making a change  of  i  constant variable  X = v ^ p ( V- w )  135 (D6)  we have  136 and making the change o f v a r i a b l e s —  hi -  J ?  1  a f t e r some  Aw  ^  w  ~  w  •b  simplification TT  i (-b-l) (eric -ti - er$c-tl) -a (erkt? -ertct,"  A vTfr  (*-^(cr(ctl-erttt;y+  now Thus S ( t ) reduces to  -erf*/ )] (D8) 1  t(erf  t [  137 A computer programme was w r i t t e n function and H  r  to c a l c u l a t e  f o r v a r i o u s v a l u e s o f f , iY a n d / , .  used i n t h i s experiment  0  For the f i x e d  Jl \  the e f f e c t •Z has on widening  the FWHM o f the observed s i g n a l 4 f t h e o r e c t i c a l s i g n a l &t  the above  as compared  to the  i s summarized i n F i g . 26 where T E ' t  .  APPENDIX E BEPBINTED fSOM ith INTL. SYMPOSIUM Off M E F t E O GAS BYKABiCJ, t ©  196?  ACADEMIC PRESS INC, NEW YORK  A LOW TEMPERATURE NOZZLE BEAM FOR  A POLARIZED H e 3  +  ION SOURCE  R. Vyse, J.C. Heggie and M.K. Craddock P h y s i c s Department, U n i v e r s i t y o f B r i t i s h Columbia H e l i u m beam i n t e n s i t i e s o b t a i n e d from n o z z l e s c o o l e d t o 77°K and 4.-2°K a r e s t u d i e d f o r p o s s i b l e use as an atomic beam s o u r c e i n a p o l a r i z e d H e i o n source. ' J  P o l a r i z e d i o n s o u r c e s r e q u i r e atomic beams o f h i g h i n t e n s i t y t o c o u n t e r a c t the v e r y low i o n i z a t i o n e f f i c i e n c i e s o b t a i n a b l e by e l e c t r o n bombardment. F u r t h e r m o r e , 3 e atoms have o n l y t h e i r s m a l l n u c l e a r magnetic moment, so t h a t S t e r n - G e r l a c h s p l i t t i n g o f the two s p i n s t a t e s r e q u i r e s an u n r e a s o n a b l y l o n g magnet u n l e s s the atomic v e l o c i t i e s a r e s u f f i c i e n t l y s m a l l . A n o z z l e o f the s t y l e suggested by K a n t r o w i t z and Grey^, c o o l e d t o l i q u i d h e l i u m temperatures, t h e r e f o r e appeared t o be a p o s s i b l e s o l u t i o n t o the r e q u i r e ments o f h i g h i n t e n s i t y and low v e l o c i t y . H  Many groups have s t u d i e d the b e h a v i o u r o f atomic beams produced by s m a l l n o z z l e s and have found s u b s t a n t i a l depart u r e s from the i d e a l b e h a v i o u r o r i g i n a l l y p o s t u l a t e d . These d e p a r t u r e s a r e a t t r i b u t e d t o the i n t e r a c t i o n ^ between t h e skimmer and the s u p e r s o n i c beam, and the background gas s c a t t e r i n g - * t a k i n g p l a c e i n the r e g i o n between the n o z z l e and the skimmer. P r e v i o u s work u s i n g c r y o g e n i c a l l y c o o l e d n o z z l e s ^ and h e l i u m gas, however, has been aimed more a t e x a m i n i n g c o n d e n s a t i o n than a t m a x i m i z i n g the beam i n t e n s i t y . The atomic beam s o u r c e has been b r i e f l y d e s c r i b e d by Axen^ and c o n s i s t s o f a D = 0.2 mm diameter n o z z l e and 0.4 mm d i a m e t e r skimmer a t t a c h e d t o a c r y o s t a t c a p a b l e o f s u s t a i n e d o p e r a t i o n a t 4.2°K. The d i f f e r e n t i a l pumping system s i m u l t a n e o u s l y p r o v i d e s the vacuum r e q u i r e d f o r the o p e r a t i o n o f the atomic beam and the c r y o g e n i c system. W i t h t h i s s o u r c e we a r e examining the b e h a v i o u r  939  o f an  VYSE, HEGGIE, A N D CRADDOCK  a t o m i c He beam w i t h the n o z z l e a t room, l i q u i d n i t r o g e n and l i q u i d h e l i u m temperatures. In each case the skimmer and c o l l i m a t o r a r e c o o l e d to the same temperature as the nozzle. O p e r a t i o n o f the atomic beam s o u r c e a t room temp e r a t u r e u s i n g an 0.2 mm diameter c o n v e r g i n g n o z z l e shows the s t a n d a r d dependence^ o f i n t e n s i t y on nozzle-skimmer s e p a r a t i o n measured i n n o z z l e d i a m e t e r s , L/D, ( F i g . 1 ) . At 77°K measurements have so f a r been made a t f o u r d i f f e r e n t s e p a r a t i o n s , and i n d i c a t e a s i m i l a r dependence over a compressed distance scale. At 4.2°K measurements have been r e s t r i c t e d to two s e p a r a t i o n s w i t h the t u b i n g n o z z l e d e s s c r f b e d below. 4  F i g u r e 2 shows the e f f e c t o f n o z z l e temperature ( T ) and p r e s s u r e ( P ) on beam i n t e n s i t y f o r two f i x e d n o z z l e skimmer s e p a r a t i o n s . F o r t h e s e measurements the o r i f i c e c o n s i s t e d o f a s e c t i o n o f 0.0095" diameter t u b i n g a p p r o x i m a t e l y 10 n o z z l e d i a m e t e r s i n l e n g t h . The behavour o f the t u b i n g n o z z l e i s s i m i l a r to t h a t of a c o n v e r g i n g n o z z l e , as can be seen i n the i n s e r t o f i n t e n s i t y v a r i a t i o n w i t h nozzle-skimmer s e p a r a t i o n . The p e r i o d i c s c a t t e r i n e x p e r i m e n t a l p o i n t s i n the i n s e r t i s due to an alignment d i f f i culty. T y p i c a l n o z z l e exhaust chamber p r e s s u r e s (PgQ-mTorr) a r e shown i n b r a c k e t s b e s i d e the r e l e v a n t e x p e r i m e n t a l points. A s i m i l a r s e t of c u r v e s i s shown i n F i g . 3 f o r a 0.2 mm d i a m e t e r n o z z l e made by p i e r c i n g a h o l e i n a p i e c e of 0.001" b r a s s shim shock. A g a i n the t y p i c a l background p r e s s u r e s i n the n o z z l e exhaust chamber a r e shown. 0  0  There i s e v i d e n c e t h a t the beam i s b e i n g a t t e n u a t e d by s c a t t e r i n g by background gas i n b o t h the n o z z l e exhaust chamber and i n the r e g i o n between the skimmer and c o l l i m a t o r . T y p i c a l p r e s s u r e s i n the s k i m m e r - c o l l i m a t o r r e g i o n , P , measured 2 cm from the beam a x i s and c o r r e c t e d f o r t h e r m a l t r a n s p i r a t i o n , a r e t a b u l a t e d i n T a b l e 1 a l o n g w i t h the e s t i m a t e d r e s u l t i n g f r a c t i o n o f beam o b s e r v e d ( l / I ) f o r t y p i c a l p o i n t s chosen from F i g . 3. The l / I r a t i o was c a l c u l a t e d assuming a s i m p l e e x p o n e n t i a l s c a t t e r i n g r e l a t i o n s h i p u s i n g a v i s c o s i t y based mean f r e e p a t h . U n c e r t a i n t i e s i n the e f f e c t i v e mean f r e e p a t h f o r s c a t t e r i n g out o f a beam a t 4.2°K, and i n the p r e s s u r e measurements, g i v e r i s e to l a r g e r u n c e r t a i n t i e s s t i l l i n the a t t e n u a t i o n because o f i t s e x p o n e n t i a l dependence. The u n c e r t a i n t i e s quoted i n T a b l e 1 a r e based on i 50% u n c e r t a i n t i e s i n mean f r e e p a t h . s c  D  0  The  r a t i o o f observed  to t h e o r e t i c a l beam  940  intensities,  S I X T H R A R E F I E D GAS D Y N A M I C S  uncorrected f o r attenuation, i s plotted as a function of the Knudsen to Mach number r a t i o i n F i g . 4 f o r the experimental points shown i n the previous figure. The Knudsen number i s based on calculated free stream conditions at the skimmer entrance and the Mach number i s determined using the nozzleskimmer separation and the method of c h a r a c t e r i s t i c s solut i o n of Owen and T h o r n h i l l ^ . Considering the extent of the attenuation of the higher P measurements at 4.2°K, the r e s u l t s of F i g . 4 show a considerable increase i n beam i n tensity over what we might expect based on the results of Fenn and Deckers as indicated by the straight l i n e . 0  .REFERENCES 1. 2. 3. 4. 5. 6.  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