UBC Theses and Dissertations

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UBC Theses and Dissertations

Scattering of light from a plasma jet. Kamp, Garth Stephen John Paul, van der 1968

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'SCATTERING OF LIGHT FROM A PLASMA JET by G a r t h S.J.P. van d e r Kaxnp  B.Sc,  U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1966  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF • MASTER IN SCIENCE i n t h e 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 t o t h e required standard  THE UNIVERSITY OF BRITISH COLUMBIA May, 1968  In  presenting  for  an  that  advanced  thesis  shall  | further  agree  for scholarly  Department  or by  publication  without  thesis  degree  the Library  Study.  or  this  my  fills  make  i t freely  that  may  thesis  permission.  Columbia  the  granted  by  requirements  Columbia,  t h e Head  shall  and  copying  It i s understood  gain  I agree  for reference  f o r extensive  for financial  Department  Date  be  of  of British  available  permission  representatives.  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  fulfilment  the U n i v e r s i t y  purposes  of this  written  at  in partial  of  of  this  my  that  n o t be  copying  allowed  ABSTRACT  The e l e c t r o n d e n s i t y i n a plasma j e t has been d e t e r m i n e d as a f u n c t i o n o f p o s i t i o n i n t h e j e t by measurements o f t h e c o h e r e n t s c a t t e r i n g of l a s e r l i g h t .  The e l e c t r o n d e n s i t y p r o f i l e s t h u s o b t a i n e d  w i t h p r o f i l e s obtained  from measurements o f s p e c t r a l l i n e  a r e compared  intensities.  The r e s u l t s o f t h e s e two d i a g n o s t i c methods a r e seen t o agree w i t h i n experimental  error.  For t h e e x p e r i m e n t d e s c r i b e d h e r e , t h e s c a t t e r i n g  i s from c o r r e l a t e d m o t i o n o f t h e e l e c t r o n s , and the s c a t t e r e d spectrum has d i s t i n c t e l e c t r o n s a t e l l i t e s .  light  I t i s shown t h a t t h e w i d t h  o f t h e s e s a t e l l i t e s , observed i n e a r l i e r work by Chan and N o d w e l l ( 1 9 6 6 ) , may be a c c o u n t e d f o r by t h e e l e c t r o n d e n s i t y g r a d i e n t s i n t h e plasma. T h i s t h e s i s g i v e s a s h o r t r e v i e w o f t e c h n i q u e s and r e l e v a n t t h e o r y , emphasis on e x p e r i m e n t a l  problems.  with  A b r i e f discussion of perturbation  o f t h e plasma by t h e l a s e r l i g h t i s a l s o  included.  - iii  -  TABLE OP CONTENTS Page ABSTRACT  . . . . . . .  TABLE OF CONTESTS  i i i iv  LIST OF ILLUSTRATIONS . „ . . . ' ACKNOWLEDGEMENTS Chapter I  INTRODUCTION  Chapter I I  THEORY  v . . . .  4  B - Application to Diagnostics  8  ...  C - A p p a r a t u s and Technique  Chapter IV  10  MEASUREMENTS OF EXCITATION TEMPERATURES . . . . .  17  A - Theory  17  B - The A b e l Transform  20  C - Absolute Intensity Calibration  23  RESULTS  . . . . .  28  A - P e r t u r b a t i o n o f t h e Plasma  28  B - Preliminary Scattering Results  30  C - Plasma D i a g n o s i s R e s u l t s  31  . . . . . . . . .  D - S a t e l l i t e Widths Chapter V  1 .4  A - Theory o f S c a t t e r i n g  Chapter I I I  i i  CONCLUSIONS  33 '  37  A - Discussion of Results . . . . . . . . . . .  37  B - S u g g e s t i o n s f o r F u t u r e Yvork  37  BIBLIOGRAPHY  39  - iv-  L I S T OF  ILLUSTRATIONS  Figure  Page  1  Typical scattered l i g h t spectra .  2  Schematic o f E x p e r i m e n t a l Arrangement . . .  3  C a l i b r a t i o n of absorbtion  4  P e r t u r b a t i o n o f Plasma by L a s e r .  5  R a d i a l E l e c t r o n D e n s i t y P r o f i l e i n Argon J e t  6  R a d i a l E l e c t r o n Density P r o f i l e i n Helium J e t . . . . .  32  7  R a d i a l E l e c t r o n D e n s i t y P r o f i l e s i n Argon J e t . . . . .  34  8  Observed and T h e o r e t i c a l S a t e l l i t e P r o f i l e s  35  filters  ...  6 11  . . . . . .  25 .28  . . . . .  32  ACKNOWLEDGMENTS  My thanks go f i r s t o f a l l t o my s u p e r v i s o r , D r . R.A. N o d w e l l , f o r h i s guidance  d u r i n g t h e e x p e r i m e n t a l work and h i s p a t i e n c e  during the preparation o f t h i s t h e s i s . Mr. Mo C h u r c h l a n d  I would a l s o l i k e t o t h a n k  f o r h i s a i d and a d v i c e i n t h e e x p e r i m e n t a l work,  and t h e members o f t h e t e c h n i c a l s t a f f , i n p a r t i c u l a r Mr. J . Dooyev/eerd, f o r t h e i r f r e q u e n t a i d and u s e f u l s u g g e s t i o n s .  CHAPTER I - INTRODUCTION  I n r e c e n t y e a r s t h e s c a t t e r i n g o f l a s e r l i g h t by a plasma h a s r e c e i v e d much a t t e n t i o n , b o t h t h e o r e t i c a l l y and e x p e r i m e n t a l l y . i n t e r e s t i s duo a t l e a s t i n p a r t t o t h e advantages o f u s i n g s c a t t e r i n g as a plasma d i a g n o s t i c t o o l , t h e most i m p o r t a n t  This  light o f these  b e i n g t h e good r e s o l u t i o n i n space and t i m e -which c a n be o b t a i n e d . Besides  t h a t t h e r e i s t h e p r a c t i c a l , and perhaps b a s i c advantage t h a t  t h e r e l i a b i l i t y o f t h i s d i a g n o s t i c method does-not depend on i n t e r m e d i a t e t h e o r i e s and assumptions about t h e n a t u r e and p r o p e r t i e s o f t h e plasma t h e weak p o i n t i n most o t h e r d i a g n o s t i c methods. The theory' o f t h e s c a t t e r i n g o f l i g h t h a s been d e r i v e d and d i s c u s s e d by a number o f a u t h o r s and R o s e n b l u t h (1962).  such as S a l p e t e r ( i 9 6 0 ) , and R o s t o k e r  The case o f t h e p a r t i c u l a r experiment d e s c r i b e d  i n t h i s t h e s i s i s discussed by W i l l i a m s o n  e t a l (1966), and by P.W. Chan (1966)  When t h e plasma e l e c t r o n s a c t i n d e p e n d e n t l y , l i g h t i s e s s e n t i a l l y Gaussian, motion o f the e l e c t r o n s .  the p r o f i l e of the scattered  due t o d o p p l e r b r o a d e n i n g b y t h e t h e r m a l  When t h e e l e c t r o n s a c t c o h e r e n t l y , t h e s c a t t e r e d  l i g h t p r o f i l e c o n s i s t s o f a c e n t r a l peak, and o f weak e l e c t r o n s a t e l l i t e s , s h i f t e d t o e i t h e r s i d e o f t h e c e n t r a l l i n e by a p p r o x i m a t e l y frequency.  t h e plasma  The s a t e l l i t e s h i f t t h u s g i v e s a measure o f e l e c t r o n d e n s i t y .  T h i s l a t t e r case o f c o h e r e n t s c a t t e r i n g h o l d s f o r t h e experiment described  here.  Among t h e e x p e r i m e n t a l  problems a s s o c i a t e d w i t h s c a t t e r i n g  the low i n t e n s i t y o f t h e s c a t t e r e d l i g h t i s o f o v e r r i d i n g importance. For t h e experiment d e s c r i b e d h e r e , t h e i n t e n s i t y o f t h e observed -14 s c a t t e r e d l i g h t i s down by a f a c t o r o f about 10 of the i n c i d e n t l i g h t .  - 1 -  from t h e i n t e n s i t y  - 2 -  S e v e r a l w o r k e r s have r e p o r t e d t h e use o f s c a t t e r i n g as a diagnostic tool.  Among t h e s e a r e Rflhr (1967) vfho used t h e s a t e l l i t e  6 h i f t t o g i v e a measure o f e l e c t r o n d e n s i t y ; Izawa e t a l (1966) who used s c a t t e r i n g t o o b t a i n e l e c t r o n d e n s i t i e s i n a shock f r o n t ; and, most i m p o r t a n t f o r t h e p r e s e n t p u r p o s e s , Chan and Nodwell  (1966) who  f i r s t observed t h e s a t e l l i t e s f o r s c a t t e r i n g from a l a b o r a t o r y plasma, (plasma j e t ) and showed t h a t t h e observed s a t e l l i t e s h i f t was i n good agreement w i t h t h e expected v a l u e s o f t h e plasma p a r a m e t e r s .  The  work d e s c r i b e d i n t h i s t h e s i s i s a c o n t i n u a t i o n o f t h e work r e p o r t e d by Chan and N o d w e l l . One problem encountered by Chan and N o d w e l l was t h a t t h e observed s a t e l l i t e w i d t h was much l a r g e r t h a n t h a t expected from t h e t h e o r y . T h i s b r o a d e n i n g was t e n t a t i v e l y a t t r i b u t e d t o e l e c t r o n d e n s i t y g r a d i e n t s i n t h e s c a t t e r i n g volume.  A t f i r s t t h e purpose o f t h e c o n t i n u e d work  was t o v e r i f y t h i s a s s u m p t i o n . to  A f t e r some t i m e i t became apparent t h a t  a c c o m p l i s h t h i s purpose, e l e c t r o n d e n s i t y p r o f i l e s o f t h e plasma j e t  must be o b t a i n e d .  This consideration, together with the fact that  s a t e l l i t e w i d t h c o u l d n o t be measured v e r y r e l i a b l y , changed t h e emphasis of t h e experiment towards plasma d i a g n o s t i c s , u s i n g t h e s a t e l l i t e to  shift  determine e l e c t r o n d e n s i t y . In  c o n n e c t i o n w i t h t h i s d i a g n o s t i c approach, e l e c t r o n d e n s i t y  p r o f i l e s o f t h e plasma j e t were a l s o o b t a i n e d u s i n g s p e c t r a l  line  i n t e n s i t y measurements, w i t h a t e c h n i q u e s i m i l a r t o t h a t o f O l s e n (1963). These measurements a l l o w e d a comparison o f t h e two d i a g n o s t i c methods, both w i t h r e g a r d t o r e s u l t s and w i t h r e g a r d t o a p p l i c a b i l i t y and r e l i a b i l i t y . In  a d d i t i o n of course  such an independent measurement o f plasma  parameters  makes i t p o s s i b l e t o v e r i f y t h a t t h e s a t e l l i t e s h i f t i s indeed t h a t  p r e d i c t e d by t h e t h e o r y . w i t h independently  A d e t a i l e d agreement o f s c a t t e r i n g o b s e r v a t i o n s  measured plasma parameters has as y e t n o t been  reported i n the l i t e r a t u r e . F i n a l l y , t h e e l e c t r o n d e n s i t y p r o f i l e s o b t a i n e d by t h e d i a g n o s t i c methods mentioned above were used t o d e t e r m i n e what p a r t o f t h e o b s e r v e d s a t e l l i t e widths  c o u l d be a t t r i b u t e d t o e l e c t r o n d e n s i t y g r a d i e n t s i n  t h e plasma. T h i s t h e s i s r e p o r t s and compares t h e r e s u l t s o b t a i n e d by t h e two d i a g n o s t i c methods one u s i n g s c a t t e r i n g o f l i g h t , and t h e o t h e r using spectral l i n e i n t e n s i t i e s .  Some r e s u l t s as t o s a t e l l i t e  widths,  and p e r t u r b a t i o n o f t h e plasma by t h e l a s e r l i g h t a r e a l s o g i v e n . Chapter I I g i v e s a summary and s i m p l e p h y s i c a l e x p l a n a t i o n o f t h e r e l e v a n t s c a t t e r i n g t h e o r y , and a l s o d i s c u s s e s , t h e apparatus and experimental  techniques  used i n s c a t t e r i n g o b s e r v a t i o n s .  This  d i s c u s s i o n i s f o r a l a r g e part a continuation o f the d i s c u s s i o n given i n P.W.  Chan's t h e s i s .  Chapter I I I c o n t a i n s a s h o r t p r e s e n t a t i o n o f  t h e t h e o r y and t e c h n i q u e s  used i n t h e s p e c t r a l l i n e i n t e n s i t y measurements  Chapter IV r e p o r t s and a n a l y z e s t h e e x p e r i m e n t a l  r e s u l t s on e l e c t r o n  d e n s i t y g r a d i e n t s , s a t e l l i t e w i d t h , and p e r t u r b a t i o n o f t h e plasma. C h a p t e r V g i v e s some c o n c l u s i o n s based on t h e s e r e s u l t s , and a l s o g i v e s some s u g g e s t i o n s  a s . t o f u t u r e work.  The work r e p o r t e d i n t h i s t h e s i s has been p u b l i s h e d r e c e n t l y , (Nodwell  and van d e r Kamp, 1963).  CHAPTER I I - SCATTERING OF LIGHT FROM A PLASMA  .The t h e o r y f o r t h e s c a t t e r i n g o f l i g h t from a plasma has become w e l l established i n recent years.  I n f a c t , p a r t l y because o f t h e  d i f f i c u l t i e s i n h e r e n t i n t h e o b s e r v a t i o n of s c a t t e r i n g , t h e theory i s a t p r e s e n t w e l l ahead o f experiment,  being e a s i l y capable o f  a c c o u n t i n g f o r a l l e x p e r i m e n t a l r e s u l t s o b t a i n e d up t i l l  now. F o r  t h a t reason the d i s c u s s i o n o f s c a t t e r i n g i n t h i s chapter w i l l t h e p r a c t i c a l problems i n v o l v e d i n t h i s p a r t i c u l a r  emphasize  experiment.  A - Theory o f S c a t t e r i n g . .From a t h e o r e t i c a l p o i n t o f v i e w t h e s c a t t e r i n g o f l i g h t b y a plasma i s a complex phenomenon.  Some r a t h e r i n v o l v e d mathematics i s  required to describe i t i n f u l l d e t a i l .  The complete t h e o r y h a s been  d e r i v e d and d i s c u s s e d by a number o f a u t h o r s , i n c l u d i n g f i r s t o f a l l S a l p e t e r ( i 9 6 0 ) , and R o s t o k e r and R o s e n b l u t h a n a l y z e s t h e p a r t i c u l a r case o f t h e experiment  (1962).  W i l l i a m s o n e t a l (1966)  described i n t h i s  thesis,  i n c l u d i n g a F o r t r a n program t o c a l c u l a t e t h e spectrum o f t h e s c a t t e r e d light.  A complete t h e o r e t i c a l d e r i v a t i o n i s a l s o g i v e n i n t h e t h e s i s  by P.W. Chan (1966) who d i d t h e f i r s t work i n t h i s The f u l l t h e o r y w i l l n o t be reproduced r e s u l t s r e l e v a n t t o t h e experiment  experiment.  here, since the t h e o r e t i c a l  can be s i m p l y summarized and  q u a l i t a t i v e l y e x p l a i n e d on t h e b a s i s o f p l a u s i b l e p h y s i c a l arguments. More d e t a i l c a n be found i n t h e r e f e r e n c e s g i v e n above. The r e s u l t s o f t h e f u l l t h e o r y may be r o u g h l y summarized as follows.  We c o n s i d e r a plasma w i t h e l e c t r o n d e n s i t y N , e l e c t r o n  temperature  e  T , i o n temperature e  T^, and e l e c t r o n Debye l e n g t h  where K-j-, i s Boltzmann c o n s t a n t and e t h e e l e c t r o n i c charge.  L ^I t turns  out t h a t t h e n a t u r e o f t h e s c a t t e r e d l i g h t spectrum i s c h a r a c t e r i z e d by  -  4  j  t h e parameter  cx  ^ A l < J \_j  —  "  v  v  f  t  e  r  e  &  k  ^  s  t'  n e  d i f f e r e n c e between t h e  wave v e c t o r s o f t h e i n c i d e n t and t h e s c a t t e r e d l i g h t . t h i s parameter, o<, has a s i m p l e e x p l a n a t i o n  As we w i l l  i n terms o f plasma waves.  Some t y p i c a l s c a t t e r e d l i g h t s p e c t r a a r e shown i n F i g . 1. case  see,  The  cx« | c o r r e s p o n d s r o u g h l y t o t h e case o f the w a v e l e n g t h o f t h e  i n c i d e n t l i g h t b e i n g much s m a l l e r t h a n t h e Debye l e n g t h .  The  electrons  a c t i n d i v i d u a l l y and t h e s c a t t e r e d spectrum approaches t h a t o f Thomson s c a t t e r i n g , d o p p l e r broadened by t h e t h e r m a l m o t i o n o f the e l e c t r o n s . I n t h e case electrons.  I  c<  t h e s c a t t e r i n g i s by c o l l e c t i v e m o t i o n o f t h e  The s c a t t e r e d spectrum has a narrow c e n t r a l peak, and weak  e l e c t r o n " s a t e l l i t e " peaks s e p a r a t e d from t h e c e n t r a l peak by a p p r o x i m a t e l y t h e plasma f r e q u e n c y . satellite shift  A CJ  More p r e c i s e l y , t h e t h e o r y p r e d i c t s t h a t t h e i s g i v e n by  where o., i s t h e plasma f r e q u e n c y and  t h e Eoltzmann c o n s t a n t .  case oi^n | has c h a r a c t e r i s t i c s l y i n g somewhere between t h e two cases g i v e n above.  The  extreme  We a r e p a r t i c u l a r l y concerned w i t h t h e case  ) I .  The t h e o r y a l s o p r e d i c t s t h a t f o r a p a r t i c u l a r s c a t t e r i n g a n g l e \ + c<  and s o l i d a n g l e , t h e t o t a l s c a t t e r e d i n t e n s i t y i s p r o p o r t i o n a l t o ^ ^ ^ w h i l e t h e i n t e g r a t e d i n t e n s i t y o f each s a t e l l i t e i s p r o p o r t i o n a l t o -7— |  The r a t i o of t h e i n t e n s i t y o f each s a t e l l i t e t o t h a t of t h e c e n t r a l peak i s thus * ^  • w h i c h approaches  —ro  for large  e< .  These r e s u l t s can be q u a l i t a t i v e l y u n d e r s t o o d i f we c o n s i d e r  that  t h e c o l l e c t i v e m o t i o n s of t h e e l e c t r o n s a r e j u s t plasma waves, so t h a t i n t h e case  c< yy  \  , t h 9 s c a t t e r e d l i g h t spectrum i s d e t e r m i n e d by t h e  spectrum o f t h e plasma waves.  In p a r t i c u l a r , consider  t h e diagram shown  2  , .  r  -  10  20  A X  (A )  6  -  15  30  0  A  X  (A )  F i g u r e 1 - T y p i c a l s c a t t e r e d l i g h t s p e c t r a f o r the argon plasma j e t .  0  -  <—  7  -  on t h e l e f t ( H o l t and H a s k e l l ,  cx  1965,  p. 364).  O n l y plasma  waves w i t h wave number  k - &  k  c o n t r i b u t e t o the s c a t t e r i n g .  ^*=^~Q  k »  «  lj  For  no plasma  waves e x i s t , s i n c e the w a v e l e n g t h i s l e s s t h a n t h e Debye l e n g t h For t h e c o r r e s p o n d i n g v a l u e s  L^. o f c<  we would e x p e c t t h e spectrum o f  k-y  t h e s c a t t e r e d l i g h t t o be c h a r a c t e r i s t i c of uncorrelated can e x i s t and  e l e c t r o n motion.  For  k<£—j^o<= j^TJ^)') plasma waves  produce s a t e l l i t e s w i t h f r e q u e n c y s h i f t s a t i s f y i n g  d i s p e r s i o n equation  o f the plasma waves (Eq 2-1).  The  the  s p e c t r a l w i d t h of  t h e s a t e l l i t e s i s r e l a t e d t o t h e Landau damping of the waves, which i n t u r n depends on the d e r i v a t i v e o f the o n e - d i m e n s i o n a l v e l o c i t y d i s t r i b u t i o n function at  ~ K  ( t h e phase v e l o c i t y o f the plasma wave).  Also,  since  t h e e l e c t r o n s most e f f e c t e d by the waves are t h e ones w h i c h t r a v e l w i t h i t a t i t s phase v e l o c i t y , t h e i n t e n s i t y of t h e s a t e l l i t e s depends on v a l u e of t h e v e l o c i t y d i s t r i b u t i o n a t  ^  .  Thus b o t h the w i d t h  i n t e g r a t e d i n t e n s i t y of the s a t e l l i t e s i n c r e a s e w i t h d e c r e a s i n g U s i n g t h i s p i c t u r e one  can e a s i l y see how  oi  the i n t e n s i t y of  the  and (increasin the  s a t e l l i t e s can be enhanced t h r o u g h e x c i t a t i o n o f the plasma waves which do the s c a t t e r i n g , t h a t i s by an i n c r e a s e of t h e number o f s u p e r - t h e r m a l e l e c t r o n s t r a v e l l i n g w i t h t h e wave a t i t s phase v e l o c i t y . The  r e s t of the e l e c t r o n s a r e not c o r r e l a t e d t o ' e a c h o t h e r ,  t h e i r random t h e r m a l v e l o c i t i e s a r e t o o h i g h , b u t t o t h e i o n s .  since  Thus t h e  - 8 -  c e n t r a l peak e x h i b i t s a s p e c t r a l d i s t r i b u t i o n dependent on t h e i o n m o t i o n , i . e . dependent on i o n t h e r m a l v e l o c i t i e s and i o n waves.  B - Application to Diagnostics. Yftien s c a t t e r i n g o f l i g h t  i s . u s e d f o r plasma d i a g n o s t i c s , the  problem i s t o d e t e r m i n e t h e unknown plasma parameter from t h e observed s c a t t e r e d spectrum.  The s c a t t e r e d s i g n a l u s u a l l y i s v e r y weak, so t h a t  o n l y some o f t h e g r o s s e r parameters o f t h e s c a t t e r e d spectrum such as satellite  s h i f t , i n t e g r a t e d i n t e n s i t i e s , and h a l f w i d t h s can be measured.  C o n s e q u e n t l y o n l y a few plasma parameters such as t e m p e r a t u r e s and d e n s i t i e s can be d e t e r m i n e d . I n t h e experiment d e s c r i b e d were measured were t h e s a t e l l i t e  h e r e the s c a t t e r i n g parameters  s h i f t and h a l f w i d t h .  For l a r g e  that o<  the  s a t e l l i t e h a l f w i d t h w h i c h i s s t r o n g l y dependent on e l e c t r o n t e m p e r a t u r e , i s t o o s m a l l t o measure a c c u r a t e l y . dependence o f t h e s a t e l l i t e estimate equation,  shift i s small,  of temperature, obtained  i s s u f f i c i e n t t o a l l o w an a c c u r a t e  f o r the s a t e l l i t e s h i f t  see Eq. l - 2 ) a rough  from e l e c t r o n d e n s i t y through t h e Saha  d e n s i t y from t h e observed s a t e l l i t e  s m a l l c<,  However, s i n c e t h e t e m p e r a t u r e  shift.  e v a l u a t i o n of e l e c t r o n In p r a c t i c e equation ( l )  i s found t o be not s u f f i c i e n t l y a c c u r a t e f o r  The e x a c t r e l a t i o n between e l e c t r o n d e n s i t y and  satellite  shift  can be determined by d i r e c t computer c a l c u l a t i o n o f t h e s c a t t e r e d  light  spectrum ( W i l l i a m s o n  e t a l 1966) w i t h t e m p e r a t u r e dependent on  e l e c t r o n d e n s i t y t h r o u g h t h e Saha e q u a t i o n .  T a b l e 1 g i v e s plasma  and  s c a t t e r i n g parameters f o r argon and h e l i u m a t a t m o s p h e r i c p r e s s u r e , a s c a t t e r i n g a n g l e o f 45°. t h e t a b l e were o b t a i n e d  Values intermediate  and  between t h o s e g i v e n i n  by g r a p h i c a l methods, and by i n t e r p o l a t i o n .  T a b l e 1 - Plasma and s c a t t e r i n g Parameters f o r Argon and H e l i u m J e t s TEMP (°k)  EL DEN (om-3)  NEUTRALS D M (cm" 3)  PARTITION FN  .14-5E16 .535E16 .151E17 .346E17 .667E17 .109E18 .152E18 .184E18 .199E18 .202E18 .197E18 .190E18  .914E18 .805E18 .704E18 .599E18 ;480E18 .349E18 .224E18 .125E18 .643E17 .325E17 .172E17 „987E16  1.000 1.000 1.000 1.001 1.003 1.006 1.014 1.030 1.063 1.124 1.231 1.409  .621E15 •159E16 .355E16 .713E16 .130E17 .220E17 .344E17 .503E17 .686317 .873E17 .104E18 .117E18  .610E18 .561E18 .517E18 .475E18 .433E18 .388E18 .339E18 .28 6E18 .230E18 .175E18 .125E18 .843E17  1.000 1.000 1.000 1.000 l.OCO 1.000 1.000 1.000 1.001 1.002 1.003 1.005  ALPHA  SAT SHIFT ( °) A  ARGON 8000 9000 10000 11000 12000 13000 . 14000 15000 16000 17000 18000 19000  0.89 1.61 2.57 3.71 4.93 6.06 6.91 7.34 7.39 7.21 6.93 6.63  15.5 22.3 30.2 39.7 49.7 58.1 63.7 66.3 66.8 66.2 65.2  HELIUM 12000 13000 14000 15000 16000 17000 18000 19000 20000 21000 22000 23000  Note:  .48 .73 1.05 1.44 1.89 2.38 2.89 3.40 3.88 4.27 4.56 4.73  18.2 23.0 27.7 32.7 36.9 41.9 46.3 50.0 52.7  These d a t a a r e f o r p r e s s u r e o f 1 atm. Argon c o m p o s i t i o n d a t a a r e from Popenoe and Schumaker (1965), H e l i u m d a t a from Drawin and Felenbok (1965).  - 10 -  C - A p p a r a t u s and  Technique.  A diagram of the experimental o f s c a t t e r i n g i s g i v e n i n F i g . 2.  arrangement f o r the  observation  As has been mentioned b e f o r e ,  this  e x p e r i m e n t i s a c o n t i n u a t i o n o f t h e work done by P.W.  Chan, and t h e a p p a r a t u s  and t e c h n i q u e  Thus t h e f o l l o w i n g  a r e e s s e n t i a l l y t h o s e w h i c h Chan used.  d i s c u s s i o n w i l l be l a r g e l y c o n f i r m e d  t o v a r i o u s improvements T f h i c h have  been made, and t h e r e a d e r i s asked t o r e f e r t o Chan's t h e s i s f o r comparison or a d d i t i o n a l information. (a) L a s e r .  The l a s e r used was  l a s e r , w i t h a Daly-Sims attachment.  a TRG Model 104A  Q-switched r u b y  The Daly-Sims a c c e s s o r y  shortens  the  t i m e d u r i n g w h i c h l a s i n g can t a k e p l a c e , and t h u s i n c r e a s e s t h e power of The  the l a s e r p u l s e , w h i l e e l i m i n a t i n g the p o s s i b i l i t y of m u l t i p l e p u l s e s . combined u n i t s a r e r a t e d f o r a p u l s e - w i d t h  divergence  of  o f 30 nanoseconds, beam  10 m i l l i r a d i a n s , and peak power o f 30 megawatts.  TRG Model 104 l a s e r used by Chan was Thus t h e model 104A  The  r a t e d f o r a peak power o f 10 megawatts.  r e p r e s e n t s an i m p o r t a n t  improvement i n l a s e r power,  and i n t h e r e s u l t a n t i n t e n s i t y of s c a t t e r e d l i g h t . (b) Plasma J e t . Chan. 10  The plasma j e t i s s i m i l a r t o t h e one used  by  I t g i v e s a r e p r o d u c i b l e plasma w i t h an e l e c t r o n d e n s i t y between and 10  cm"  and a t e m p e r a t u r e o f 1 t o 2 ev.  The j e t i s o p e r a t e d  a t a t m o s p h e r i c p r e s s u r e w i t h a c u r r e n t o f 150 t o 300 amperes and a (argon or h e l i u m ) f l o w r a t e o f 75 t o 150 m i l l i l i t r e s per second.  gas As  the  f l o w r a t e t h r o u g h t h e j e t i s i n c r e a s e d t o about 100 ml/sec t h e r e i s a marked t r a n s i t i o n from l a m i n a r t o t u r b u l e n t f l o w . work was  Most o f the  experimental  done i n t h e l a m i n a r f l o w regime because i t g i v e s a much s t e a d i e r  and more r e p r o d u c i b l e plasma.  For more d e t a i l on the c o n s t r u c t i o n , o p e r a t i o n ,  F i g u r e 2 - Schematic o f t h e E x p e r i m e n t a l Arrangement  -  and p r o p o r t i e s P.W.  Chan (196$  -  12  of the j e t , the r e a d e r i s r e f e r r e d t o the t h e s i s and -E.M,  Morris  (1968).  The  j e t was  by  mounted on a base  w h i c h a l l o w e d c o n t r o l l e d m o t i o n o f the j e t i n any d i r e c t i o n , so -by-moving the j e t , t h e l a s e r f o c u s c o u l d be p o s i t i o n e d p o i n t i n t h e j e t t o w i t h i n .02 (c) was  1,-Ionoohromator.  a t any  that, pre-selected  millimetres.  The monochromator, a J a r r e l l - A s h 82-010,  the same as t h e one used by Chan.  I t has  an f number of 10, and  a  r e c i p r o c a l d i s p e r s i o n of 16 Angstroms per m i l l i m e t r e a t 6700 Angstroms. The monochromator i s b l a z e d  a t 7500 A°,  so t h a t u l t r a v i o l e t l i g h t  e n t e r i n g the monochromator appears m o s t l y i n t h e second o r d e r , t h a t i s i n t h e r e d and  infrared.  Thus f o r o b s e r v a t i o n  o f l i g h t - s i g n a l s a.bove  O  u  about 6500 A , a r e d t r a n s m i t t i n g f i l t e r was ultraviolet  u s u a l l y needed t o absorb  the  light.  (d) P h o t o m u l t i p l i e r . I 9558B.  The  photomultiplier  used i n a l l the work  was  an EM  I t i s l i n e a r f o r a dc anode c u r r e n t up t o 1  and  f o r up t o f i v e t i m e s g r e a t e r v a l u e s o f c u r r e n t under p u l s e d  The  photomultiplier  has  ma, conditions.  a peak quantum e f f i c i e n c y o f 50% a t 5500 A°,  and  an e f f i c i e n c y o f about Z% a t the l a s e r w a v e l e n g t h . (e) O p t i c a l System and R e d u c t i o n o f S t r a y L i g h t . s u r p r i s i n g l y . , i t was satisfactory.  The  Not  f o u n d t h a t t h e s i m p l i e s t o p t i c a l system was  l a s e r beam was  convex l e n s w i t h 10 cm  most  f o c u s s e d on the plasma t h r o u g h a s i m p l e  focal length.  ( D o u b l e t l e n s e s c o u l d n o t be used  Iri t h e d i r e c t l a s e r beam because t h e g l u e a t t h e i n t e r f a c e was' soon burned t h r o u g h a b s o r p t i o n t h e l a s e r l i g h t was and  of the beam).  A f t e r p a s s i n g t h r o u g h the plasma  absorbed i n a l a r g e box,  suitably baffled.  painted  d u l l black  A f a s t - r i s e photo d i o d e , i n s i d e the box,  inside, monitored  - 1 3 -  "the l a s e r p u l s e , and p r o v i d e d a t r i g g e r i n g p u l s e f o r t h e CRO.  This  p u l s e a l s o gave a u s e f u l check on t h e l a s e r i n t e n s i t y , so l o n g as t h e d i o d e was  operated i n the l i n e a r r e g i o n of small s i g n a l s ( l e s s than 1 v o l t ) .  The plasma was  f o c u s s e d on t h e monochromator e n t r a n c e s l i t  through  a p a i r o f achromat d o u b l e t s , w i t h a p p r o x i m a t e l y one-to-one m a g n i f i c a t i o n . B a f f l e s t o reduce s t r a y l i g h t seemed t o be more h a r m f u l ( p r o b a b l y t h r o u g h r e f l e c t i o n and d i f f r a c t i o n ) t h a n b e n e f i c i a l , and s i n c e t h e y were r a t h e r a h i n d r a n c e d u r i n g a l i g n m e n t , t h e y were f i n a l l y d i s p e n s e d w i t h a l t o g e t h e r . I n any c a s e , by f a r t h e most s e r i o u s s o u r c e of s t r a y l i g h t s i g n a l s was  found t o be a t t h e j u n c t i o n between t h e p h o t o m u l t i p l i e r  and t h e e x i t s l i t o f t h e monoohromator.  The o n l y o t h e r i m p o r t a n t  c o n c e r n s i n t h e r e d u c t i o n o f s t r a y l i g h t were t h a t t h e l a s e r beam s h o u l d n o t s t r i k e t h e t o p o f t h e j e t , and s h o u l d n o t r e f l e c t o f f t h e f r o n t s u r f a c e o f t h e a b s o r b i n g box.  And  even when t h i s o c c u r r e d , most of t h e  s t r a y l i g h t entered the p h o t o m u l t i p l i e r d i r e c t l y through the  gap  between i t and t h e e x i t s l i t , and n o t t h r o u g h t h e monochromator.  The  reason f o r t h i s i s t h a t the s a t e l l i t e frequency i s r e l a t i v e l y f a r removed from t h e l a s e r l i n e .  Any  s t r a y l i g h t e n t e r i n g through the  monochromator e n t r a n c e s l i t shows up m a i n l y as p a r t o f t h e c e n t r a l peak.  P a r t l y f o r t h i s r e a s o n , and p a r t l y t h r o u g h c a r e f u l  shielding,  s t r a y l i g h t c o u l d be reduced t o n e g l i g i b l e p r o p o r t i o n s . (f)  S t a t i s t i c a l methods.  t h e whole experiment  The one problem which c h a r a c t e r i z e s  i s t h e weakness o f t h e s c a t t e r e d l i g h t s i g n a l .  For  a t y p i c a l e x p e r i m e n t a l s i t u a t i o n , t h e i n t e n s i t y of s c a t t e r e d s i g n a l i n -12 one s a t e l l i t e i s about 10  o f t h e i n c i d e n t l i g h t , and t h e number o f  photons a c t u a l l y observed i s o f t h e o r d e r of 100.  Taking i n t o c o n s i d e r a t i o n  t h e s i g n a l f l u c t u a t i o n s due t o t h e cascade i n t h e p h o t o m u l t i p l i e r , p l u s  - 14 -  t h e n o i s e due  t o s t r a y l i g h t and background l i g h t from t h e j e t , we  t h a t t h e e x p e c t e d s i g n a l - t o - n o i s e r a t i o may  see  be l i t t l e b e t t e r t h a n u n i t y .  S t a t i s t i c a l methods can be a p p l i e d i n v o l v i n g many shots a t each w a v e l e n g t h s e t t i n g , b u t t h e number o f s h o t s i s l i m i t e d because t h e e l e c t r o d e s o f t h e plasma j e t b e g i n t o d e t e r i o r a t e a f t e r a few h o u r s . Thus s a t e l l i t e o b s e r v a t i o n s  must be done q u i c k l y , w i t h as few l a s e r  s h o t s as p o s s i b l e . If •is  s t a t i s t i c a l methods have l i m i t e d u s e f u l n e s s , t h e n e x t  t o maximize t h e s c a t t e r e d s i g n a l , and m i n i m i z e s t r a y l i g h t  background l i g h t from t h e j e t .  step and  We w i l l enumerate t h e v a r i o u s  possibilities  p o i n t by p o i n t . (g) I n t e n s i t y o f s c a t t e r e d s i g n a l .  We  have f o r t h e  integrated  i n t e n s i t y o f each s a t e l l i t e  ri i s t h e number o f s c a t t e r e d photons observedo TJ i s t h e t o t a l energy o f t h e i n c i d e n t l i g h t hv  and  i s t h e energy o f each i n c i d e n t photon.  U i s l i m i t e d by t h e a v a i l a b l e power, and by p e r t u r b a t i o n o f t h e plasma by  the l a s e r , L i s t h e l e n g t h o f s c a t t e r i n g volume.  It  i s determined by t h e w i d t h o f t h e e n t r a n c e s l i t and t h e  o f t h e o p t i c a l system. and  magnification  I n c r e a s i n g L decreases the s p a t i a l r e s o l u t i o n ,  i n c r e a s e s the b r o a d e n i n g o f t h e observed s a t e l l i t e s due t o  g r a d i e n t s i n t h e plasma. r  o  - 2.82  x 10  x  cm  i s t h e r a d i u s of t h e e l e c t r o n ,  density  - 15 -  Y i s t h e a n g l e between t h e p l a n e o f p o l a r i z a t i o n o f t h e i n c i d e n t l i g h t and t h e s c a t t e r e d p l a n e . sin  J  2  I n t h i s case  X =. ' a n d  1.  =  n  e  i s the electron density.  For l a r g e  o< t h e term  n  &  ^ is  2 p r a c t i c a l l y c o n s t a n t , independent o f n to n  e  g  , since  i s proportional  . q i s t h e quantum e f f i c i e n c y o f t h e p h o t o m u l t i p l i e r , a p p r o x i m a t e l y  .03. f o r t h e EMI 9558 B . i s the s o l i d angle i n t o which the l i g h t i s s c a t t e r e d . I n p r i n c i p l e A i l c o u l d be maximized by p l a c i n g a l a r g e p o w e r f u l c o l l i m a t i n g l e n s v e r y c l o s e t o t h e plasma.  A n g u l a r r e s o l u t i o n would  be d e c r e a s e d , b u t t h e e f f e c t o f t h a t on t h e s c a t t e r e d spectrum i s s m a l l , •&n& moreover s p a t i a l r e s o l u t i o n c o u l d be improved ( i ) R e d u c t i o n o f background r a d i a t i o n from t h e plasma. Plasma l u m i n o s i t y i s due t o s p e c t r a l and continuum r a d i a t i o n .  Spectral  r a d i a t i o n can be a v o i d e d by n o t w o r k i n g a t w a v e l e n g t h s n e a r s p e c t r a l l i n e s , and by c h o o z i n g a gas w i t h few s p e c t r a l l i n e s n e a r t h e l a s e r w a v e l e n g t h . The continuum due t o r e c o m b i n a t i o n r a d i a t i o n and b r e m s t r a h l u n g i s dependent m a i n l y on t h e t e m p e r a t u r e and d e n s i t y of t h e e l e c t r o n .  It  can n o t be a v o i d e d , b u t i t s e f f e c t can be g r e a t l y reduced by w o r k i n g a t low e l e c t r o n d e n s i t i e s ( s a t e l l i t e i n t e n s i t y i s independent o f n for large  c< ) and by r e s t r i c t i n g o b s e r v a t i o n  e  t o r e g i o n s where t h e  plasma column, e q u a l t o plasma e m i s s i v i t y i n t e g r a t e d a l o n g t h e l i n e of s i g h t . P o s i t i o n i n g o f S c a t t e r i n g Volume i n J e t .  One i m p o r t a n t  purpose o f t h e e x p e r i m e n t was t o measure t h e s a t e l l i t e s h i f t as a  - 16 -  function  o f t h e p o s i t i o n o f t h e s c a t t e r i n g volume i n t h e j e t , t h e  s c a t t e r i n g volume b e i n g d e f i n e d as t h a t p a r t o f t h e f o c u s s e d l a s e r beam from which s c a t t e r e d  l i g h t p a s s e s t h r o u g h t h e monochromator.  Thus i t was i m p o r t a n t t o have a c c u r a t e measurements o f t h e d i s t a n c e o f t h e s c a t t e r i n g volume f r o m t h e c e n t r a l a x i s o f t h e j e t . done i n t h e f o l l o w i n g manner. C  C o n s i d e r t h e diagram.  T h i s was  The j e t moves, w h i l e  t h e s c a t t e r i n g volume, l y i n g a t t h e i n t e r s e c t i o n o f AB and CD, remains f i x e d  Lasers  A - — -J^( o,yo)  \  x  -— - - B •  i n t h e c o o r d i n a t e system x y z (The y a x i s l i e s i n the d i r e c t i o n of the scattered light.  X  ^  The z a x i s i s p a r a l l e l t o t h e  c e n t r a l a x i s o f the j e t ) . The  height z of the scattering  volume above t h e cathode t i p o f t h e j e t i s e a s i l y measured w i t h v e r n i e r ^ c a l i p e r s .  I f the p o s i t i o n of the j e t  a x i s i s g i v e n by t h e c o o r d i n a t e s ( x ' , y ' ) , we want t h e v a l u e s , x y  Q  Q  and  , o f x' and y' when t h e s c a t t e r i n g volume l i e s on t h e j e t axis<>  Moving t h e j e t a l o n g t h e x - a x i s g i v e s a p r o f i l e o f t h e dc l i g h t from the j e t as a f u n c t i o n  o f x , w i t h a c l e a r maximum a t x . 1  0  To d e t e r m i n e y  we u s e t h e f a c t t h a t i n argon t h e A r I I l i n e s can be s t r o n g l y by t h e l a s e r l i g h t .  The r e s u l t a n t  o f y' has a maximum a t y the  Q  .  large  s i g n a l , measured as a  F o r any p o s i t i o n  excited function  (x' , y*) o f t h e j e t ,  s e p a r a t i o n o f t h e s c a t t e r i n g volume from t h e a x i s i s j u s t  2 The  whole p r o c e d u r e must o f c o u r s e be r e p e a t e d from t i m e t o  t i m e w h i l e t h e j e t i s b e i n g run,  Q  so t h a t a l l o w a n c e can be made f o r  changes i n p o s i t i o n o f t h e j e t due t o t h e changes i n t h e e l e c t r o d e s .  \  'CAPTER I I I - MEASUREMENTS OF EXCITATION TEMPERATURES.  Jix c o n j u n c t i o n w i t h use a n o t h e r method was  o f s c a t t e r i n g f o r plasma  diagnostics,  u s e d , namely t h a t o f m e a s u r i n g e x c i t a t i o n t e m p e r a t u r e  t h r o u g h plasma e m i s s i v i t y .  The  purpose was  t o compare t h e  results  o b t a i n e d by s c a t t e r i n g w i t h t h o s e o b t a i n e d by a more e s t a b l i s h e d and  a l s o t o compare t h e p o t e n t i a l u s e f u l n e s s o f the two  the primary concern of the  experiment was  methods.  s c a t t e r i n g , and n o t  t e m p e r a t u r e measurements, t h e l a t t e r w i l l be t r e a t e d r a t h e r h e r e , o n l y a s h o r t m e n t i on o f t h e d i f f i c u l t i e s i n v o l v e d . may  be o u t l i n e d as f o l l o w s .  The  photomultiplier  method,  The  Since  excitation quickly method  i s calibrated for  a b s o l u t e i n t e n s i t y measurements w i t h a s t a n d a r d s o u r c e .  Intensity  p r o f i l e s of the j e t a r e t a k e n u s i n g t h e p h o t o m u l t i p l i e r ,  and  are  by t h e A b e l t r a n s f o r m t o g i v e r a d i a l e m i s s i o n p r o f i l e s .  The  emission  o f t h e plasma i s i n t u r n r e l a t e d t o i t s t e m p e r a t u r e . v e r y s i m i l a r t o t h a t used by O l s e n (1963), who  The  applied  unfolded  method i s  i t to  the  mesurement o f atomic t r a n s i t i o n p r o b a b i l i t i e s .  A - Theory. (a) E m i s s i v i t y as F u n c t i o n o f Temperature. o f a plasma due  £ E  m  t o one  atomic s p e c t r a l l i n e we  For t h e  emissivity  have  i s t h e e m i s s i v i t y per u n i t a n g l e . and  E  n  a r e t h e e n e r g i e s o f the upper and a  r r  lower s t a t e s  for  this transition; A^ n  ffl  i s the a t o m i c t r a n s i t i o n p r o b a b i l i t y f o r the t r a n s i t i o n , and i s the number d e n s i t y  of atoms i n the upper energy s t a t e .  ( T r a n s i t i o n p r o b a b i l i t i e s f o r h e l i u m were t a k e n from t a b l e s of atomic t r a n s i t i o n p r o b a b i l i t i e s p u b l i s h e d by the U.S.  - 17  -  Department o f Commerce  - 18 -  "{Wlese e t a l - 1 9 6 6 ) .  These a r e t h e o r e t i c a l l y c a l c u l a t e d v a l u e s  w i t h an e s t i m a t e d p o s s i b l e e r r o r o f about lO?o.  For the t r a n s i t i o n  p r o b a b i l i t y o f t h e Argon I 6965 l i n e t h e v a l u e measured Schumaker (1965) v/as u s e d .  by Popenoe and  The p o s s i b l e e r r o r quoted f o r i t i s 11%.)  I f we assume t h a t c o l l i s i o n a l p r o c e s s e s predominate o v e r •spontaneous r a d i a t i o n a l t r a n s f e r i n e x c i t a t i o n o f t h e upper s t a t e , t h e n HJJJ  i s d e t e r m i n e d by t h e energy d i s t r i b u t i o n o f t h e c o l l i d i n g p a r t i c l e s . C r i t e r i a g i v e n by Griem (1966) show t h a t . f o r t y p i c a l v a l u e s o f  n  e  and T i n t h e plasma j e t , t h i s a s s u m p t i o n h o l d s f o r a l l energy l e v e l s ,  w i t h p r i n c i p a l quantum g r e a t e r t h a n 1.  .  h  m = oxTf) n  I n t h i s case n ^ i s g i v e n by  ( -2)  e  3  n ^ i s t h e d e n s i t y o f atoms i n t h e ground g  i s t h e degeneracy o f t h e upper  m  state  state  Z(T) i s t h e p a r t i t i o n f u n c t i o n o f t h e atom T i s t h e e x c i t a t i o n t e m p e r a t u r e o f t h e upper s t a t e j T i s t h e same f o r a l l s t a t e s f o r w h i c h t h e above a s s u m p t i o n h o l d s , and s h o u l d a l s o be e q u a l t o T  g  , the e l e c t r o n temperature, since  c o l l i s i o n s predominate i n t h e p r o c e s s o f e x c i t a t i o n .  electron  The d e n s i t y n  p a r t i c l e s i n t h e ground s t a t e , e f f e c t i v e l y e q u a l t o t h e d e n s i t y n  &  Q  of  n e u t r a l s , i s dependent on t h e t e m p e r a t u r e o f t h e v a r i o u s s p e c i e s i n t h e plasma.  The v a l u e o f n  a  i s governed by t h e f o l l o w i n g e q u a t i o n s ;  neutrality n  e  *  n • =  o  ( 3 - 3 )  gas l a w  Saha  of  - .19 -  and  Z  a  a r e t h e p a r t i t i o n s o f the s i n g l y i o n i z e d  and  neutral states. E  a  i s t h e i o n i z a t i o n o f t h e n e u t r a l atom, c o r r e c t e d f o r plasma  interactions. T i n t h e Saha e q u a t i o n  i s e s s e n t i a l l y e l e c t r o n temperature  s i n c e i o n i z a t i o n i s m a i n l y "by c o l l i s i o n w i t h e l e c t r o n s . solve these equations,  In order  T, Q  to  we must assume complete t h e r m a l e q u i l i b r i u m ,  t h a t i s vre assume t h a t t h e energy d i s t r i b u t i o n s of a l l v a r i o u s s p e c i e s a r e c h a r a c t e r i z e d by t h e same t e m p e r a t u r e T. eq. 3-4  t h e n becomes  .  T,  and  3-6  e  a r e two  h  +  a  ) k  b  T  P  =  (3-6)  e q u a t i o n s i n t h r e e unknowns n  (P = 1 atmosphere) w h i c h can be s o l v e d f o r n The  3-3  *  ( ^ E q u a t i o n s 3-5  U s i n g eq.  &  Q  , n  a  as a f u n c t i o n of  and T.  d e t a i l e d c a l c u l a t i o n has been done (Popenoe and Schumaker (1965),  Drawin and F e l e n b o k (1965)) and the r e s u l t s are t a b u l a t e d i n T a b l e I . The  condition that T  s  T.  e  g  T_ a  I  i s a s t r i n g e n t one, s i n c e ° *  e q u i l i b r i a t i o n t i m e f o r e l e c t r o n s and  the  i o n s or n e u t r a l s i s r e l a t i v e l y  l o n g , due m a i n l y t o t h e d i f f e r e n c e i n mass.  There a r e i n d i c a t i o n s t h a t  t h i s c o n d i t i o n does n o t h o l d f o r t h e h e l i u m plasma j e t ( M o r r i s 1968). F i n a l l y combining t h e e q u a t i o n s g i v e n above, we  obtain for  the e m i s s i v i t y : c  - ynl m-t ) A k  n  n  v  n  -jjfTj  t h e v a l i d i t y of t h i s e q u a t i o n  being  complete t h e r m a l e q u i l i b r i u m .  The  by g r a p h i c a l t e c h n i q u e s , f u n c t i o n of  £ .  g, -e  (3-7)  ri  s u b j e c t t o the h a r s h c o n d i t i o n of equation  t o g i v e T, and  can be r e a d i l y i n v e r t e d  therefore also n  e  , as a  - 20 -  II  The-Abel  Transform.  .. We have seen i n t h e p r e v i o u s s e c t i o n how temperature we may  i f t h e plasma i s i n complete t h e r m a l e q u i l i b r i u m . Thus .  determine t h e plasma t e m p e r a t u r e  temperature  emission i s r e l a t e d t o  by measuring e m i s s i o n .  But  and t h e r e f o r e e m i s s i o n a r e f u n c t i o n s of p o s i t i o n i n t h e  p l a s m a , and i n a c t u a l f a c t we a r e l i m i t e d t o o b s e r v i n g t o t a l i . e . i n t e n s i t y , from a r e g i o n w i t h v a r y i n g emission.  emission,  From such  data  e m i s s i o n as a f u n c t i o n o f p o s i t i o n , can be o b t a i n e d by means o f t h e Abel transform. I n our p a r t i c u l a r case we may symmetry.  assume a plasma w i t h c y l i n d i s o a l  t  For t h e e x p e r i m e n t a l arrangement shown i n t h e diagram we 2  0  1(Y)  have :  -.21  l ( y ) i s t h e observed  -  i n t e n s i t y as a f u n c t i o n o f y  £(r) i s t h e e m i s s i o n c o e f f i c i e n t as a f u n c t i o n o f r E q u a t i o n 3-8 h o l d s o n l y i f t h e plasma i s o p t i c a l l y t h i n .  Using  t h e e s t i m a t e s g i v e n b y Griem (1965) we f i n d t h a t t h e assumption o f o p t i c a l thinne§s i s v a l i d f o r t h e case o f t h e plasma j e t .  The s p e c t r a l  p r o f i l e s o f some o f t h e more i n t e n s e l i n e s do however show sosie s i g n s o f s e l f - a b s o r p t i o n , amounting i n some cases t o about 5 t o 10 p e r c e n t .of t h e t o t a l i n t e n s i t y o f t h e l i n e . The i n v e r s i o n o f e q u a t i o n 3-8 t o f i n d  6 ( r ) i s accomplished  by means o f . t h e A b e l t r a n s f o r m :  D i r e c t n u m e r i c a l i n t e g r a t i o n methods f o r d e t e r m i n i n g  £ (r)  a r e n o t v e r y s a t i s f a c t o r y because o f t h e d e r i v a t i v e i n t h e i n t e g r a n d . The  observed  f u n c t i o n l ( y ) has v a r i o u s e r r o r s , random and o t h e r w i s e ,  imposed on i t , which cause t h e d e r i v a t i v e defined.  dX(y)/cly t o be p o o r l y  A more s a t i s f a c t o r y method i s t o approximate l ( y ) by s u i t a b l e  l e a s t - s q u a r e - f i t p o l y n o m i a l s and p e r f o r m t h e i n t e g r a t i o n a n a l y t i c a l l y . I n g e n e r a l we w r i t e ^  I(Y)  =  -t  o  F^(y) a r e t h e e x p a n s i o n  a,  F^y)  polynomials,  a^ a r e c o e f f i c i e n t e t o be d e t e r m i n e d The A b e l t r a n s f o r m  by f i t t i n g .  F ^ ( r ) o f t h e F ^ ( y ) can be found  analytically.  - 22 -  and t h e n  £ ( . < • ) = .1 a ( r ) (  1=0 which i s t h e r e q u i r e d  solution.  The c h o i c e o f t h e F^(y) depends on t h e n a t u r e o f t h e experiment. One t r i e s t o s e l e c t them such t h a t t h e y w i l l n o t g i v e u n p h y s i c a l maxima, minima, o r i n f l e c t i o n p o i n t s .  For the "bell-shape" i n t e n s i t y  profile  o f t h e plasma j e t Freeman and K a t z ( i 9 6 0 ) used  F ( ) L  where R the six.  o  = (Ro -y ) Z  y  2  (3-.o)  1  i s t h e d i s t a n c e from t h e c e n t e r o f t h e j e t t o t h e p o i n t where The i n d e x i v a r i e s from z e r o t o about  i n t e n s i t y drops t o z e r o .  These a r e t h e p o l y n o m i a l s used i n t h e s o l u t i o n o f t h e A b e l  transform f o r t h i s  experiment.  A r o u t i n e i n t e g r a t i o n (Eq. 3-9) y i e l d s f o r t h e t r a n s f o r m F ^ ( r ) ;  The problem now r e m a i n i n g i s t o f i n d t h e c o e f f i c i e n t s a^ by means o f a l e a s t squares f i t .  [0(  I  R j  )-  The q u a n t i t y t o be m i n i m i z e d i s  ?  aiF^Rj)]  1  O(Rj) i s t h e observed i n t e n s i t y a t t h e p o i n t R j , and F ( R j ) i s g i v e n b y Eq 3-10. i  The a l g e b r a i c m a n i p u l a t i o n s i n v o l v e d a r e r o u t i n e and need n o t be reproduced h e r e . The a c t u a l c o m p u t a t i o n was done by computer, u s i n g a F o r t r a n program w r i t t e n f o r t h e purpose. I t was found t h a t .the b e s t f i t was o b t a i n e d f o r a f i t t i n g p o l y n o m i a l o f t h e form  F(y) V . (C-y )' 1  =  Q  - 23 -  2 f o r c e s F and i t s f i r s t d e r i v a t i v e  - S t a r t i n g t h e summation a t i ; to  z e r o a t t h e end p o i n t y r R  expected p h y s i c a l s i t u a t i o n .  D  .  T h i s c o n d i t i o n corresponds t o t h e  I f F i s o f h i g h e r o r d e r i ) 5, i t  b e g i n s t o f i t t h e n o i s e on t h e i n t e n s i t y p r o f i l e , and a p h y s i c a l l y untrustworthy emission p r o f i l e r e s u l t s . to  The t r a n s f o r m was a p p l i e d  each h a l f o f t h e i n t e n s i t y p r o f i l e s e p a r a t e l y , s i n c e t h e j e t i s  not' l i k e l y t o be c o m p l e t e l y symmetric.  With t h i s procedure small  p h y s i c a l l y impossible discont i n u i t i e s w i l l occur a t the centre of the  e m i s s i o n p r o f i l e , w h i c h can however be l a r g e l y e l i m i n a t e d by a  judicious choice f o r the centre of the i n t e n s i t y p r o f i l e .  I l l - Absolute Intensity Calibration.. The f i n a l problem i n d e t e r m i n i n g e x c i t a t i o n t e m p e r a t u r e from i n t e g r a t e d l i n e i n t e n s i t y , i s t o r e l a t e t h e e l e c t r i c a l s i g n a l from the  photomultiplier t o the absolute i n t e n s i t y of the r a d i a t i o n emitted  by t h e s o u r c e .  To do t h i s , we u s e a s t a n d a r d s o u r c e , t h e carbon a r c ,  w h i c h may be assumed t o be a b l a c k b o d y r a d i a t o r w i t h a t e m p e r a t u r e o f 3800° k.  The carbon a r c i s p l a c e d i n t h e p o s i t i o n o f t h e j e t ,  so t h a t  l i g h t from e i t h e r soxirce i s c o l l e c t e d t h r o u g h t h e same o p t i c a l  system.  For arc  t h e i n t e n s i t y o f l i g h t p e r u n i t s o l i d a n g l e from t h e carbon  we have :  \ X 2~ ^ j i s t h e w i d t h o f t h e e x i t s l i t i n angstroms the  energy f l u x from a b l a o k b o d y p e r u n i t s o l i d a n g l e  - 24 -  g i v e n by  For t h e i n t e g r a t e d i n t e n s i t y o f t h e l i n e r a d i a t i o n we have:  . » The  /  dX  i ( A)  e x i t s l i t width equals  2 &  , and s h o u l d be made l a r g e enough t o  e n v e l o p most o f t h e l i n e , i ( A ) . ( T h i s c o n d i t i o n may be d i f f i c u l t t o s a t i s f y - i f the l i n e p r o f i l e i s Lorentzian, a s l i t with a width of 10 f u l l l i n e h a l f , w i d t h s would s t i l l m i s s 6% o f the t o t a l l i n e radiation). I f t h e p h o t o m u l t i p l i e r i s l i n e a r , t h e v o l t a g e output i s p r o p o r t i o n a l t o t h e i n t e n s i t y o f incoming  radiation.  t h e v o l t a g e due t o t h e carbon a r c continuum  radiation  signal  We have f o r  V ( X ) = k(X) I (A) on. C  k(X)  c  i s a calibration factor i s t h e s o l i d a n g l e o f l i g h t a c c e p t e d by t h e o p t i c a l  system  S i m i l a r l y f o r 1^ we have U =  I  We measure 3-11 and 3-12.  I A) A .a c  (M  and V  V  L  / V  (X)  C  (3-13)  ( , \ )  , and compute I  Q  (X) u s i n g  equations  Thus t h e i n t e g r a t e d l i n e i n t e n s i t y 1^ i s determined.  1^ i s measured as a f u n c t i o n o f t h e p o s i t i o n  y of the j e t .  This  i n t e n s i t y p r o f i l e 1^ (y) i s c o n v e r t e d t o a r a d i a l e m i s s i o n p r o f i l e £^(r) u s i n g A b e l t r a n s f o r m , ^ ( r ) i n t u r n g i v e s t e p e r a t u r e e q u a t i o n 3-10.  T ( r ) through  - 25 -  B - Apparatus and Technique. (a)  Carbon A r c .  The carbon a r c used i n t h e a b s o l u t e i n t e n s i t y -  c a l i b r a t i o n was a s t a n d a r d p i e c e o f a p p a r a t u s , and has been a d e q u a t e l y d e s c r i b e d e l s e w h e r e (see N u l l and L o z i e r (1962) and M a c l a t c h y (1966) ) . Under t h e p r o p e r c o n d i t i o n s o f e l e c t r o d e p o s i t i o n s and a r c c u r r e n t , as described i n the l i t e r a t u r e , the arc w i l l  o p e r a t e v e r y q u i e t l y and  s t e a d i l y , and t h e i n t e n s i t y o f l i g h t coming from t h e anode s u r f a c e i s t h e n w e l l r e p r o d u c i b l e and c h a r a c t e r i s t i c o f a b l a c k b o d y w i t h e m i s s i v i t y o f one and a t e m p e r a t u r e o f 3800°k. p o s i t i o n o f t h e plasma j e t ,  The a r c was p l a c e d i n t h e  as t h e b e s t a n d . s i m p l e s t assvirance t h a t  the  same optica.1 system was used f o r . l i g h t coming from t h e j e t and from  the  arc.  the  monochromator e n t r a n c e s l i t was f o c u s s e d on t h e c e n t r e o f t h e  The p o s i t i o n o f t h e a r c was a d j u s t e d so t h a t t h e image o f  anode s u r f a c e o f t h e a r c . (b) C a l i b r a t i o n o f n e u t r a l d e n s i t y f i l t e r s .  The v o l t a g e  s i g n a l due t o t h e carbon a r c continuum was measured over a range o f wavelengths from 4000 A° t o 8000 A  0  i n small steps of wavelength.  For  most o f t h i s range, t h e i n t e n s i t y o f t h e carbon a r c l i g h t was enough t o s a t u r a t e t h e p h o t o m u l t i p l i e r , and a b s o r b i n g f i l t e r s were needed. f i l t e r s used were g e l a t i n e W r a t t e n ND f i l t e r s .  The  Their density i s  w a v e l e n g t h dependent, and t h u s i t was a l s o n e c e s s a r y t o measure t h i s dea s i t y as a f u n c t i o n o f w a v e l e n g t h . of  I t t u r n s out t h a t i f we r e p r e s e n t t h e d e n s i t y  a f i l t e r by  d( x) = m(x)a d then  Q  0  o  .  i s t h e d e n s i t y a t some p a r t i c u l a r w a v e l e n g t h , (5000 A i n o u r case)  m(X)  i s t h e same f o r a l l f i l t e r s ,  independent o f d e n s i t y .  The r e s u l t s f o r m ( X ) a r e g i v e n i n F i g . 3 .  T h i s same c a l i b r a t i o n  - .26 -  \ 1.20 \  1.00 •-  I  m(A) .80--  X  X  1^.000  (A)  >  Figure 3 - C a l i b r a t i o n o f absorbtion  filters  800.0  7<?cc  r r  " ' ^ x = <,->oy  )  i s u s e f u l f o r t h e measurement o f i n t e n s i t y o f l i g h t coming from t h e plasma, s i n c e , e s p e c i a l l y f o r t h e s p e c t r a l l i n e s , t h i s i n t e n s i t y i s i n many cases enough t o s a t u r a t e t h e p h o t o m u l t i p l i e r . V  c  or  The a c t u a l  voltage  used i n e q u a t i o n 3-13, i s t h e n c a l c u l a t e d from t h e observed  voltage V by 1  _m ( M d  0  • l,c = V  d  V  Cc»°  i s t h e t o t a l d e n s i t y ( a t 5000 A ) o f the a b s o r p t i o n 0  Q  used i n reducing  filters  the l i g h t i n t e n s i t y .  (c) I n t e g r a t e d  l i n e i n t e n s i t y as f u n c t i o n o f p o s i t i o n .  I n order  t o do t h e A b e l u n f o l d i n g , i n t e g r a t e d l i n e i n t e n s i t i e s have t o be measured as a f u n c t i o n o f p o s i t i o n y a c r o s s t h e j e t .  A p o t e n t i o m e t e r was m e c h a n i c a l l y  connected t o t h e mechanism f o r moving t h e j e t , i n such a manner  that  - 27 -  " h o r i z o n t a l p o s i t i o n o f t h e j e t was l i n e a r l y r e l a t e d t o change i n v o l t a g e a t the potentiometer t a p . With t h i s voltage fed to the h o r i z o n t a l input o f an o s o i l l o s c o p e , and t h e s i g n a l from t h e p h o t o m u l t i p l i e r s i m u l t a n e o u s l y f e d t o t h e v e r t i c a l i n p u t , continuous  i n t e n s i t y p r o f i l e s c o u l d be v e r y  e a s i l y obtained. I n o r d e r t o a l l o w f o r t h e background continuum o f t h e j e t , i n t e n s i t y p r o f i l e s were t a k e n a t w a v e l e n g t h o f t h e c e n t r e o f each l i n e , and a t some w a v e l e n g t h n e a r t h e l i n e b u t w e l l away from a l l s p e c t r a l  lines.  The i n t e n s i t y o f t h e background continuum was much l e s s t h a n t h e i n t e n s i t y o f t h e s p e c t r a l l i n e s , so t h a t e r r o r s i n measurements o f t h e background were n o t v e r y i m p o r t a n t . observed  S u b t r a c t i n g t h e background p r o f i l e from t h e  l i n e i n t e n s i t y p r o f i l e , gives the true l i n e i n t e n s i t y p r o f i l e .  D u r i n g most o f t h e f i n a l e x p e r i m e n t a l work o b s e r v a t i o n s o f l i n e were done between o b s e r v a t i o n s o f s c a t t e r i n g .  This procedure  gave  r e p e a t e d q u i c k checks on f l u c t u a t i o n s i n p o s i t i o n and temperature t h e j e t , so t h a t t h e e f f e c t o f f l u c t u a t i o n s c o u l d be a l l o w e d f o r and m i n i m i z e d . .  intensities  of  I V - RESULTS.  The i m p o r t a n t r e s u l t s o f t h i s experiment came from t h e f i n a l •series o f experimental runs, which involved  a combination o f s c a t t e r i n g  o b s e r v a t i o n s and e x c i t a t i o n t e m p e r a t u r e measurments.  During e a r l i e r  w o r k some i n t e r e s t i n g d a t a and o b s e r v a t i o n s on s a t e l l i t e h a l f w i d t h s and perturbation  o f t h e plasma were o b t a i n e d , and t h e s e a r e r e p o r t e d i n t h i s  chapter along w i t h the p r i n c i p a l r e s u l t s . Perturbation  o f t h e Plasma.  I t i s t o be expeoted t h a t t h e  extreme i n t e n s i t i e s o f l i g h t i n t h e f o c u s s e d l a s e r beam w i l l have some p e r t u r b i n g e f f e c t on t h e plasma, and such e f f e c t s were i n d e e d o b s e r v e d . H e a t i n g o f t h e plasma due t o a b s o r p t i o n o f l a s e r l i g h t i s e v i d e n c e d by a momentary i n c r e a s e i n t h e continuum r a d i a t i o n when t h e l a s e r i s f i r e d , and by t h e appearance o f s p e c t r a l r a d i a t i o n from species of higher i o n i z a t i o n . large  electron  densities  Under c o n d i t i o n s  o f h i g h l a s e r power and  such h e a t i n g s i g n a l s were o b s e r v e d .  Some  rough graphs o f t h e i r dependence on l a s e r power and e l e c t r o n  density  a r e g i v e n i n F i g . 4.  o! c  (b)  (a)  I •p •H  to  W  0)  © -P  o  -p  M  c _y %. n  -o, 2 d-  -9 o  15 30 L a s e r Power (Megawatts)  5  1  0  i -3 (10 cm ) 1 5  6  Electron  density  F i g u r e 4 - P e r t u r b a t i o n o f plasma by l a s e r . C i r c l e s a r e e x p e r i m e n t a l p o i n t s . (a) shows t h e dependence o f t h e i n c r e a s e o f continuum s i g n a l on l a s e r power. (b) shows t h e v a r i a t i o n o f t h e i n t e n s i t y o f A r I I r a d i a t i o n w i t h e l e c t r o n d e n s i t y a t constant power-of l a s e r .  - 28 -  The Spitzer  mechanism o f t h i s h e a t i n g e f f e c t i s not w e l l  understood.  (1962) g i v e s a f o r m u l a f o r t h e a b s o r p t i o n o f photons by  electrons  i n an i n v e r s e  bremstrahlung process.  5 x . o -  3  6  ^  T  2  I t has  the  free  form :  cm"'  , / 2  k i s the a b s o r p t i o n c o e f f i c i e n t .  W i t h a maximum h e a t i n g e f f e c t ,  A r I I I r a d i a t i o n does n o t a p p e a r , w h i l e Ar I I r a d i a t i o n i s m o m e n t a r i l y strongly  i n evidence.  From t h i s f a c t we  can  deduce an  approximate  f i g u r e f o r t h e a b s o r p t i o n of l a s e r energy by the ' e l e c t r o n s , r e s u l t agrees w i t h i n  an o r d e r of magnitude Y r i t b / t h a t  t h e above e q u a t i o n .  O n l y a s m a l l f r a c t i o n , about 10"**  and  the  computed from , of the  incident  l i g h t i s a b s o r b e d , so t h a t t h e amount o f a b s o r p t i o n i s d i f f i c u l t measure d i r e c t l y .  The  c u r v e i n F i g . 4-(b)  c o u l d p o s s i b l y be  to  in  2 agreement w i t h the n  dependence g i v e n i n t h e above e q u a t i o n ,  Q  t h e r e s u l t s i n f i g u r e 4-(a)  seem t o i n d i c a t e a n o n - l i n e a r i t y w i t h  r e s p e c t t o l a s e r power, though t h e r e i s no n o n - l i n e a r i t y i n the The  but  i n d i c a t i o n o f such a  equation.  h e a t i n g s i g n a l i t s e l f p r e s e n t s a problem because i t tends  t o obscure s i g n a l due  to scattered  of course t h a t d i a g n o s t i c be i m m e d i a t e l y t r u s t e d  A more b a s i c p r o b l e m i s  r e s u l t s o b t a i n e d by l a s e r s c a t t e r i n g cannot  s i n c e the  p e r t u r b e d t o some degree by the these perturbation  light.  s c a t t e r i n g volume i s i n e v i t a b l y laser.  In the  experiment d e s c r i b e d h e r e  e f f e c t s were a v o i d e d as much as p o s s i b l e by use  powers w e l l below t h e bend i n the  curve given i n F i g . 4-(a).  s i g n a l has  i t a l l o w s an a c c u r a t e d e t e r m i n a t i o n  one  advantage, i n t h a t  t h e p o s i t i o n o f the  s c a t t e r i n g volume i n the j e t . (see  The  of  laser  heating of  c h a p t e r I I ( j ) ).  - 30 -  One o t h e r p e r t u r b a t i o n e f f e c t i s t h e momentary d e c r e a s e i n t h e i n t e n s i t y o f some A r I s p e c t r a l l i n e s due t o passage o f l a s e r t h r o u g h t h e plasma.  light  T h i s d e c r e a s e i s o f t h e o r d e r o f 5 t o 10 p e r c e n t  o f t h e t o t a l l i n e i n t e n s i t y , b u t s i n c e most o f the observed  line  r a d i a t i o n comes f r o m plasma r e g i o n s o u t s i d e t h e s c a t t e r i n g volume, t h e small decrease or "negative emission" probably represents a v e r y l a r g e d e c r e a s e i n t h e i n t e n s i t y o f l i n e r a d i a t i o n e m i t t e d from t h e s c a t t e r i n g •volume.  T h e ' n e g a t i v e e m i s s i o n " e f f e c t may w e l l be r e l a t e d t o t h e h e a t i n g  s i g n a l s d e s c r i b e d above t h r o u g h a g e n e r a l i n c r e a s e o f e l e c t r o n and  excitation  t e m p e r a t u r e s i n t h e s c a t t e r i n g volume.  B - Preliminary Scattering Results. As was mentioned i n t h e i n t r o d u c t i o n , t h e o r i g i n a l  purpose  o f t h i s experiment was t o d e t e r m i n e what p a r t o f t h e observed  satellite  w i d t h c o u l d be a t t r i b u t e d t o e l e c t r o n d e n s i t y g r a d i e n t s i n t h e s c a t t e r i n g volume.  A t f i r s t i t was  attempted t o a c h i e v e t h i s  purpose  b y v a r y i n g t h e s i z e o f t h e s c a t t e r i n g volume, w h i l e k e e p i n g i t s position in.the j e t fixed.  The r e s u l t s , i t was hoped, would show a  d e c r e a s e o f s a t e l l i t e w i d t h w i t h d e c r e a s e i n l e n g t h o f s c a t t e r i n g volume, t e n d i n g t o t h e t h e o r e t i c a l s a t e l l i t e w i d t h f o r a u n i f o r m plasma a t z e r o s c a t t e r i n g volume l e n g t h .  The a c t u a l r e s u l t s were n o t c o n c l u s i v e ,  though t h e y were c o m p a t i b l e w i t h t h e expected r e s u l t .  A decrease of  s a t e l l i t e w i d t h w i t h d e c r e a s e i n t h e l e n g t h o f t h e s c a t t e r i n g volume was  o b s e r v e d , but t h e e x p e c t e d r e s u l t s were obscured by poor  s i g n a l - t o - n o i s e r a t i o s i n t h e s a t e l l i t e o b s e r v a t i o n s , and by f l u c t u a t i o n s i n t h e plasma j e t , b o t h d u r i n g and between r u n s .  The method was  - 31 -  abandoned as u n s a t i s f a c t o r y , and t h e o r i g i n a l o b j e c t o f t h e experiment was  o b t a i n e d by t h e d e t e r m i n a t i o n o f e l e c t r o n d e n s i t y p r o f i l e s i n  t h e plasma j e t .  C - Plasma D i a g n o s i s R e s u l t s * During the f i n a l experimental runs observations of s c a t t e r i n g •were combined w i t h measurements o f s p e c t r a l l i n e i n t e n s i t i e s . same o p t i c a l system was  used f o r b o t h methods, except t h a t a  e x i t s l i t was u s e d f o r t h e i n t e n s i t y measurements.  The wider  The two methods  a r e d e s c r i b e d i n C h a p t e r s I I and I I I . F i g u r e 5 shows t h e v a r i a t i o n o f e l e c t r o n d e n s i t y w i t h p o s i t i o n at a fixed height  (12.5 mm)  above t h e cathode o f an a r g o n j e t  o p e r a t e d a t a c u t r e n t o f 280 amperes.  The  e l e c t r o n d e n s i t i e s as  d e t e r m i n e d by s c a t t e r i n g a r e i n d i c a t e d by t h e e x p e r i m e n t a l w i t h e r r o r bars i n d i c a t e d .  The  radial  points  e l e c t r o n d e n s i t i e s as d e t e r m i n e d by  t h r e e s e p a r a t e measurements o f t h e  A r I 6965 l i n e a r e a l s o shown.  These p r o f i l e s were t a k e n i n between s c a t t e r i n g o b s e r v a t i o n s , and  the  d i f f e r e n c e s between t h e t h r e e a r e an i n d i c a t i o n o f the magnitude o f t h e f l u c t u a t i o n s i n the j o t . p r o f i l e s i s due t o f i t t i n g  The d i s c o n t i n u i t y a t t h e c e n t r e o f t h e s e and A b e l i n v e r s i o n as d e s c r i b e d i n Chapter I l l ( b ) .  F i g u r e 6 shows s i m i l a r c u r v e s f o r e l e c t r o n d e n s i t y i n the h e l i u m jet  a t a f i x e d h e i g h t o f 6.6 mm  and a c u r r e n t o f 220 amperes.  e r r o r bars are given f o r the p o s i t i o n of the s c a t t e r i n g  observations  because t h e p o s i t i o n o f the s c a t t e r i n g volume c o u l d not be determined due t o l a c k o f h e a t i n g s i g n a l i n t h e h e l i u m j e t . plasma was  No  q u i t e r e p r o d u c i b l e i n t h i s case, as shown by t h e  completely The two  -  -  -32  -  ^ 1 2 to  . 0 I  -2.0  1 -1.5  —L  -1.0  1  1  -0.5  0  0.5  I—  I  1  1.0  1.5  L  2.0  D i s t a n c e f r o m c e n t e r o f jet/mm F i g u r e 5.  E l e c t r o n d e n s i t i e s i n t h e a r g o n plasma j e t . E r r o r b a r s i n d i c a t e e s t i m a t e d e r r o r s f o r p o i n t s determined by s c a t t e r i n g . Continuous c u r v e s r e p r e s e n t l i n e i n t e n s i t y measurements.  to  0  I  -2.0  i  -1.5  i  i  i  -1,0  -0.5  0  i  0.5  J 1.0  .  i  1.5  i  2.0  D i s t a n c e from c e n t e r o f jet/mm F i g u r e 6.  E l e c t r o n d e n s i t i e s i n t h e h e l i u m plasma j e t . E r r o r bars i n d i c a t e e s t i m a t e d e r r o r s f o r p o i n t s determined by s c a t t e r i n g . Continuous c u r v e s r e p r e s e n t l i n e i n t e n s i t y measurements.  t y p i c a l p r o f i l e s o b t a i n e d from t h e i n t e n s i t y of t h e  He  I  5016  lino,  but d i f f e r e n t s p e c t r a l l i n e s g i v e d i f f e r e n t e l e c t r o n d e n s i t i e s . Comparing t h e r e s u l t s o f t h e two methods, we  see t h a t t h e r e i s \  agreement as t o t h e shape o f the p r o f i l e , much f l a t t e r f o r h e l i u m t h a n f o r a r g o n , b u t t h e r e i s a l s o a s y s t e m a t i c d i s c r e p a n c y , t h e cause which i s d i f f i c u l t t o determine.  of  The d e n s i t i e s as d e t e r m i n e d by  s c a t t e r i n g a r e measured d i r e c t l y w i t h s m a l l p o s s i b l e e r r o r s , and a r e dependent o n l y s l i g h t l y on t h e assumption t h a t e l e c t r o n t e m p e r a t u r e and d e n s i t y a r e r e l a t e d t h r o u g h t h e Saha e q u a t i o n .  These s c a t t e r i n g  r e s u l t s a r e c o n s e q u e n t l y much more r e l i a b l e t h a n t h e r e s i i l t s o b t a i n e d by t h e l i n e i n t e n s i t y method w h i c h i n v o l v e s a b s o l u t e c a l i b r a t i o n o f t h e d e t e c t o r system {+_ 10%),  i n t e g r a t e d l i n e i n t e n s i t i e s (+_  t r a n s i t i o n p r o b a b i l i t i e s (+_ 10%),  A b e l u n f o l d i n g (+_ 5%),  5%),  approximate  and t h e  assumptions o f complete l o c a l t h e r m a l e q u i l i b r i u m and an o p t i c a l l y t h i n plasma.  A thorough d i s c u s s i o n o f t h e e r r o r s i n v o l v e d i n t h e s p e c t r o s c o p i c  t e m p e r a t u r e measurement can be found i n t h e papers by O l s e n (1963) Popenoe and Schumaker ( 1 9 6 5 ) .  and  The t o t a l p o s s i b l e e r r o r may be as h i g h  as ZQ%or more, s u f f i c i e n t t o a c c o u n t f o r t h e d i s c r e p a n c i e s  noted  above.  F i g u r e 7 shows a more complete s e t o f e l e c t r o n d e n s i t y p r o f i l e s f o r t h e argon j e t o p e r a t e d a t 280 amperes.  The c u r v e s shown a r e a  c o m b i n a t i o n o f r e s u l t s from s c a t t e r i n g and l i n e i n t e n s i t y measurements.  D - S a t e l l i t e Widths. The e l e c t r o n d e n s i t y p r o f i l e s o b t a i n e d from t h e s a t e l l i t e were used t o p r e d i c t t h e s p e c t r a l shape o f t h e observed  shifts  satellites.  I n p a r t i c u l a r , the observed p r o f i l e o f a s a t e l l i t e v / i l l be a c o n v o l u t i o n  - 34 -  F i g u r e 7.  E l e c t r o n d e n s i t i e s i n t h e argon plasma j e t . C u r r e n t i s 280 A. z i s t h e d i s t a n c e a l o n g t h e j e t a x i s measured from t h e cathode t i p . r i s t h e s e p a r a t i o n from t h e c e n t e r o f t h e j e t . C i r c l e s r e p r e s e n t s c a t t e r i n g measurements. Dashed c u r v e s a r e p r o f i l e s f r o m s p e c t r o s c o p i c measurements n o r m a l i z e d t o f i t t h e e l e c t r o n d e n s i t y as d e t e r m i n e d from s c a t t e r i n g .  o f t h e i n s t r u m e n t p r o f i l e , t h e s a t e l l i t e p r o f i l e f o r a u n i f o r m plasma, and t h e b r o a d e n i n g due t o g r a d i e n t s i n the s c a t t e r i n g volume. F i g u r e 8(a) shows an observed s a t e l l i t e f o r the h e l i u m j e t .  Here  t h e e l e c t r o n d e n s i t y i s p r a c t i c a l l y c o n s t a n t o v e r the s c a t t e r i n g volume, -and  no c o r r e c t i o n f o r v a r i a t i o n i n e l e c t r o n d e n s i t y need be a p p l i e d .  The t h e o r e t i c a l c u r v e i s t h u s c a l c u l a t e d by c o n v o l u t i o n o f t h e monochromator . r e s p o n s e p r o f i l e w i t h t h e s a t e l l i t e p r o f i l e f o r a u n i f o r m plasma. e x p e r i m e n t a l p o i n t s f i t t h e p r e d i c t e d curve v e r y w e l l .  The  I n f a c t the  w i d t h o f t h e observed s a t e l l i t e f i x e s t h e e l e c t r o n t e m p e r a t u r e a t 17000  +_  3000 °k, i n good agreement w i t h t h e v a l u e of 17000°k  c a l c u l a t e d from t h e e l e c t r o n d e n s i t y t h r o u g h t h e Saha e q u a t i o n . F i g u r e 8(b) shows an observed s a t e l l i t e f o r the argon j e t . t h e s a t e l l i t e p r o f i l e f o r a u n i f o r m plasma i s q u i t e narrow  Here  (about .4  A  0  - 35  -  (a)  -20  -25 Separation  -30  -35  f r o m l a s e r l i n e / A'  (b)  -P •H  CO Pi ©  -20  -25 Separation  F i g u r e 8.  -30 from l a s e r l i n e /  A°  Comparison o f observed and p r e d i c t e d s a t e l l i t e p r o f i l e s . E r r o r bars represent standard d e v i a t i o n s f o r experimental p o i n t s ; instrument p r o f i l e ; - - - scattered l i g h t p r o f i l e for u n i f o r m plasma; c o n v o l u t i o n of i n s t r u m e n t p r o f i l e , s c a t t e r e d l i g h t p r o f i l e , and b r o a d e n i n g due t o e l e c t r o n - d e n s i t y g r a d i e n t s .  -  36  -  h a l f w i d t h ) , and t h e b r o a d e n i n g i s ' p r i m a r i l y due t o e l e c t r o n d e n s i t y g r a d i e n t s i n t h e s c a t t e r i n g volume.  Again the experimental p o i n t s are  i n good agreement w i t h t h e t h e o r e t i c a l l y e x p e c t e d r e s u l t s .  Thus i t i s  v e r i f i e d t h a t t h e observed b r o a d e n i n g o f t h e s a t e l l i t e s can be accounted f o r by t h e s p a t i a l i n h o m o g e n e i t y o f t h e plasma.  "CHAPTER V - CONCLUSIONS.  Discussion of Results. We have seen i n t h e p r e v i o u s c h a p t e r t h a t the w i d t h o f t h e s a t e l l i t e s , f i r s t observed by Chan and N o d w e l l (1966) can i n d e e d be a c c o u n t e d f o r by t h e v a r i a t i o n s i n e l e c t r o n d e n s i t y w i t h i n the s c a t t e r i n g volume.  Because o f poor s i g n a l - t o - n o i s e r a t i o s encountered  i n the s a t e l l i t e observations, these r e s u l t s are not e n t i r e l y conclusive b u t t h e y make any l a r g e d i s c r e p a n c y from t h e t h e o r y h i g h l y u n l i k e l y . I t has a l s o been shown t h a t t h e v a l u e s f o r plasma parameters o b t a i n e d from s c a t t e r i n g and from l i n e i n t e n s i t i e s agree w i t h i n t h e p o s s i b l e e x p e r i m e n t a l e r r o r o f about 30/S.  Thus i t i s c o n f i r m e d t h a t  t h e o b s e r v e d valvie o f t h e s a t e l l i t e s h i f t agrees w i t h t h e t h e o r e t i c a l v a l u e w i t h i n t h i s range o f a c c u r a c y . On t h e w h o l e , t h e s c a t t e r i n g method o f plasma d i a g n o s i s i s more d i r e c t and r e l i a b l e , but t h e l i n e i n t e n s i t y method i s f a s t e r and e a s i e r , and t h u s a l l o w s more complete d a t a g a t h e r i n g .  The  intensity  method however depends on t h e assumption o f complete l o c a l t h e r m a l e q u i l i b r i u m i n the plasma.  The r e s u l t s g i v e n h e r e , and t h o s e  o b t a i n e d by M o r r i s (1968), i n d i c a t e t h a t t h i s c o n d i t i o n does n o t s t r i c t l y hold f o r the helium j e t .  I t i s d i f f i c u l t t o d e t e r m i n e how  v a l i d t h e r e s u l t s o f t h e l i n e i n t e n s i t y method a r e , but i n any case we have h e r e a p o i n t i n f a v o u r o f the s c a t t e r i n g method of plasma d i a g n o s i s , w h i c h does n o t depend on q u e s t i o n a b l e assumptions about t h e n a t u r e o f t h e plasma.  Sugge s t i o n s f o r f u t u r e work.^ The method o f u s i n g l i g h t s c a t t e r i n g t o o b t a i n e l e c t r o n d e n s i t i e s d e s c r i b e d i n t h i s t h e s i s c o u l d perhaps be improved by  - 37 -  - 38 -  - a measurement o f t h e i n t e g r a t e d i n t e n s i t y o f t h e s c a t t e r e d l i g h t  because  t h i s i n t e n s i t y i s roughly p r o p o r t i o n a l t o the electron density. I f t h e d e t e c t o r system i s c a l i b r a t e d by R a y l e i g h s c a t t e r i n g , o r by means o f a s t a n d a r d  s o u r c e , one o r two s h o t s o f t h e l a s e r - w o u l d , be  s u f f i c i e n t t o determine e l e c t r o n d e n s i t y .  The s i g n a l would be much  l a r g e r t h a n f o r s a t e l l i t e o b s e r v a t i o n s , and n o i s e problems would t h e r e f o r e be c o n s i d e r a b l y l e s s . important.  S t r a y l i g h t o f course would be more  E l e c t r o n d e n s i t y p r o f i l e s c o u l d be v e r y e a s i l y  obtained  by t h i s method, and i t w o u l d i n any case be u s e f u l i n d e t e r m i n i n g t h e p o s i t i o n o f t h e s c a t t e r i n g volume i n t h e j e t by t h e method d e s c r i b e d i n c h a p t e r I I ('j). A n o t h e r p o s s i b l e method o f o b s e r v i n g s c a t t e r e d l i g h t would be by phase-sensitive detection techniques.  The problem o f t h e l o w i n t e n s i t y  o f s c a t t e r e d l i g h t c o u l d p r o b a b l y be overcome, b u t f l u c t u a t i o n s i n t h e plasma c o u l d a l s o g i v e d i f f i c u l t i e s .  An i n t e r e s t i n g p o s s i b i l i t y i s  t h e u s e o f an image c o n v e r t e r camera t o t a k e p i c t u r e s o f t h e e n t i r e s c a t t e r e d l i g h t spectrum.  I f such an approach were s u c c e s s f u l i t  c o u l d y i e l d a g r e a t d e a l o f i n f o r m a t i o n about t h e plasma under investigation.  .BIBLIOGRAPHY  -Chan, P.W., Chan, P.W.,  1S66, Ph D T h e s i s , U n i v e r s i t y o f B.C. and E.A. N o d w e l l , 1966, Phys. Rev. L e t t e r s , lj6, 267  D r a i v i n , H.W., and P. F e l e n b o k , 1965, "Data f o r Plasmas i n L o c a l Thermodynamic E q u i l i b r i u m " , G a u t h i e r - V i l l a r s - P a r i s . Freeman, M.P., and S. K a t z , 1960, J . Opt. Soc. Am., 50, 826. Griem, H.R., 1S64, "Plasma S p e c t r o s c o p y " , McGraw - H i l l . H o l t , E . H . , and R.E. H a s k e l l , 1965, " F o u n d a t i o n s o f Plasma The M a c M i l l a n Company, New Y o r k .  Dynamics",  Izawa, Y., H . Kabuto, M. Yokoyama, and C. Yamanaka, 1966, Tech. Dept. Osaka U n i v . , 16, 515. M a c L a t c h y , C , 1966, M Sc T h e s i s , U n i v e r s i t y o f B.C. M o r r i s , R.N., 1968, 11 Sc Thesis,. U n i v e r s i t y o f B.C. N o d w e l l , R.A., and G.S.J.P. v a n d e r Kamp, 1968, Can. J . Phys., 46_, 833. N o l l , M.R., and W.W.Lozier, 1962, J . Opt. Soc. Am 52, 1156. O l s e n , H.N., 1963, J . Quant. S p e c t r y . Rad. T r a n s f e r , 3_, 59. Popenoe, C . H . , and J . B. Schumaker J r . , 1965, J . Res. N a t l . B r r . S t d s . , J 3 , 495. R8hr, H., 1967, Phys. L e t t e r s , 25, 167. R o s e n b l u t h , M.N., and N. R o s t o k e r , 1962, Phys. F l u i d s , 5, 776. S a l p e t e r , E.E., 1960, Phys. Rev., 120, 1528. S p i t z e r , L. J r . , 1965, " P h y s i c s o f F u l l y I o n i z e d Gasses", Interscience Publishers. Wiese, W.L., M.W. S m i t h , and B.M. Glennon, 1966, "Atomic T r a n s i t i o n P r o b a b i l i t i e s H t h r o u g h Ne", U.S. Dept. o f Commerce, NSRDS - NBS V o l . 1. W i l l i a m s o n , J . H . , R.A. N o d w e l l , and A . J . B a r n a r d , 1966, J . Quant. S p e c t r y . Rad. T r a n s f e r , j$, 895.  - 39 -  

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