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UBC Theses and Dissertations

Interaction of CO2 laser light with a dense Z-pinch plasma Albrecht, Georg F. 1979

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INTERACTION OF C 0  2  LASER LIGHT  WITH A DENSE Z-PINCH PLASMA  by GEORG F. ALBRECHT D i p l . Phys, U. o f S t u t t g a r t , 1974  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES Department o f P h y s i c s v 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 May, 1979 0  Georg F. A l b r e c h t , 1979  In p r e s e n t i n g t h i s  thesis in partial  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  shall  the U n i v e r s i t y  make i t  agree that  freely  this  thesis for  It  f i n a n c i a l gain shall  Department The 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 2075 W e s b r o o k P l a c e V a n c o u v e r , Canada V6T 1W5  75-51 1 E  the  requirements I agree  r e f e r e n c e and copying of  this  that  not  copying or  for  that  study. thesis  by t h e Head o f my D e p a r t m e n t  i s understood  permission.  of  B r i t i s h Columbia,  extensive  s c h o l a r l y p u r p o s e s may be g r a n t e d  written  BP  of  available for  permission for  by h i s r e p r e s e n t a t i v e s . of  fulfilment  or  publication  be a l l o w e d w i t h o u t  my  Research Supervisor:  J . Meyer  Abstract The  i n t e r a c t i o n o f a 250 MW  been observed.  CO^  l a s e r p u l s e w i t h a Z - p i n c h plasma has  H e a t i n g by i n v e r s e b r e m s s t r a h l u n g  and s t i m u l a t e d  ^ . • rr i c . i 7 electrons B r i l l o u m s c a t t e r i n g o f f a plasma w i t h a few times 1 0 5 . cnw i n  T^ °u 150 eV and The observed  temperature s c a l e l e n g t h s of a few mm  w  i s shown to o c c u r .  a n g u l a r dependence of the B r i l l o u i n b a c k s c a t t e r e d  i s i n good agreement w i t h - c u r r e n t t h e o r i e s .  light  Some of the  b a c k s c a t t e r e d l i g h t shows i n t e n s i t y m o d u l a t i o n s  a t the e l e c t r o n g y r o  frequency. Finally,  the s u c c e s s f u l nano second g a t i n g of an O p t i c a l M u l t i c h a n n e l  A n a l y s e r i s d e s c r i b e d and a p p l i e d t o s p e c t r o s c o p i c a l d e n s i t y measurements of the plasma.  II  TABLE OF CONTENTS Page ABSTRACT  i i i  LIST OF SYMBOLS  iv  INTRODUCTION  1  CHAPTER I : Theory o f p a r a m e t r i c  decay i n an i n f i n i t e  homogeneous^.plasma^and: i t s a p p l i c a t i o n t o stimulated B r i l l o u i n scattering  3  1.1  Introduction  3  1.2  O u t l i n e of the theory  5  1.3  D e r i v a t i o n of the general d i s p e r s i o n r e l a t i o n  6  1.4  S p e c i a l i z a t i o n f o r stimulated backscattering  15  1.5  Stimulated B r i l l o u i n Scattering  19  1.6  The cj - k diagram  23  1.7  L i m i t a t i o n s o f t h e t h e o r e t i c a l model  25  1.8  Numerical values  26  CHAPTER I I : E x p e r i m e n t a l and  i n v e s t i g a t i o n of the backscattered  t r a n s m i t t e d CO2 l a s e r l i g h t  30  2.1  Introduction  30  2.2  The Z-pinch plasma, measurements o f r a d i u s , temperature and d e n s i t y and t h e CO2 l a s e r used for the laser-plasma  interaction studies  2.3  Experimental  2.4  S p e c t r a l l y integrated backscattered  32  provisions  35 C0£ l a s e r  l i g h t as a f u n c t i o n o f p i n c h - t i m e 2.5  39  S p e c t r a l l y i n t e g r a t e d t r a n s m i t t e d CO2 l a s e r l i g h t as a f u n c t i o n o f pinch-time  2.6  S p e c t r a l l y resolved backscattered  41 CO2 l a s e r  l i g h t a t p i n c h time t = 0 ± 25 nsec and t h e a n g u l a r dependence o f t h e b a c k s c a t t e r e d  III  light  45  TABLE OF CONTENTS Page CHAPTER I I I :  E v a l u a t i o n o f the e x p e r i m e n t a l r e s u l t s  49  3.1  The t r a n s m i t t e d C 0  49  3.2  The b a c k s c a t t e r e d CO2 l a s e r l i g h t  2  laser light  3.21 Enhancement o f t h e b a c k s c a t t e r e d CO2  55 laser  l i g h t above t h e r m a l l e v e l s and the r e s u l t i n g i o n wave a m p l i t u d e s  i n t h e plasma  3.22 D i s c u s s i o n o f t h e observed  56  w a v e l e n g t h s h i f t ':  o f t h e b a c k s c a t t e r e d CO2 l a s e r l i g h t  62  3.23 The a n g u l a r dependence o f the b a c k s c a t t e r e d C0  2  l a s e r l i g h t and comparison w i t h t h e o r y  67  3.24 The wavelength dependence o f t h e l i g h t b a c k s c a t t e r e d through  t h e " s m a l l mask"  CONCLUSIONS CHAPTER IV:  70 76  The f a s t g a t i n g of an OMA and a c o n t r i b u t i o n to t h e d i a g n o s t i c s o f the Z - p i n c h plasma  78  4.1  Introduction  78  4.2  Nanosecond g a t i n g of an OMA  82  4.3  S p e c t r o s c o p i c measurements o f plasma d e n s i t y and  temperature u s i n g the 4686S 1 i n e o f He I I  SPECIFICATIONS  91 94  REFERENCES  101  IV  wave v e c t o r s o f t h e plasma d e n s i t y f l u c t u a t i o n s , 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 waves f r e q u e n c i e s of t h e plasma d e n s i t y f l u c t u a t i o n , 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 waves e l e c t r i c f i e l d s of t h e i n c i d e n t and s c a t t e r e d e l e c t r o m a g n e t i c waves c u r r e n t s i n t h e plasma a t t h e s c a t t e r e d f r e q u e n c i e s c o n d u c t i v i t y o f the plasma a t t h e s c a t t e r e d f r e q u e n c i e s a m p l i t u d e o f t h e enhanced d e n s i t y f l u c t u a t i o n e l e c t r i c u n i t charge o f e i t h e r i o n o r e l e c t r o n e l e c t r i c u n i t charge o f e l e c t r o n q u i v e r v e l o c i t y o f an e l e c t r o n i n t h e i n c i d e n t e l e c t r o m a g n e t i c wave a t f r e q u e n c i e s ± u> mass of t h e e l e c t r o n mass o f t h e atom (He) d i e l e c t r i c constant at w electronic, ionic  +  susceptibility  speed o f l i g h t average e l e c t r o n d e n s i t y plasma f r e q u e n c i e s o f e l e c t r o n s / i o n s ponderomotive see  potential  (1-12)  high frequency coordinate of e l e c t r o n s o s c i l l a t i n g i r i an e l e c t r o m a g n e t i c  field  c o o r d i n a t e a l o n g which t h e e l e c t r i c f i e l d v a r i e s  d i s t r i b u t i o n function f o r ions,  electrons  Maxwellian equilibrium d i s t r i b u t i o n function s e l f - c o n s i s t e n t p o t e n t i a l w i t h i n plasma damping o f e l e c t r o m a g n e t i c and  wave and i o n wave (Landau  collisional)  Debye l e n g t h a n g l e between k and V  q  also angular coordinate  (Ch. I ) (3.21)  growth r a t e f o r a p a r a m e t r i c decay  instability  Shape f a c t o r o f t h e Thomson s c a t t e r e d i o n f e a t u r e i o n , e l e c t r o n temperature inverse bremsstrahlung absorption  length  thermal c o n d u c t i v i t y Boltzmann' c o n s t a n t Coulomb l o g a r i t h m ,  f« 10  l a s e r l i g h t i n t e n s i t y i n c i d e n t on t h e plasma backscattered  laser light intensity  (thermal,  enhanced, denoted by s u p e r s c r i p t s ) angular divergence of backscattered  light for  d i f f e r e n t p h y s i c a l models l e n g t h o f i n t e r a c t i o n volume; s c a l e  lengths  i n v e r s e g a i n l e n g t h o f l i g h t a m p l i f i e d by SBS i o n - a c o u s t i c speed l a s e r - p l a s m a i n t e r a c t i o n volume  VI  t o my  father,  f o r h i s i n f i n i t e l o v e , t r u s t and  support,  to M a r i l y n , f o r a l l she  taught  t o the p l e a s u r e  me.  of a l o v i n g woman's t o u c h ,  i t i s the d i f f e r e n c e between l i v i n g and  vegetating.  VII  1.  Introduction The c u r r e n t e f f o r t s i n c o n t r o l l e d thermonuclear f u s i o n r e s e a r c h have brought about a g r e a t i n t e r e s t i n l a s e r . p l a s m a - i n t e r a c t i o n s t u d i e s . The " i n e r t i a l c o n f i n e m e n t " type of experiment a t t e m p t s t o a c h i e v e c o n t r o l l e d f u s i o n by f o c u s s i n g enormous l a s e r powers (.5 p e t a w a t t s ) on s m a l l DT p e l l e t s (some lOOy d i a m e t e r ) and thus heat and compress the c r e a t e d plasma t o t e m p e r a t u r e s and d e n s i t i e s a t which  thermonuclear 1 2  r e a c t i o n s y i e l d more energy than was put i n i n form of l a s e r energy. ' The key q u e s t i o n s t h a t a r i s e i n t h i s approach concern the c o u p l i n g of l a s e r l i g h t t o the plasma, a problem of surmounting c o m p l e x i t y .  ;  -  The.type.of e x p e r i m e n t s i n which the plasma i s m a g n e t i c a l l y c o n f i n e d a t t e m p t s t o a c h i e v e c o n t r o l l e d f u s i o n not so much by r e d u c i n g t h e mean f r e e p a t h between r e a c t i o n s by plasma compression but by i n c r e a s i n g the confinement time t o an e x t e n t t h a t a s u f f i c i e n t amount of t h e r m o n u c l e a r energy can be r e l e a s e d b e f o r e the plasma decays.  One of t h e most  i m p o r t a n t problems i n t h i s approach i s the h e a t i n g of the plasma t o 5 6 s u f f i c i e n t temperatures. Dawson et a l . suggested t h a t h i g h power l a s e r s be used t o a c h i e v e s i g n i f i c a n t  h e a t i n g of m a g n e t i c a l l y c o n f i n e d  plasmas because t h e s e t y p e s of plasmas a r e i n a d e n s i t y regime where the i n v e r s e b r e m s s t r a h l u n g a b s o r p t i o n f o r CO2  l a s e r l i g h t becomes  s i g n i f i c a n t . A number of experiments have been performed a l o n g these . 5,7,8,9,28 lxnes. n  I n e i t h e r case  i t . i s of g r e a t importance t o i n v e s t i g a t e l a s e r  plasma  i n t e r a c t i o n s under d i f f e r e n t c o n d i t i o n s i n o r d e r t o l e a r n about the p o s s i b l e p h y s i c a l p r o c e s s e s i n v o l v e d and t o a i d t h e o r i e s t h a t t r y t o p r e d i c t such p r o c e s s e s .  2. The  experiment d e s c r i b e d i n t h i s r e p o r t was s e t up t o i n v e s t i g a t e which  l a s e r plasma i n t e r a c t i o n p r o c e s s e s  can be s t u d i e d w i t h t h e means  currently available i n this laboratory. Chapter I d e s c r i b e s t h e b a s i c s o f t h e t h e o r y o f one o f t h e most important  types o f p r o c e s s e s  happening i n h i g h power l a s e r plasma i n t e r s  a c t i o n s , namely t h e p a r a m e t r i c decay o f a l i g h t wave i n plasma waves and s c a t t e r e d l i g h t waves.  The case o f s t i m u l a t e d B r i l l o u i n s c a t t e r i n g  i s t r e a t e d i n some d e t a i l . Chapter I I d e s c r i b e s t h e e x p e r i m e n t s performed w i t h a 250 MW CO2 l a s e r and a h i g h d e n s i t y Z-pinch plasma and the r e s u l t s t h a t were o b t a i n e d . Chapter I I I d i s c u s s e s these r e s u l t s and c o n c l u s i o n s a r e drawn about the o c c u r r e n c e  of stimulated B r i l l o u i n s c a t t e r i n g , the angular  of i t s b a c k s c a t t e r e d backscattered  divergence  l i g h t and t h e i n t e n s i t y m o d u l a t i o n o f some o f t h e  l i g h t w i t h t h e g y r o frequency  of CO2 l a s e r l i g h t by i n v e r s e b r e m s s t r a h l u n g  of e l e c t r o n s .  The a b s o r p t i o n  i n some e x p e r i m e n t s i s  verified. Chapter IV d e s c r i b e s a c o n t r i b u t i o n t o t h e d i a g n o s t i c s o f t h e Z - p i n c h plasma.  A new t e c h n i q u e  f o r s a t i s f a c t o r y nsec g a t i n g o f an O p t i c a l  M u l t i c h a n n e l A n a l y s e r i s a p p l i e d t o s p e c t r o s c o p i c a l s t u d i e s o f t h e plasma d e n s i t y u s i n g t h e 4686S l i n e o f He I I .  3.  CHAPTER I Theory of p a r a m e t r i c decay i n an i n f i n i t e , homogeneous plasma and i t s a p p l i c a t i o n t o s t i m u l a t e d B r i l l o u i n  scattering.  1.1 I n t r o d u c t i o n T h i s c h a p t e r attempts  t o p r o v i d e an e a s i l y r e a d a b l e p r e s e n t a t i o n of the  t h e o r y of p a r a m e t r i c decay i n s t a b i l i t i e s i n an i n f i n i t e homogeneous plasma.  As i t i s n e i t h e r supposed t o be a comprehensive r e v i e w nor a  cumbersome r e p r o d u c t i o n of work a l r e a d y done,"^  the p r e s e n t a t i o n i s  l i m i t e d t o the p r o c e s s most r e l e v a n t f o r t h e experiment l a t e r , e.g.  t h e p r o c e s s of l o w e s t t h r e s h o l d and h i g h g r o w t h r a t e namely  stimulated B r i l l o u i n Furthermore,  t o be d e s c r i b e d  scattering.  the emphasis w i l l be on p h y s i c a l i n t e r p r e t a t i o n r a t h e r than  the m a t h e m a t i c a l  apparatus.  F i r s t , a s i m p l e p i c t u r e o f a p a r a m e t r i c p r o c e s s s h a l l be g i v e n . an e l e c t r o m a g n e t i c wave (& , Q  density fluctuations.  w) o  i n c i d e n t on a plasma w i t h  Imagine  thermal  L e t us assume t h a t the e l e c t r o m a g n e t i c wave  s c a t t e r s o f f a f o u r i e r component (1c, OJ) of these d e n s i t y f l u c t u a t i o n s thus c r e a t i n g a s c a t t e r e d e l e c t r o m a g n e t i c wave a t k ( c o n s e r v a t i o n o f wave momentum) and f r e q u e n c y OJ  = k^ — k  = a) - oo ( c o n s e r v a t i o n Q  of e n e r g y ) . I n the case of s m a l l i n c i d e n t i n t e n s i t i e s t h i s s c a t t e r e d wave w i l l the plasma w i t h o u t p e r t u r b i n g i t any f u r t h e r .  leave  With i n c r e a s i n g i n c i d e n t  i n t e n s i t i e s however, a s i t u a t i o n w i l l a r i s e i n which the i n t e n s i t y o f the s c a t t e r e d l i g h t at" ( u _ , k*_) w i l l i n d e e d be h i g h enough t o i t s e l f the plasma.  Now  we have the new  namely one a t (& > Q  i n t h e plasma.  affect  s i t u a t i o n of two e l e c t r o m a g n e t i c waves,  aj ) and one a t (1c , a)_) b e i n g s i m u l t a n e o u s l y p r e s e n t Q  4.  I f b o t h waves i n t e r a c t l i n e a r l y w i t h t h e plasma, n o t h i n g s p e c t a c u l a r w i l l happen and e l e c t r o n s w i l l o s c i l l a t e a t f r e q u e n c i e s w  and o> . I f ,  however, t h e two waves couple t o each o t h e r v i a t h e plasma, n o t o n l y t h e f r e q u e n c i e s a t OJ  and to  w i l l o c c u r i n t h e plasma, but a l s o t h e sum and  d i f f e r e n c e f r e q u e n c i e s to + to and o nonlinear coupling  indeed  be e x p l a i n e d l a t e r . the low frequency the a m p l i t u d e  to - to . o -  I t w i l l be seen, t h a t ! t h i s  t a k e s p l a c e v i a t h e ponderomotive f o r c e , t o  Of these two f r e q u e n c i e s , to  at m  + to  and O) - t o _ , q  - oi w i l l c o u p l e much s t r o n g e r t o the plasma as  o f an e l e c t r o n o s c i l l a t i n g i n an e l e c t r o m a g n e t i c  p r o p o r t i o n a l t o -^r.  Therefore, the simultaneous  field i s  p r e s e n c e o f t h e two  e l e c t r o m a g n e t i c waves a t (k » w ) and (k , to ) w i l l s e t up a plasma wave ->-->-»-->-->-->atk - k = k - (k - k ) = k and to - t o =00 - (w - to) = t o . 0  -  0  0  0  -  0  0  I n o t h e r words, t h e b e a t o f t h e i n c i d e n t and s c a t t e r e d e l e c t r o m a g n e t i c wave i n t h e plasma w i l l enhance e x a c t l y t h a t d e n s i t y f l u c t u a t i o n which i n i t i a l l y s c a t t e r e d t h e i n c i d e n t e l e c t r o m a g n e t i c wave. I f the plasma wave a t ( k , to) i s b u i l t up t o an e x t e n t t h a t t h e r m a l i z a t i o n cannot d e s t r o y i t anymore, more f l i g h t y e t w i l l be s c a t t e r e d a t t h e now enhanced d e n s i t y f l u c t u a t i o n , w h i c h i n t u r n w i l l beat a g a i n w i t h t h e i n c i d e n t l i g h t wave t o enhance t h e d e n s i t y f l u c t u a t i o n even more and thus a s c a t t e r i n g i n s t a b i l i t y or " s t i m u l a t e d s c a t t e r i n g " w i l l take p l a c e . The  t h r e s h o l d w i l l , as i n d i c a t e d , depend on how e f f e c t i v e t h e beat wave  i s i m p r i n t e d onto t h e plasma by the e l e c t r o m a g n e t i c f i e l d s a g a i n s t t h e randomizing  e f f e c t s o f c o l l i s i o n a l and Landau damping.  W i t h t h i s s i m p l e p i c t u r e i n mind, t h e t h e o r e t i c a l model d e s c r i b i n g these parametric processes  can e a s i l y be f o l l o w e d .  5.  1.2 O u t l i n e o f t h e t h e o r y Maxwell's e q u a t i o n s d e s c r i b e the g e n e r a t i o n o f e l e c t r o m a g n e t i c waves a t f r e q u e n c i e s U J = u> ± w  due t o source terms a t t h e same f r e q u e n c i e s .  +  The f o r c e s i n the plasma a r i s i n g from t h e b e a t of t h e i n c i d e n t and the s c a t t e r e d l i g h t wave a r e b e s t d e s c r i b e d by i n t r o d u c i n g the ponderomotive p o t e n t i a l .  Together w i t h t h e s e l f - c o n s i s t e n t p o t e n t i a l ,  c a l c u l a t e d from P o i s s o n ' s e q u a t i o n , i t w i l l p r o v i d e t h e f o r c e terms i n the V l a s o v e q u a t i o n .  The l a t t e r then a l l o w s d e n s i t y f l u c t u a t i o n s a t  a), it i n t h e plasma due t o t h e beat o f two e l e c t r o m a g n e t i c waves t o be calculated. The V l a s o v e q u a t i o n f o r t h e d e n s i t y f l u c t u a t i o n s <5n and t h e e q u a t i o n s f o r it  form a s e t o f coupled e q u a t i o n s  f o r fin and  the s o l u t i o n of  t h i s system i s a d i s p e r s i o n r e l a t i o n d e s c r i b i n g t h e p r o p a g a t i o n of e l e c t r o m a g n e t i c waves as a f u n c t i o n o f t h e p r o p a g a t i o n o f plasma waves under v a r i o u s c o n d i t i o n s .  T h i s r e l a t i o n makes i t p o s s i b l e t o c a l c u l a t e  t h r e s h o l d s and g r o w t h r a t e s  f o r d i f f e r e n t t y p e s of p r o c e s s e s .  =  E(OJ  ± CJ  )  1.3 D e r i v a t i o n o f t h e g e n e r a l d i s p e r s i o n r e l a t i o n  As p o i n t e d o u t i n the o u t l i n e o f the t h e o r y , we s t a r t out w i t h M a x w e l l ' s equations  t o d e s c r i b e t h e g e n e r a t i o n o f e l e c t r o m a g n e t i c waves a t t h e  s c a t t e r e d f r e q u e n c i e s to , = to ± to . ± o E l i m i n a t i n g H out o f +  (*) 1 ' + ' = - - — — c 8t  V x H  3B  V x E  where B = y H one  and  V  and  4TT ~ 1 + = — j . + -rr=± c ± c 8t 3g  (I-D  J  (1-2)  u = 1  gets V x (V x E )  4-TT  =  +  :  2  '  8  J  1  ±  at  c  8^E , at  2  (1-3)  2  and w i t h V x (v x E )  =  (grad d i v - A) E  (1-4)  +  t h i s becomes 1  9 2 f i  4TT  3  2  The R.H.S. o f e q u a t i o n  J  ±  —75- — c 3t  +  6  grad  (1-5)  d i v E^ ±  (1-5) means t h a t t h e e l e c t r o m a g n e t i c wave E  s o u r c e terms due t o c u r r e n t s j  +  has  f l o w i n g i n t h e plasma and due t o  s e l f - c o n s i s t e n t f i e l d s w h i c h w i l l have t o be c a l c u l a t e d u s i n g  Poisson's  equation. Fourier transforming the equation E ( x , t) =  1  4TT2  >. i ( k x - w t ) 3 E ( k , a)) e d kdtj 3  all w all k  K  '  E E-  +  =  E(u)+)  =  E(co  )  ..  (1-5) u s i n g (1-6)  7.  we  f ind  cIn  i  ±  z  -k :.k +  4iri  (*)  (1-7)  +  o r d e r t o a r r i v e a t a d i s p e r s i o n r e l a t i o n , we have t o e x p r e s s j  terms of the e l e c t r i c f i e l d E,.  T h i s c u r r e n t i , a r i s e s due t o the  l i n e a r response of the e l e c t r o n s t o the o s c i l l a t i n g f i e l d E beat of the i n c i d e n t wave E Thus we  in  and  +  the  w i t h d e n s i t y f l u c t u a t i o n s 6n a t k, o>.  o±  get (1-8)  E ,. The c o n d u c t i v i t y a can be d e s c r i b e d i n terms r>+ xm a) o± e o of the d i e l e c t r i c c o n s t a n t 'e through  where v  J  o±  ±  1U  1 -k  (£  ±  =  (1-9),  1 }  I n s e r t i n g the e x p r e s s i o n i n (1-7) we  find  2  \ i e ] I - k -k  ,2  The  +  +  +  a)  i.  2  —£  6n (£, a))E (±uj ) o±  f i r s t term i n (1-8) m o d i f i e s the vacuum p a r t of e q u a t i o n  one f o r a medium by s e t t i n g e  +  ^ 1. The  (1-10)  o  o  second term o f eq.  (1-7)  into  (1-8) as i t  appears i n e q u a t i o n (1-10) d e s c r i b e s d i r e c t l y the g e n e r a t i o n of  fields  at E,(ti),) due t o the b e a t of the i n c i d e n t f i e l d E ,'(±ci) ) w i t h the d e n s i t y ± ± o± o f l u c t u a t i o n s 6n(to) .  I = E , = E (+w ) + E (-0) ) *** T h i s i s a g e n e r a l r e l a t i o n s h i p f o r e l e c t r o m a g n e t i c waves i n c o n d u c t i n g media and f o l l o w s from Maxwell's e q u a t i o n s . 0 ±  0  0  0  0  8. convenience t o s o l v e f o r E +  I t w i l l l a t e r be of m a t h e m a t i c a l i n v e r t i n g (1-10).  The r e s u l t i s Sn  2  ±  p  There, D with  k  k^ ±  =  k±k,  e+  =~  x  2 +  ^  !  k  ±  k  ± \  1  k  ±  k  ±  E  n o  =  +  by  c  - to  2  o 2 0) 1 - M^ o -2 to ^  2 +  e  us ±  . o±  (1-11)  (1-12)  +  =  and  to ± to , o k  +  2  o  c  2  - o>  2  + o> o p 2  =  0  T h i s form w i l l be used l a t e r . A f t e r the e q u a t i o n " f o r the e l e c t r o m a g n e t i c f i e l d s (1-11) "has been e s t a b l i s h e d , we now  proceed t o c a l c u l a t e the d e n s i t y f l u c t u a t i o n s S n ^ k ,  from the beat of the i n c i d e n t and the s c a t t e r e d l i g h t w a v e E E ( c o ) by s o l v i n g the V l a s o v e q u a t i o n . +  +  f o r c e concept f i r s t has t o be  to) a r i s i n g , (±to ) and o± o  To do t h i s , the ponderomotive  introduced.  We w i s h t o s o l v e , a t l e a s t a p p r o x i m a t e l y ,  the e q u a t i o n of m o t i o n f o r a  s i n g l e e l e c t r o n i n an e l e c t r o m a g n e t i c f i e l d w h i c h i s a slow f u n c t i o n of p o s i t i o n i n the sense t h a t i t s s t r e n g t h v a r i e s o n l y s l i g h t l y w i t h i n the range of a m p l i t u d e  of the e l e c t r o n due  t o the o s c i l l a t i o n i n t h i s  field. In  zero order approximation,  the e l e c t r o n w i l l o s c i l l a t e i n the a p p l i e d  f i e l d according to ? E, =  e + o- E m to^ e  , £ where E  =  £ , itot , -itot,. E (e + e ) o  A l l o t h e r symbols have the u s u a l obvious meaning.  s (1-14)  / T  The  however, a d d i t i o n a l l y e x p e r i e n c e a slow movement due  1 7  electron w i l l ,  t o the f a c t t h a t  the e l e c t r i c f i e l d 1? i s not c o n s t a n t a l o n g the c o o r d i n a t e s of  oscillation.  9.  We t h e r e f o r e expand  E  =  E (R) + (,6R V) E  Choosing  (1-15)  6R = £ means t o a s k : how much does E change i f t h e e l e c t r o n  p o s i t i o n i s changed d u r i n g t h e o s c i l l a t i o n .  An e f f e c t o f e q u a l  a r i s e s because t h e e l e c t r o n n o t o n l y o s c i l l a t e s  order  i n a pure e l e c t r i c  field  but i n t h e e l e c t r o m a g n e t i c f i e l d o f t h e l i g h t wave. The complete e q u a t i o n o f m o t i o n can a p p r o x i m a t e l y m(R + 1) ~t with K = -  =  e E lwm  - e ,  be w r i t t e n a s  E (R) + (|-V) E + | x B  (1-16)  ~* e -> 5 = -=7- E moj^  (1-17)  -y  and |5- = 3t  - V x E  hence  B = -  X03  5Z x E  (1-18)  We see t h a t t h e second and t h i r d terms o f t h e R.H.S. o f e q u a t i o n r e s u l t i n m o t i o n a t t h e f r e q u e n c i e s 0 and  2OJV'- r e s p e c t i v e l y .  (1-16)  As h i g h  f r e q u e n c i e s (2co) a r e o f no i n t e r e s t h e r e , we can f i n a l l y w r i t e t h e low_ frequency  m R  p a r t of the equation  =  -  (1-16) as  t (E'V)E + E x (V x E) ]  The f i r s t term a r i s e s from t h e s p a t i a l n o n - u n i f o r m i t y  (1-19) of the e l e c t r i c  f i e l d and i s a d r i f t . t e r m analogous t o t h e ( v V ) v term i n f l u i d e q u a t i o n s ; thei.second..term  i s d u e t t o t h e i n f l u e n c e o f t h e magnetic p a r t  of t h e e l e c t r o m a g n e t i c f i e l d on t h e e l e c t r o n and i s a f o r c e p o i n t i n g a l o n g t h e v e c t o r o f p r o p a g a t i o n o f t h e e l e c t r o m a g n e t i c wave. Rewriting  E x 07, x E)  =  V E  2  - (EV)E  (1-4)  10. we see t h a t b o t h f o r c e s combine t o form a ponderomotive f o r c e  m R which  can be d e r i v e d from a ponderomotive p o t e n t i a l ip g i v e n by  m  *  " *  =  7  ~ 2m^2  =  V  ^  ( I  "  2 0 )  I t must be understood t h a t t h i s f o r c e v a r i e s s l o w l y w i t h t i m e , e.g. t »  R and thus a t f r e q u e n c e s a t which i o n s can respond v i a s e l f -  consistent f i e l d s .  I f t h e d e s c r i b e d c a l c u l a t i o n i s c a r r i e d out f o r more  than one e l e c t r o m a g n e t i c wave t h e ponderomotive p o t e n t i a l i s found t o b e ^ *  =  2 E f - Re | I 2m f lco 1  1  A  2  (1-21)  1  A  I n t h e case c o n s i d e r e d h e r e , t h e r e a r e t h r e e f i e l d s p r e s e n t ,  E (±to"), o o  E (to ) and E_(o)_) . +  An e x p l i c i t e v a l u a t i o n of (1-21) f o r these t h r e e f i e l d s shows t h a t the ponderomotive p o t e n t i a l f o r t h e slow frequency  o f t h e plasma wave a t to  i s g i v e n by i|> to  =  0  2mto o z  ( E E + E E ) o+ o- +  (1-22)  We now t u r n t o t h e p r o b l e m o f c a l c u l a t i n g t h e induced d e n s i t y f l u c t u a t i o n s w i t h the Vlasov equation.  I t should; be u n d e r s t o o d t h a t an e l e c t r o n  i n a plasma e x p e r i e n c i n g a s t r o n g e l e c t r o m a g n e t i c  f i e l d i s subject to  t h r e e f o r c e s a t two types of f r e q u e n c i e s : The d i r e c t f o r c e of t h e e l e c t r i c p a r t o f t h e i n c i d e n t  electromagnetic  f i e l d E (to ) w h i c h makes the e l e c t r o n o s c i l l a t e ' ' at: to , a f o r c e due t o o o o' -  c  the s e l f - c o n s i s t e n t f i e l d between i o n s and e l e c t r o n s a r i s i n g from l o c a l d e n s i t y p e r t u r b a t i o n s , and a f o r c e d e r i v e d from t h e ponderomotive potential.  The i o n s , on t h e o t h e r hand, a r e c o n s i d e r e d  only to  e x p e r i e n c e a f o r c e due t o t h e s e l f - c o n s i s t e n t f i e l d s , s i n c e t h e d i r e c t  lief f e e t on them v i a t h e i n c i d e n t e l e c t r o m a g n e t i c  f i e l d and t h e  ponderomotive f o r c e i s s m a l l e r than t h a t f o r e l e c t r o n s by a f a c t o r o f q./ra. * 1  ^  1  -  • e e To c a l c u l a t e a d i s t r i b u t i o n f u n c t i o n f . f o r i o n s and f f o r e l e c t r o n s l e we t h e r e f o r e w r i t e q  7 /m  9f.  • , 3f. + v. V f . + - (Z elV $) T - 2 1 = )t i i m " " 3v.  0  1  v  9 f  —  i 3 - - [ e V ( $ + - ) ] — — e m e 8v e  (1-23)  f  3t  v  e  V f  1  =  0  (1-24)  As t h e ponderomotive p o t e n t i a l appears o n l y as a m o d i f i c a t i o n o f t h e s e l f - c o n s i s t e n t p o t e n t i a l b o t h e q u a t i o n s can be s o l v e d by an, e x p a n s i o n f = f + f o  1  around t h e e q u i l i b r i u m d i s t r i b u t i o n f u n c t i o n f o n  i n any t e x t b o o k on plasma p h y s i c s " ^  as i s shown  and t h e r e s u l t f o r t h e d e n s i t y  fluctuations i s Sn  = e  y— (* + -) X 4ire e e k -f— $:-v. 4ire i 2  6n. i  =  (1-25)  +  (1-26)  A  The t h i r d e q u a t i o n f o r t h e t h r e e unknowns 6n ... <5n. and $ i s P o i s s o n ' s e' i equation.  - k $ z  =  4ir (e 6n  - e 6n )  (1-27)  g  E l i m i n a t i n g 6n^ out o f (1-26) and (1-27) and then e l i m i n a t i n g $ out o f the r e m a i n i n g two e q u a t i o n s y i e l d s  * t charge-to-mass r a t i o f o r e l e c t r o n s / i o n s . X »X** e I c|> i s t h e s e l f - c o n s i s t e n t p o t e n t i a l i n t h e plasma  s e e  P- 14  12.  r  Sn  = e  - (1 + . ) — I x  2  T^T e 4Tre E  x  (  I _ 2 8  >  z  1" i s the ponderomotive p o t e n t i a l due t o t h e b e a t o f the i n c i d e n t and t h e s c a t t e r e d e l e c t r o m a g n e t i c wave and i s g i v e n by (1-22). With e q u a t i o n (1-28) t h e second g o a l i s a c h i e v e d , namely t h e d e s c r i p t i o n of how d e n s i t y f l u c t u a t i o n s a r e s e t up due t o t h e beat o f two e l e c t r o magnetic waves i n a plasma. I t remains t o e x t r a c t a d i s p e r s i o n r e l a t i o n out o f the two e q u a t i o n s (1-28) and (-1-11). Equations  (1-11) and (1-28) a r e a s e t o f c o u p l e d e q u a t i o n s f o r E  Combining (1-28) and (1-22) E  +  +  and 6n.  and r e p l a c i n g i n t h e r e s u l t i n g e x p r e s s i o n  and E_ from (1-11) one can c a n c e l out fin^. The r e s u l t i n g e q u a t i o n i s  the wanted d i s p e r s i o n r e l a t i o n I  (1 + X,)X„ 1  =  e  e  2  •> ->•  2 w k p 4iTmcoi n o o V  -  -'r?- •+  +  2  +  *  (\*+  1  k k  1+  )  (1-29)-  I n o r d e r t o b r i n g t h i s e x p r e s s i o n i n t o t h e more f a m i l i a r form a p p e a r i n g i n R e f . 14 note t h a t 1 ^ 1 + — xe i+ xi  (i + x±)xe  E [(k*k) E ] = o o  1  |E.£| o  , and  =  2  1  E k o 2  sin H E ,^) o  2  2  so t h a t  E  (  o.L•  Y - | ^ ) E 1 = k oJ z  t k [ l - s i n ( * E , k)] o o 2  2  2  = | k x E c  13.  4im e  _^ E was t h e 0 o r d e r p m imu) o o q u i v e r v e l o c i t y o f the e l e c t r o n i n t h e i n c i d e n t f i e l d E one a r r i v e s  Substituting u  2  &  2  =  and remembering  that — :  v  q  at  t h e f i n a l form o f t h e d i s p e r s i o n r e l a t i o n k.xv K i + o D k 2 1  . •  1  k x v —  D k  + +  z  o  2  .- -  1  k, • v r + a k 2 2 1  .-.+  U  e  +'+  1  k «v+ 2 o ' k 2 2 -  U  (1-30)  e  From the d e r i v a t i o n o f (1-30) i t f o l l o w s t h a t the k«v  terms i n t h e o R.H.S. o f (1-30) a r i s e from t h e grad d i v FJ term i n t h e i n i t i a l wave e q u a t i o n ( 1 - 5 ) , e.g. from t h e e l e c t r o s t a t i c components a t t h e s i d e b a n d f r e q u e n c i e s u>, and w . + n  -*--»The k x v terms a r i s e from t h e -AH o  1  3 -r—b c 9t 2  z  term i n t h e wave e q u a t i o n ( 1 - 5 ) , e.g. from t h e e l e c t r o m a g n e t i c components a t t h e s i d e b a n d f r e q u e n c i e s .  The r e a s o n f o r b o t h o f t h e s e  modes depending on each o t h e r i s t h a t t h e term - ^  ^+3 + ( l - I 7 ) e <  2  _  i n v o l v e s a c o u p l i n g v i a t h e ponderomotive f o r c e o f the e l e c t r o s t a t i c components. To g e t a f e e l i n g f o r how t h i s d i s p e r s i o n r e l a t i o n d e s c r i b e s t h e p r o p a g a t i o n o f a d e n s i t y wave and e l e c t r o m a g n e t i c s i d e b a n d modes as a f u n c t i o n o f each o t h e r , c o n s i d e r t h e f o l l o w i n g s i m p l i f i e d c a s e : imagine some k i n d o f p r o c e s s where o n l y the second term i n (1-30) on the  R.H.S. i s o f i m p o r t a n c e , e.g. D_ -> 0, and where t h e i o n s can be  neglected.  Then, (1-30) r e d u c e s t o  ( — + 1) D X e A  =  k 2  1  l  -  k x  v  o  1  I  2  t " 1  3 1  )  I f t h e r e would be no ponderomotive f o r c e t e r m , t h e n t h e R.H.S. o f e q u a t i o n (1-31) would be z e r o and the e q u a t i o n would reduce t o (— *e  + 1) • D  =0  (1-32)  14.  Then  one s o l u t i o n i s  and, hence, to = to d e s c r i b e s an xe P plasma o s c i l l a t i o n a t to ;:;or D = 0 hence, k c + to = to p' ' P -  undisturbed  + 1=0  2  2  2  2  2  p  describes the undisturbed frequency  2  propagation  o f an e l e c t r o m a g n e t i c wave a t  to through t h a t plasma.  The R.H.S. o f (1-31) t h e r e f o r e , a r i s i n g due t o t h e ponderomotive f o r c e , i s t h e c o u p l i n g c o e f f i c i e n t between t h e e l e c t r o m a g n e t i c the plasma o s c i l l a t i o n a t to^.  wave a t to_ and  The s t r e n g t h o f t h i s c o u p l i n g i s c l e a r l y  p r o p o r t i o n a l t o k , i . e . t h e l e n g t h o f t h e wave v e c t o r o f t h e d e n s i t y 2  f l u c t u a t i o n squared.  T h i s means t h a t s h o r t wavelength f l u c t u a t i o n s w i l l  couple s t r o n g e r t o t h e e l e c t r o m a g n e t i c  sideband  modes than l o n g wave-  l e n g t h f l u c t u a t i o n s , and t h e c o u p l i n g 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 of the i n c i d e n t electromagnetic  wave a t to . o The s u s c e p t i b i l i t i e s x^ ^ X given through the Vlasov equation 14-19 i n terms o f t h e e q u i l i b r i u m d i s t r i b u t i o n f u n c t i o n f by b  a n c  a  r  e  e  3f 2 X e,i  d  oe, i 5Z -k.v  v  k2  X  For f  3  being Maxwellian,  a  n  X-^  d  X e  h  (1-33)  a  v  e  t  h  e  f o l l o w i n g approximate forms  w h i c h w i l l be used throughout t h e c a l c u l a t i o n s :  for  — » k  v  —  tr  to « 7~ k  ve  e  A  A  to .^ Tv. 7 T » k l v  Xe  =  —  —  9  o)2  1k 2? X ^„ 29 (! + I e) De„ _ P Vx= ~ — o x to =  (1-34)  1  =  v  to k «  X~ e  a/  A  i  x  2  ±  = ksfr  ( 1  •+  I  ) 1  Di Here, w i t h v ^ << v , 1^ g  &  are the imaginary  p a r t s of t h e s u s c e p t i b i l i t i e s .  Note t h a t waves w i t h l a r g e k ( s h o r t wavelength) a r e s t r o n g l y damped, waves w i t h s m a l l k ( l o n g w a v e l e n g t h s ) a r e weakly damped.  15.  1.4  Specialization for stimulated backscatterlng  Consider  the case where an i n c i d e n t e l e c t r o m a g n e t i c  plasma wave and a s c a t t e r e d e l e c t r o m a g n e t i c reasonably  underdense plasma (co >> w ) 2  propagate a c c o r d i n g dominate.  For the case of a  the e l e c t r o m a g n e t i c  2  t o D « 0, t h e r e f o r e the k x V  At moderate i n c i d e n t powers E  ( g e n e r a t i o n of e l e c t r o m a g n e t i c 0) + w^)  wave.  wave decays i n t o a  2 q  ,  q  terms i n (1-30) w i l l  p r e d o m i n a n t l y downconversion  s i d e b a n d modes a t in - a  w i l l o c c u r , so t h a t the D  +  wave w i l l  term can be n e g l e c t e d  r a t h e r than s i n c e i t i s non  resonant. T h i s reduces (1-30) t o  The R.H.S. of t h i s e q u a t i o n  s h a l l now  be s i m p l i f i e d u s i n g p h y s i c a l  arguments. For underdense plasmas, the d i s p e r s i o n r e l a t i o n f o r the l i g h t and waves show t h a t - OJ < < O) and u)_, hence |k | a> |lc_| . q  Q  plasma  |k| however need  by no means be s m a l l and because the c o u p l i n g c o e f f i c i e n t i n (1-35) i s proportional to k , 2  at small  the i n s t a b i l i t y w i l l o c c u r a t l a r g e r a t h e r than  k.  These c o n s i d e r a t i o n s l e a d t o the f o l l o w i n g p o s s i b i l i t i e s t o a r r a n g e k , It o  and Ic:  16.  For a l l cases t h e diagram shows t h a t  |k |»2|k |cos 0 which i s as Q  approximate as |k_| » | k | and means t h a t t h e i n s t a b i l i t y w i l l predomQ  i n a n t l y o c c u r a t k_«*. -k- > t h a t i s t h e e l e c t r o m a g n e t i c 0  ->  co w i l l be b a c k s c a t t e r e d -  and k w i l l be about 2k . o  d e n s i t y f l u c t u a t i o n w i l l propagate p a r a l l e l vector.  |k  Therefore, \t  x v | o'  x v | — o j-—2  s i d e b a n d mode a t  T h i s means t h a t t h e  t o t h e i n c i d e n t l i g h t wave  2  can be w r i t t e n as  2  2  • 2  O w i t h <f> the a n g l e between k and V  b e i n g near 90 .  q  We now t r y t o s i m p l i f y D_, a l s o u s i n g p h y s i c a l arguments.  Introducing  damping f o r t h e l i g h t wave means t h a t D  = k c 2  2  - co  + co  2  -  2  -  P  i s complex because co = co + co * • o -  where co i s now w r i t t e n as co + i T . o o o Using k c o 2  2  - o o + c o = 0, t h e e x p r e s s i o n o p 2  2  r  ,2  D  = -  2  2co (co + o 2co  k'k c — co  for D  reduces t o  + .1 T ) o  I n c l u d i n g a l l t h e s e a p p r o x i m a t i o n s i n (1-35), one o b t a i n s i i 1 , 1 X„ l + X, +  e  1  k v sin d> o .2.2 t^Tc o / , k c o 2co (co + -= o 2co co 2  "  2  2  2  z  z  , .„ . + ir ) o  U s i n g t h e d i s p e r s i o n r e l a t i o n s f o r t h e i n c i d e n t and t h e s c a t t e r e d wave t o g e t h e r w i t h t h e a p p r o x i m a t i o n s (to (k  2  o 2  o  - co ) -  «*  2to (co — co ) o o -  - k ) -  »  -2 k k  2  2  + k o  2  and  (1-36)  light  17.  It follows  that o  CO  o  o  o  -  =  CO  (1-37)  Aco  Aco i s t h e d i f f e r e n c e between 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 wave which has t o be e q u a l t o t h e f r e q u e n c y o f t h e plasma wave. The  dispersion r e l a t i o n therefore k v  t a k e s t h e f o l l o w i n g form:  sin <j>. o 2co (co-Aco + i f ) o o 2  2  2  (1-38)  I t s h o u l d be remembered t h a t , a c c o r d i n g t h i s dispersion r e l a t i o n describes  t o t h e a p p r o x i m a t i o n s made,  t h e decay o f an i n c i d e n t e l e c t r o -  magnetic wave i n t o a plasma wave ( i o n o r e l e c t r o n ) and a electromagnetic  backscattered  wave i n a plasma t h a t i s underdense enough so t h a t  D_, * 0. Three d i s t i n c t cases o f i n s t a b i l i t i e s e x i s t : (1)  The s c a t t e r i n g plasma wave i s l a r g e l y undamped and hence c l o s e t o an eigenmode.  I f t h e s c a t t e r i n g o c c u r s o f f e l e c t r o n waves, the  process i s c a l l e d "Stimulated  Raman S c a t t e r i n g " ; i f i t o c c u r s o f f  i o n waves, i t i s c a l l e d " S t i m u l a t e d henceforth abbreviated (2)  Brillouin  Scattering"  SBS.  I f e i t h e r mode i s s t r o n g l y damped, t h e p r o c e s s e s a r e c a l l e d " s c a t t e r i n g o f f r e s i s t i v e q u a s i modes".  (3)  F i n a l l y , t h e r e i s a more e x o t i c form o f t h i s type o f i n s t a b i l i t y 14 w h i c h o c c u r s a t t o o h i g h powers t o c o n c e r n us any f u r t h e r . i s termed " s c a t t e r i n g o f f r e a c t i v e q u a s i modes".  I t r e f e r s to the  case where t h e f r e q u e n c y s h i f t <^-co_ i s l a r g e r t h a n t h e e i g e n o  f r e q u e n c y o f t h e plasma o s c i l l a t i o n .  This  As t h e Landau damping of the plasma/wave depends c r i t i c a l l y on the parameter kA.^, w i t h A  Q  b e i n g t h e Debye s h i e l d i n g d i s t a n c e , t h e d i s t i n c -  t i o n between the f i r s t two cases w i l l be f o r m u l a t e d m a t h e m a t i c a l l y by kX  < 1 o r kA  >> 1 r e s p e c t i v e l y .  19. 1.5  Stimulated B r i l l o u i n Scattering  As s t i m u l a t e d s c a t t e r i n g o f f i o n modes was observed i n the experiment d e s c r i b e d l a t e r , t h i s case s h a l l now b e " t r e a t e d i n some d e t a i l . F i r s t , c o n s i d e r the case where t h e i o n wave i s o n l y w e a k l y damped. Then, t h e s u s c e p t i b i l i t i e s  can be w r i t t e n as ( s e e 1-34) CO .  1 D  l k A ( u ) - u T . ) + co = = P w - c po i . 2  1  hence, .  1  2  2  2  2  D  h -—; 1 + X-l  Xe  2  1  9  2  2  co . k A 2  CO  2  with  -  co^ =  2^!vL  l+k x 2 2  co. -> co. - 2 i r co. 1 1 a I 2  a n  2  —  CO  .  2  pi  d i n c l u d i n g weak Landau damping, e.g.  k v sin (i>(to - co . ) ° ( 2 , 2) o D 2  (  U  - .  2  U  2  (1-38) can be w r i t t e n a s :  2  2  2  + 21 T ,.H. - Aco + i r ) a  Q  =  2  2  2  2  P  2  Thereby Aco i s , a c c o r d i n g t o i t s d e f i n i t i o n ,  1+  (1-39)  1  k  about e q u a l t o U K .  I n order  to f i n d r e g i o n s o f i n s t a b i l i t y , one s e t s co = co^ + iy> m u l t i p l i e s out t h e L.H.S., and s e p a r a t e s r e a l and i m a g i n a r y  parts.  The r e a l p a r t d e s c r i b e s  the a c t u a l d i s p e r s i o n o f t h e waves and the i m a g i n a r y  part, i f negative,  the damping; i f p o s i t i v e , thew growth '-.of t h e -longwave as na f u n c t i o n o f time. S e t t i n g Y = 0 means t o a s k f o r t h e c o n d i t i o n s under w h i c h t h e wave n e i t h e r grows n o r decays w i t h time w h i c h d e s c r i b e s t h e t h r e s h o l d f o r t h e  20.  instability.  The r e s u l t f o r t h e g r o w t h r a t e y i s k v (sin <j>)to .. 2  Y  r o + ra -  = " j  J V  2  2  2  (r o - ra) + c—o co.(l ° . .+ k.A. )^ 2  :  z  o i  Note t h a t the damping r a t e s r ,  2  z  (1-40)  2  D  a r e p a s s i v e plasma p a r a m e t e r s .  d r i v i n g term t h a t d e t e r m i n e s when t h r e s h o l d i s o b t a i n e d  The  and how l a r g e  the g r o w t h r a t e a t t h r e s h o l d w i l l be i s k v co . sin cf> o pi co u).(l + k A ) o l D 2  2  2  2  2  2  When t h i s term i n c r e a s e s  ( e . g . w i t h i n c r e a s i n g i n p u t power) t h e v a l u e  o f t h e r o o t i n c r e a s e s u n t i l i t i s l a r g e r t h a n t h e sum o f t h e two damping r a t e s , a t w h i c h p o i n t t h e i n s t a b i l i t y The t h r e s h o l d c o n d i t i o n f o r weak damping ( k A  grows.  2  (* = 90") i s c a l c u l a t e d from k V C0 2  4r r o a  =  .  2  ° co co. p  O  2 Q  << 1) and b a c k s c a t t e r i n g  (1-40):  2  sin *  l  (1-41)  2  1  Note t h a t the t h r e s h o l d d e c r e a s e s as the plasma d e n s i t y d e c r e a s e s and the temperature i n c r e a s e s and t h a t i t goes t o z e r o w i t h the damping o f e i t h e r t!he l i g h t wave o r t h e i o n a c o u s t i c wave g o i n g t o z e r o . To f i n d the g r o w t h r a t e j u s t above t h r e s h o l d f o r r » a r o o t i n t o a T a y l o r s e r i e s around T t o g e t cl k V c o _^ sin cf> 2  2  2  T  we expand the o  2  Q  Y  at  threshold  see a l s o page 29  =  4co co. ( l + k 2 A ) r o l D a 2  (1-^2)  21-. Large g r o w t h r a t e s a r e o b t a i n e d when the d r i v i n g term becomes dominant as compared to the damping terms. Then the g r o w t h r a t e i s ,  v T  max  for k X z  Next we  2  «1  z D  k v  i  =  v/co•  co . sin<f>  °_E± co.  V  (1 + k A z  o i  v  and <j>  D  2  ,  k v  •>  v  I )  \/o)  V  ¥  4 3 )  o i  2  =  _  U  c o n s i d e r the case where the i o n wave i s h e a v i l y damped ( k A  1 + I.  ^ 7  ;  = T. i t i s L . I Dx  x  ±  D  2  >  1).  1-34) .  ^ d 7  =  = Z L  2  e  ( I  co.  90 .  1  for T  P1  w  T h i s means f o r t h e s u s c e p t i b i l i t i e s (see  X E  co .  o  2  De  , I:'.. i s the i m a g i n a r y p a r t of Yl ° l r  I n s e r t i n g t h i s i n t o e q u a t i o n (1-38) , s e t t i n g co = U K + i y b u t making no f u r t h e r assumptions  on k X ^ 2  <;< or >> 1 we o b t a i n  2  v sin cJ) ° . —(Zk2A 2co A „ ^ D o D 2  [to. l  Aw + i ( T  + Y)](Zk A D 2  o  2  J  + I . + 1 + Z) l  =  s o l v i n g the r e a l p a r t of t h i s e q u a t i o n f o r to  2  2  + 1. + 1 ) l  (1-44)  and assuming 1\ i s s m a l l one  obtains v sin cf .Zk A„ . + 1 o D 7 — 7 — * „, ')\—2 1 1—7~^~ 2co Zk^A + 1 + Z o D D 2  . . co = flco +  2  2  2  1  Z  f o r s t r o n g Landau damping ( k A ^ 2  2  >>  1) t h i s reduced  to  v sin <() co = Aw + ° , 2co A ^ o D 2  2  (1-45)  2  To see what t h i s e x p r e s s i o n means p h y s i c a l l y , we a p p l y the arguments p r e s e n t e d on p. 16,17  i n r e v e r s e and f i n d t h a t the second  (1-45) can a p p r o x i m a t e l y be w r i t t e n as  term of eq.  ,22.  V  o  2  V  2 ^ 7  ~  o D  ( w  o  o  1  2  k2T7  "  (  D  Hence, t h i s term r e p r e s e n t s  I  "  4  6  )  a f r e q u e n c y i m p r i n t e d by t h e l a s e r on t h e  plasma t h a t depends on t h e i n c i d e n t l a s e r power and t h e amount o f Landau damping. S o l v i n g the imaginary  p a r t :of (1-44) f o r t h e g r o w t h r a t e y one o b t a i n s  v sin <j> = — p + -5 — o 2co A „ o D 2  y Y  i where I = -=- I . i i  2  — — (Zk^X * + 1 + Z ) D  2  T h i s e x p r e s s i o n has v a r i o u s l i m i t s f o r k A 2  2  2  << 1, »  For strong'Landau -damping o f t h e i o n wave ( k  2  (1-47)  1 or« 1  ^ « 1) and Z = 2 t h e 2  g r o w t h r a t e reduces t o : , v sin <|> y = - r 4 °i2 o 25 co A ^ o D 2  2  1  ( I _ 4 8 )  and t h e t h r e s h o l d becomes  v c  Z  2  25roco oA D 2  "  Ic  (1-49)  2  one can s e e . t h a t J t h i s i n s t a b i l i t y d e r i v e s i t s e x i s t e n c e from t h e magnitude ;  of t h e i m a g i n a r y -part o f t h e i o n i c s u s c e p t i b i l i t y .  T h i s term b e i n g  s m a l l means t h a t t h e t h r e s h o l d i s h i g h , t h e g r o w t h r a t e s m a l l : Note that f o r k A ^ 2  2  >> 1 t h e r e s u l t f o r t h r e s h o l d and g r o w t h r a t e depends  much s t r o n g e r on t h e magnitude o f k A ^ . 2  2  23.  co - k diagram  1.6  The  The  s e c t i o n on s t i m u l a t e d B r i l l o u i n s c a t t e r i n g s h a l l be concluded  further i n t e r p r e t i n g stimulated backscattering diagram.  on the s o - c a l l e d  I n the c o - k diagram co and k are the axes of a  coordinate  system and  f o r l i g h t - , i o n - and  Figure  by  co-k  Carthesian  the c u r v e s r e p r e s e n t the d i s p e r s i o n r e l a t i o n s e l e c t r o n waves.  (1-1):  c o - k diagram. Curves are d i s p e r s i o n r e l a t i o n s f o r (a) l i g h t , (b) e l e c t r o n , and (c) i o n waves. Shown i s the decay of a l i g h t wave i n t o an i o n a c o u s t i c wave and a s c a t t e r e d l i g h t wave.  Note t h a t because v. << v << c, the d i s p e r s i o n c u r v e s f o r e l e c t r o n 13. G i o n waves are b a s i c a l l y h o r i z o n t a l l i n e s compared t o the p a r a b o l a representing  the l i g h t w a v e  dispersion for small  k.  and  \  24.  V e c t o r s e n d i n g on the l i g h t d i s p e r s i o n curve r e p r e s e n t  l i g h t waves.and  those e n d i n g on the e l e c t r o n wave d i s p e r s i o n curve r e p r e s e n t e l e c t r o n waves, e t c .  Therefore,  for a parametric  i t s t o - k v e c t o r s have t o add  decay p r o c e s s  t o be p o s s i b l e ,  up.  C o n s i d e r , as an example, the decay o f a l i g h t wave i n t o an i o n a c o u s t i c wave and a n o t h e r l i g h t wave as shown i n F i g . ( 1 - 1 ) . The  p r o j e c t i o n s on the frequency  energy: co^ = co + co_.  a x i s d e s c r i b e the c o n s e r v a t i o n  Because the frequency  (co) i s s m a l l compared t o the frequency frequency  of  of the i o n a c o u s t i c wave  of the l i g h t wave (^ )» Q  the  of the s c a t t e r e d l i g h t wave ( W ) w i l l be o n l y s l i g h t l y l e s s q  than the frequency  o f . t h e i n c i d e n t l i g h t wave.  of B r i l l o u i n s c a t t e r i n g .  This i s a general  feature  From the diagram, i t a l s o f o l l o w s t h a t the wave  v e c t o r o f the s c a t t e r e d l i g h t wave w i l l be -k , w i t h k b e i n g the wave ° o o v e c t o r o f the i n c i d e n t l i g h t wave. a c o u s t i c wave, w i l l be k « ~ ^  k Q  (  s e e  Hence, k, the wave v e c t o r of the i o n P«16  ).  Furthermore the co - k diagram shows t h a t s t i m u l a t e d B r i l l o u i n s c a t t e r i n g can o n l y take p l a c e i n underdense plasmas. For the decay of e.g. t h a t the p r o c e s s  a l i g h t wave i n t o two - e l e c t r o n w a v e s ^ , i t i s o b v i o u s  can o n l y take p l a c e where cb £" 2co^ whereas the decay o f Q  a l i g h t w a v e i n an e l e c t r o n and an i o n a c o u s t i c wave"''"' can o n l y occur a t CO I ..CO . o p These a r e j u s t some p o i n t s w h i c h by no means exhaust the u s e f u l n e s s o f *15 the diagram.  Q u e s t i o n s about p r o c e s s e s  l i k e cascading,  parametric  decay i n moving plasmas e t c . , can a l s o be answered by t h i s  simple  picture. The B r i l l o u i n s c a t t e r e d l i g h t wave i s i n t e n s e enough t o i t s e l f g i v e to a h i g h e r o r d e r B r i l l o u i n s c a t t e r e d l i g h t wave.  rise  25. 1.7 L i m i t a t i o n s o f t h e t h e o r e t i c a l model  The  t h e o r e t i c a l treatment o f t h e d e s c r i b e d p a r a m e t r i c i n s t a b i l i t y  shall  be concluded by p o i n t i n g o u t t h e l i m i t a t i o n s o f t h e model used and i t s relevance t o a c t u a l experiments. D e s p i t e t h e use o f M a x w e l l ' s and t h e V l a s o v e q u a t i o n s w h i c h a r e , f o r wave phenomena, q u i t e g e n e r a l , t h e p r e s e n t e d d e s c r i p t i o n i s o f v e r y  limited  validity. F i r s t l y , o n l y i n f i n i t e , homogeneous plasmas were t r e a t e d ; s e c o n d l y , a l i n e a r i s e d > t h e o r y o n l y can d e s c r i b e t h e onset o f i n s t a b i l i t i e s ; and t h i r d l y , even i n such s i m p l i f i e d cases many a p p r o x i m a t i o n s  have t o be made i n  order t o a r r i v e a t a n a l y t i c a l l y s o l v a b l e equations.  The l i n e a r  theory  f o r f i n i t e , inhomogeneous plasmas i s c o n s i d e r a b l y more complex and can 13 14 be t r e a t e d a n a l y t i c a l l y o n l y f o r v e r y s i m p l e d e n s i t y p r o f i l e s .  '  A p r e s e n t a t i o n o f t h a t t h e o r y i s c o n s i d e r e d w e l l o u t s i d e t h e scope considered here.  However, a t h r e s h o l d e x p r e s s i o n f o r s t i m u l a t e d  B r i l l o u i n s c a t t e r i n g from t h i s t h e o r y w i l l be used l a t e r ; i t s p h y s i c a l i n t e r p r e t a t i o n i s g i v e n on p. 29 .  A complete t h e o r y d e s c r i b i n g t h e  o n s e t , growth and e v e n t u a l s a t u r a t i o n o f p a r a m e t r i c i n s t a b i l i t i e s does n o t exist.  A t p r e s e n t , p r e d i c t i o n s t h a t i n v o l v e more c o m p l i c a t e d and d e t a i l e d  models a r e made w i t h t h e a i d o f computer s i m u l a t i o n s . ' ^ ' ^ " ' ^ ' ' 2  T h e r e f o r e , a l l t h a t can be expected  of the simple theory presented  here,  i s t o g i v e an i n i t i a l i n s i g h t i n t o t h e p h y s i c s o f p a r a m e t r i c decay i n plasmas and produce n u m e r i c a l v a l u e s t h a t p r o v i d e o r d e r o f magnitude e s t i m a t e s f o r t h r e s h o l d s and g r o w t h r a t e s .  26.  1.8 N u m e r i c a l v a l u e s f o r t h r e s h o l d and g r o w t h r a t e of s t i m u l a t e d  Brillouin  s c a t t e r i n g i n homogeneous and inhbmogeneous plasmas I n o r d e r t o e v a l u a t e the p r e v i o u s r e s u l t s n u m e r i c a l l y , the f o l l o w i n g of  f o r m u l a s i s handy:  Here, i n t e n s i t i e s a r e i n ^ 2 ~ W  » temperatures i n eV.  S  As t h e cgs  system  i s used, the dimensions of the r e s u l t s w i l l be i n cm, s e c , e s u , e t c .  (1)  quiver v e l o c i t y V intensity I ( v  (2)  o  q  )  s e c  °^  e l e c t r o n i n an e l e c t r i c f i e l d  a n  S  wavelength  265 / i  =  (cm)  740,/V n  :  n i n cm"  3  ,  T i n eV  plasma f r e q u e n c y (~~j") co  (4)  =  cm (  » ) f o r C0„ l a s e r cm^ z  W a t  Debye l e n g t h A^ A,, D  (3)  =  pe  5.6 x 10 * Vn~  ;  1  n i n cm  c o l l i s i o n f r e q u e n c y between e l e c t r o n s v v  =  - ^ V 5-7-. TO  2.8 Z.tf x 11U0 ~  J5  ee  m  ;  -3  (—^  & e  n.incm  ) , T i n eV  3  3/2  T (5)  c o l l i s i o n a l damping of a l i g h t wave i n a plasma r o T  (6)  o  =  1.4 x 10  2  -A—  2 k  T  1a  =  1a  6.9 x 1 0  /f~~ e  5  e l e c t r o n t h e r m a l speed v v  = e  6 x 10  7  3/2  ;  nincm  (—^-) sec.  , T i n eV  - 3  '  cm (— ) . sec  i o n a c o u s t i c speed v. v.  (7)  list  JT~  e  (  ; Tv.lneV  cm ) sec :  T i n eV  e  i n c i d e n t l a s e r l i g h t f r e q u e n c y i s t h a t of  laser  light  of  (8)  e l e c t r i c a l c o n d u c t i v i t y a(esu) T  a  =  1.7. x 1 0  The power of the CO^  3/2  ( f o r He,  1 3  l a s e r was  ^ 250 MW,  Z = 2),  TineV  f o c u s s e d t o about 1 mm . 2  Hence  the q u i v e r v e l o c i t y o f an e l e c t r o n i n t h i s f i e l d i s v  =  4.2  x 10  v -f-=  1-9  x  o  7 cm ^2sec  *  2  °  r  10-6  U s i n g the formulae p. 26 ,  the t h r e s h o l d s and g r o w t h r a t e s co.  the f o l l o w i n g e x p r e s s i o n s  reduce t o  2  ( v a l i d o n l y f o r —^r  <<  CO  1)  o A) S t i m u l a t e d s c a t t e r i n g o f f q u a s i r e s i s t i v e i o n modes Growthrate Y = - 1 . 4 x l 0 ~ Threshold  V  3/2  ' + 1.8 '  x 10 "  — T i  i — , „ -, -24 n L 13 T = L 6 x l O : " - \ l i + 2xlO" ^  29  o  •  A  n  +  2  x  v  x +-2;x  10  n  1 Q  B) S t i m u l a t e d s c a t t e r i n g o f f i o n modes Growthrate Threshold  Z-l  y  =  max  1.65  x 10  2  (T n) e  f o r a homogeneous plasma .  4  .3  M-S.  x  15 Threshold v  **  f o r an inhomogeneous plasma  2  o  =  , „ „„9 6.8 x 10-  T_  where L^, i s the s c a l e l e n g t h of temperature g r a d i e n t i n  - Note^that some. eV. * *  :  -  '."'  t h i s i s about the e l e c t r o n t h e r m a l speed i n a plasma of r  —-  -•-"'  =•  " ;  . '  „•  ""-'.„-'  ' I n .this e x p r e s s i o n , the Landau damping r a t e was t o the c o l l i s i o n a l damping r a t e .  •  *  ••'-*'  n e g l e c t e d compared  cm.  Numerical values  A)  s c a t t e r i n g o f f q u a s i r e s i s t i v e modes n  10  10  1 5  10  1 6  10  1 7  1 8  Y T . = 1 eV e T T  = 10 eV  e  = 100 eV  e  v  T T  1.8 x 1 0  9  1 0  1.7 x 1 0  1.6 x 1 0  8  1.8 x 1 0  9  1.7 x 1 0  1 x 10  7  1.6 x 1 0  8  1.8 x 1 0  1 1  1 0  9  4 x 10  1 1  1.4 x 1 0  1 1  1.7 x 1 0  1 0  2  T c T  1.8 x 1 0  e e e  10  10  1 5  = 1 eV  1.6 x 10  = 10 eV  5.5 x 1 0 "  = 100 eV  2.8 x 10  B)  10  1 6  1.6 x 10  9  1 0  1 0  l.OOx 10  8  5 x 10~ 1.8 x 10  9  1 8  1.6 x 10  7  5 x 10 1.6 x 10  9  10  1 7  6  5 x 10~  - 8  1.6 x 1 0 ~  8  7  7  s c a t t e r i n g o f f i o n modes v  n  10  10  1 5  10  1 6  10  1 7  1 8  Y T  = 1 eV  5.2 x 1 0  5  1.6 x 1 0  6  5.2 x 1 0  6  1.6 x 1 0  7  = 10 eV  1.6 x 1 0  6  5.2 x 1 0  s  1.6 x 1 0  7  5.2 x 1 0  7  = 100 eV  5.2 x 1 0  6  1.6 x 1 0  7  5.2 x 1 0  7  1.6 x 1 0  8  e T e T e t h r e s h o l d s f o r a homogeneous plasma n v c  2  2  10  10  1 5  T e = 1 eV  4.3 x 1 0 "  T e = 10 eV  1.4 x 1 0 "  T e = 100 eV  4.3 x 1 0 " ^  9  1 1  10  1 6  10  1 7  1 8  4.3^x 1 0 ~  7  4.3 x 1 0 "  5  4.3 x 1 0  1.4 x 1 0 "  9  1.4 x 1 0 ~  7  1.4 x 1 0 -  4.3 x 10"'  12  4.3 x 1 0 ~  1 0  4.3 x 1 0  - 3  5  _ 8  29.  B)  thresholds  f o r an inhomogeneous plasma L  = 1 mm  2\ n -2-  \  10  10  1 5  10  1 6  T = 1 eV  6.9 x 1 0 "  6  6.9 x 1 0 "  T = 10 eV  6.9 x 1 0 "  5  6.9 x 1 0  T = 100 eV  6.9 x 1 0  _tt  7  - 5  6.9 x 1 0 ~  5  10  1 7  ]  6.9 x 1 0 ~  8  6.9 x 1 0 "  9  6.9 x 1 0 ~  7  6.9 x 1 0 ~  8  6.9 x 1 0 "  6  6.9 x 1 0 "  7  I t may be s u r p r i s i n g t o see t h a t the t h r e s h o l d f o r a homogeneous plasma i n c r e a s e s w i t h i n c r e a s i n g d e n s i t y , however, t h e t h r e s h o l d f o r an inhomogeneous plasma d e c r e a s e s w i t h i n c r e a s i n g d e n s i t y . The r e a s o n i s t h a t i n d e r i v i n g the t h r e s h o l d e x p r e s s i o n f o r a  homogeneous  plasma the assumed model was t h a t d e n s i t y f l u c t u a t i o n s have t o be induced against v  the r a n d o m i z i n g e f f e c t of damping (see p.4  ).  Hence,  2  the t h r e s h o l d  o -^T r , i s p r o p o r t i o n a l t o the p r o d u c t o f the damping o r a t e s f o r i o n and l i g h t wave. I n d e r i v i n g the t h r e s h o l d e x p r e s s i o n 2  for  an  inhomogeneous p l a s m a " ^ ' h o w e v e r , the assumed model i s  t h a t the i n d u c e d d e n s i t y waves t r a v e l out o f the r e g i o n where t h e wave v e c t o r matching c o n d i t i o n f o r s t i m u l a t e d s c a t t e r i n g i s s a t i s f i e d and t h a t compared t o t h i s i n s t a b i l i t y s u p p r e s s i n g e f f e c t , damping i s Hence t h e t h r e s h o l d d e r i v e d f o r t h a t case depends on Y~, T the i n v e r s e temperature s c a l e l e n g t h o f the plasma.  negligible.  L  30. CHAPTER 2 Experimental  i n v e s t i g a t i o n o f t h e b a c k s c a t t e r e d and  t r a n s m i t t e d CO2 l a s e r  light  2.1 I n t r o d u c t i o n The purpose o f t h e CO2 l a s e r l i g h t s c a t t e r i n g e x p e r i m e n t s was t o i n v e s t i g a t e w h i c h i n s t a b i l i t i e s c o u l d be d e t e c t e d w i t h t h e CO2 l a s e r power a v a i l a b l e and t h e plasma parameters g i v e n by t h e Z-pinch. As the t h e o r y shows, s t i m u l a t e d s c a t t e r i n g s h o u l d m a n i f e s t i t s e l f i n l a r g e amounts o f b a c k s c a t t e r e d  light.  We t h e r e f o r e measured t h e amount o f b a c k s c a t t e r e d CO2 l a s e r l i g h t under d i f f e r e n t plasma c o n d i t i o n s (e.g. as a f u n c t i o n o f t h e c o l l a p s e phase o f the p i n c h ) . As t h e s p e c t r a l d e c o m p o s i t i o n  o f t h e b a c k s c a t t e r e d CO2 l a s e r l i g h t  will  show w h i c h s t i m u l a t e d b a c k s c a t t e r i n g p r o c e s s t a k e s p l a c e , we searched t h e b a c k s c a t t e r e d l i g h t f o r s i g n a l s a t t h e f o l l o w i n g f r e q u e n c i e s (CO b e i n g q  the f r e q u e n c y  o f t h e i n c i d e n t CO2 l a s e r l i g h t ) :  near C O , t o d e t e c t s t i m u l a t e d B r i l l o u i n s c a t t e r i n g and p o s s i b l y q  ,.15 cascading 3 -t 1 14,15,20,23 near T CO , t o d e t e c t two plasmon decay 2 o near  c o ^ , t o d e t e c t s t i m u l a t e d Raman s c a t t e r i n g a t  the c r i t i c a l  . 14,15,22 density The  t r a n s m i t t e d o r forward s c a t t e r e d l i g h t was searched n e a r C O t o l o o k q  for - t h e normal t r a n s m i s s i o n o f CO2 l a s e r l i g h t through an underdense plasma . *14,15,24,25 - fllamentation ,. • *15 - cascading see f o o t n o t e p. 24  A d d i t i o n a l l y , the a n g u l a r dependence o f the CC^ due t o s t i m u l a t e d B r i l l o u i n  s c a t t e r i n g was  laser l i g h t backscattered  i n v e s t i g a t e d as f a r as  the  setup a l l o w e d . The r e s u l t s can be summarized as  follows:  The o n l y p a r a m e t r i c i n s t a b i l i t y t h a t was was  stimulated B r i l l o u i n  scattering.  Due  detected w i t h absolute c e r t a i n t y t o the low t h r e s h o l d and  high  g r o w t h r a t e t h i s i n s t a b i l i t y i s a l s o of g r e a t i m p o r t a n c e f o r l a s e r f u s i o n 20 experiments. Filairiehtation detected.  was  not p r e s e n t t o a degree t h a t i t c o u l d have been  T h i s i s i n agreement w i t h s i m p l e t h e o r e t i c a l models about 24  this instability. because the  25 '  No o t h e r i n s t a b i l i t y was  found, most c e r t a i n l y  power a v a i l a b l e d i d not a l l o w i t to exceed any  other  thresholds. The a n g u l a r dependence of the b a c k s c a t t e r e d  l a s e r l i g h t shows a  somewhat s u r p r i s i n g r e s u l t . f o r w h i c h a p l a u s i b l e e x p l a n a t i o n w i l l  be  presented.  F i l a m e n t a t i o n i s the c e r a t i o n o f low d e n s i t y c h a n n e l s by the l a s e r l i g h t a l o n g i t s d i r e c t i o n of p r o p a g a t i o n .  32.  2.2 The Z - p i n c h plasma, measurements o f r a d i u s , t e m p e r a t u r e and d e n s i t y and t h e CO^ l a s e r used f o r t h e l a s e r - p l a s m a  interaction studies.  A d e t a i l e d p r e s e n t a t i o n o f t h e d e s i g n parameters and t h e d i s c h a r g e o f t h e Z - p i n c h i s g i v e n i n Ref. 26. intended  bank  The d e s c r i p t i o n g i v e n h e r e i s o n l y  t o p r o v i d e t h e n e c e s s a r y background f o r t h e e x p e r i m e n t s d e s c r i b e d  subsequently. The Z - p i n c h c o n s i s t s o f a p y r e x g l a s s v e s s e l w i t h h o l l o w copper e l e c t r o d e s i n s e r t e d i n each end. 5.6 k j o f e l e c t r i c a l energy s t o r e d i n a 84 uF c a p a c i t o r bank a r e discharged  i n t o 1.2 T o r r He t o produce a p i n c h plasma which r e a c h e s  maximum c o m p r e s s i o n and temperature about 2 usee a f t e r t h e i n i t i a l breakdown. End on f r a m i n g photography w i t h a TRW image c o n v e r t e r camera gave t h e 26 f i r s t photographs o f the c o l l a p s i n g plasma.  . As t h i s geometry d i d n o t  a l l o w a d e t a i l e d o b s e r v a t i o n o f t h e phase o f maximum c o m p r e s s i o n , e.g. minimum r a d i u s , s i d e on s t r e a k photography was used t o s p a t i a l l y and t-  t e m p o r a l l y r e s o l v e t h i s f i n a l phase o f c o l l a p s e . '„ These measurements r e v e a l e d a minimum luminous r a d i u s o f the plasma o f 2 mm. The f i r s t measurements o f plasma t e m p e r a t u r e and d e n s i t y were done 26 s p e c t r o s c o p i c a l l y u s i n g t h e 4686$ l i n e o f He I I . .. F o r t h e means a v a i l a b l e a t the t i m e , t h e s e measurements y i e l d e d good e s t i m a t e s o f a 18 6 maximum d e n s i t y o f 8 x 10  —  and a maximum temperature o f 30 eV t o  40 eV.  For a c t u a l d i m e n s i o n s see s p e c i f i c a t i o n s a t end o f r e p o r t . A* see F i g . 5-2 t  see f o o t n o t e p. 33  33.  N e x t , a Ruby l a s e r Thomson s c a t t e r i n g system measurements. (OMA)  26  The  was  s e t up t o v e r i f y  attempt t o use an O p t i c a l M u l t i c h a n n e l  the  Analyser  **  t o r e c o r d the e l e c t r o n f e a t u r e o f the Thomson s c a t t e r e d spectrum  r e s u l t e d i n the development of a t e c h n i q u e of the OMA  without d i s t o r t i o n s .  that allowed  the f a s t g a t i n g  A d e s c r i p t i o n of t h i s t e c h n i q u e  and  i t s a p p l i c a t i o n to improved s p e c t r o s c o p i c a l d e n s i t y measurements i s presented  i n Chapter IV.  B e f o r e the s i g n a l - t o - b r e m s s t r a h l u n g electron feature  r a t i o i n the Thomson s c a t t e r e d  c o u l d be improved t o y i e l d a t r u l y  satisfactory  spectrum however, the o b s e r v a t i o n of the Thomson s c a t t e r e d i o n f e a t u r e permitted  the making o f v e r y good measurements of plasma temperature  and d e n s i t y . ^  These r e s u l t s a r e shown i n F i g . (2-3) and w i l l be used  throughout t h i s r e p o r t . The  CO2  l a s e r used i n the l a s e r - p l a s m a  i n t e r a c t i o n s t u d i e s was  Lumonix T600 module i n u n s t a b l e r e s o n a t o r c o n f i g u r a t i o n .  a  In t h i s  laser,  an e l e c t r i c a l d i s c h a r g e t r a n s v e r s e t o the o p t i c a l a x i s i n v e r t s the v i b r a t i o n a l l e v e l s of CO2 The  i n a He.Ne.CO2 i m  x t u r e  a t  atmospheric  l a r g e g a i n of the i n v e r t e d medium a l l o w s the use o f an  r e s o n a t o r f o r c o u p l i n g .out' the l a s e r l i g h t .  pressure.  unstable  The T600 module  employed a c o n f o c a l u n s t a b l e r e s o n a t o r c o n f i g u r a t i o n as shown on  the  f o l l o w i n g page.  see Ch. IV, F i g . see  4-1.  specifications  ***see Ch.  IV.  t  I am i n d e b t e d t o B r i a n H i l k o f o r l e t t i n g me use the r e s u l t s of h i s e x p e r i m e n t a l work.  34.  k  * 1 m  F i g u r e ( 2 - 1 ) : The u n s t a b l e r e s o n a t o r of the Lumonix T600 TEA C 0 laser. 2  B o t h m i r r o r s have F as a common f o c a l s p o t .  Due  t o t h i s arrangement, the  wave l e a v i n g the c a v i t y i s a p l a n e wave and the o u t p u t a p e r t u r e o f the l a s e r has an a n n u l a r shape as shown i n F i g . (2-2) below.  F i g u r e ( 2 - 2 ) : A n n u l a r output of the CO^ l a s e r due t o the use of an u n s t a b l e r e s o n a t o r c a v i t y .  The h e i g h t i s 10.5  cm,  the w i d t h 8 cm and e q u a l t o the s e p a r a t i o n of  the e l e c t r o d e s between which the d i s c h a r g e pumping the l a s e r t r a n s i t i o n takes p l a c e .  T h i s o u t p u t a p e r t u r e shape a l l o w e d the measurements which  are d e s c r i b e d i n 2.6  and e v a l u a t e d i n  3.23.  CO,  35.  2.3 E x p e r i m e n t a l p r o v i s i o n s  B e f o r e the CC^ l a s e r c o u l d s u c c e s s f u l l y be f o c u s s e d i n t o t h e plasma, t h e p i n c h v e s s e l had t o be m o d i f i e d and new plasma p a r a m e t e r s , now changed by these m o d i f i c a t i o n s , had t o be measured. The s k e t c h below shows t h e p r i n c i p a l setup t o f o c u s t h e CC^ l a s e r  into  the plasma. Electrodes  CO2  i  in Salt lens  ^  Pinch vessel  I t i s obvious t h a t t h e l a s e r l i g h t had t o be p r o t e c t e d from the plasma t o a c t u a l l y be a b l e t o form a f o c a l spot i n t h e c e n t e r o f t h e v e s s e l . Otherwise d e f o c u s s i n g o f the l a s e r beam by the plasma would l i m i t t h e power f l u x o f the i n c i d e n t l i g h t t o t o o low v a l u e s . The problem was s o l v e d by u s i n g a q u a r t z f u n n e l as i n d i c a t e d i n t h e n e x t sketch. fr —  y  = O u a r t z funnel  Quartz must be used as g l a s s q u i c k l y s u f f e r s from a phenomenon  called  " c r a z i n g " which c o n s i s t s o f myriads o f v e r y f i n e c r a c k s , a r i s i n g from  * the temperature shock due t o absorbed UV r a d i a t i o n .  The f u n n e l must  be embedded i n s o f t e r m a t e r i a l s , e.g. n y l o n , o t h e r w i s e t h e m e c h a n i c a l shock o f t h e p i n c h i n g plasma w i l l d e s t r o y i t w i t h i n a v e r y few s h o t s . I am i n d e b t e d t o Ray  E l t o n o f N.R.L. f o r t h i s i n f o r m a t i o n .  36. I n o r d e r t o measure the t r a n s m i s s i o n of the CC^ f u n n e l has  t o be i n s t a l l e d a c c o r d i n g l y .  I t must be e x p e c t e d t h a t these  m o d i f i c a t i o n s change the plasma p a r a m e t e r s . d e n s i t y and  l a s e r l i g h t , a second  Therefore,  the plasma  temperature were measured a l s o w i t h b o t h f u n n e l s  The  time of maximum c o m p r e s s i o n , e.g.  no,  one  and  two  minimum r a d i u s was  f u n n e l s i n s t a l l e d , u s i n g s t r e a k and  installed.  measured w i t h  shadow photography.  These measurements were c a r r i e d out w i t h i n the program of B r i a n H i l k o ' s Ph. D. work, hence, d e t a i l e d comments and r e s u l t s w i l l appear i n h i s thesis. The  r e s u l t s , as f a r as they are r e l e v a n t f o r the e x p e r i m e n t s t o  d e s c r i b e d , are shown i n the F i g . (2-3)  overleaf.  The  be  top t r a c e i n each  p i c t u r e shows the d e n s i t y ; the bottom t r a c e shows the temperature of p i n c h plasma as a f u n c t i o n of time. dl  Time t = 0 i s chosen as the  the  time  **  when -jT^- = 0  ,1  being  the t o t a l c u r r e n t i n the p i n c h as measured w i t h  a  26 Rogowski c o i l . experimental  The ,top and bottom p i c t u r e (no and  data obtained  funnel)  a r e a i n d i c a t e s an e s t i m a t e d  error.  The  time axes of a l l t h r e e  the t r u e time l a g s from p i c t u r e t o p i c t u r e .  The  the u n c e r t a i n t y  i s i n f e r r e d from the o t h e r two.  l i n e i n the bottom p i c t u r e , see s e c t i o n The  are  d e n s i t y can be deduced from the e x p e r i m e n t a l  The m i d d l e p i c t u r e (one  represent  funnels)  through i o n f e a t u r e Thomson s c a t t e r i n g .  e r r o r b a r s i n d i c a t e the s p r e a d of i n d i v i d u a l d a t a and which temperature and  two  with  results.  The  shaded  pictures  About the dashed  3.1.  a d d i t i o n a l d a t a p o i n t s i n the d e n s i t y t r a c e of the top p i c t u r e a r e  measurements from the S t a r k b r o a d e n i n g of the 4686$ l i n e of He described  in  I,  4.3.  see f o o t n o t e p.  33.  ** T h i s time r e f e r e n c e w i l l be used e x c l u s i v e l y throughout the  report.  37.  14  1  200  100  1  1  100  0  •  1  0  100  i  r —  100  200  i  1  200  300  F i g u r e (2-3)  <  1  300  400  <  1  400  1  1  t[nsj  38.  The j i t t e r o f t h e p i n c h d i s c h a r g e was reduced from about 100 nsec t o f r e q u e n t l y l e s s than 10 nsec by f i r i n g a p r e i o n i z a t i o n d i s c h a r g e i n t h e v e s s e l p r i o r t o t h e main p i n c h d i s c h a r g e .  The a c t u a l c i r c u i t m o d i f i c a -  t i o n o f the Z-pinch d i s c h a r g e bank i s d e s c r i b e d i n t h e appendix.  This  r e d u c t i o n i n j i t t e r n a t u r a l l y was o f g r e a t importance i n t h e s p e c t r a l shot t o shot s c a n n i n g o f t h e b a c k s c a t t e r e d ( X ^ l a s e r l i g h t ( s e e 2 . 5 ) . An e x p e n s i v e  problem ( i n terms o f money) f i n a l l y a r i s e s due t o t h e f a c t  t h a t t h e plasma as i t p i n c h e s i s n o t c o n f i n e d a x i a l l y . t h e r e f o r e , i s e j e c t e d w i t h h i g h speed through towards t h e s a l t l e n s sufficient  Part of i t ,  t h e h o l e i n t h e cathode  ( s e e e.g. F i g . 2 . 5 ) . The r e s u l t i n g impact i s  t o i n f l i c t v i s i b l e mechanical  damage p a r t i c u l a r l y  c e n t r a l r e g i o n o f t h e s a l t l e n s a f t e r 10 s h o t s .  i n the  The problem was s o l v e d  p a r t i a l l y by p l a c i n g an o b s t a c l e i n t h e plasma beam w h i c h i s s m a l l enough t o n o t h i n d e r t h e incoming  C0„ l a s e r l i g h t .  39.  2.4 S p e c t r a l l y I n t e g r a t e d  backscattered  CO^ l a s e r l i g h t as a f u n c t i o n  of p i n c h - t i m e .  The e x p e r i m e n t a l setup i s shown i n F i g . (2-5) on t h e n e x t page.  Light  s c a t t e r e d back from t h e plasma t r a v e l s back out through t h e s a l t  lens  and  onto t h e e x i t s a l t window o f t h e CG^ l a s e r .  T h i s window i s t i l t e d  and  due t o F r e s n e l r e f l e c t i o n , ^ 4% i s r e f l e c t e d towards t h e Gen Tech  energy meter. The r e s u l t i s shown i n F i g . (2-4) below.  The background, as l a t e r  e x p e r i m e n t s showed, a r i s e s from the f a c t t h a t t h e plasma i t s e l f  radiates  i n the i n f r a r e d .  I [% of incident energy] .6-  -200 Figure  -100  0  100  200  300  (2-4): S p e c t r a l l y integrated backscattered l a s e r l i g h t as a f u n c t i o n - o f .time. E r r o r bars a r e s t a n d a r d e r r o r s o f the mean.  A  see s p e c i f i c a t i o n s a t end o f r e p o r t .  t [ns]  F i g u r e ( 2 - 5 ) : S e t u p , f o r o b s e r v i n g the - s p e c t r a l l y - ; i n t e g r a t e d b a c k s c a t t e r e d CC^ l a s e r l i g h t ( s e c t i o n 2.4).  41.  2.5  S p e c t r a l l y I n t e g r a t e d t r a n s m i t t e d CO^ of  The  l a s e r l i g h t as a f u n c t i o n  pinch-time.  experimental  s e t u p i s shown i n F i g . (2-7)  on the n e x t page.  For  high  A  transmitted energies, a calorimeter transmitted energies of the plasma i t s e l f .  used as i n d i c a t e d .  For  lower  a background a g a i n a r i s e s from the i n f r a r e d e m i s s i o n These low e n e r g i e s were t h e r e f o r e measured w i t h  a g o l d doped germanium d e t e c t o r allowed  was  , which time r e s o l v e d the s i g n a l and  t o d i s c r i m i n a t e a g a i n s t the i n f r a r e d e m i s s i o n  from the plasma.  A t y p i c a l o s c i l l o s c o p e t r a c e i s shown below. 20 mV  100 ns  Figure (2-6): Transmitted C0 l a s e r l i g h t with i n f r a r e d e m i s s i o n from the p i n c h . Au Ge d e t e c t o r . 2  The  r e s u l t s of the experiment a r e shown i n F i g . (2-8)  and F i g . ( 2 - 9 ) .  * A p o l l o energy meter, see s p e c i f i c a t i o n s at end of r e p o r t ** see s p e c i f i c a t i o n s  thus  Figure (2-7):  Setup t o measure the t r a n s m i t t e d CC^ l i g h t ( s e c t i o n 2.5).  laser  Figure (2-8):  % o f t r a n s m i t t e d l i g h t as a f u n c t i o n o f t i m e , A p o l l o energy meter. E r r o r b a r s denote t h e s t a n d a r d e r r o r of the mean.  44.  I [% of incident energy]  0 ure  t[ns]  ( 2 - 9 ) : % o f t r a n s m i t t e d l i g h t as a f u n c t i o n o f t i m e , Au Ge d e t e c t o r . E r r o r b a r s denote t h e s t a n d a r d e r r o r o f t h e mean; squares a r e s i n g l e measurements.  45.  2.6  S p e c t r a l l y r e s o l v e d b a c k s c a t t e r e d CO^  l a s e r l i g h t a t p i n c h time  t = 0 ± 25 nsec and the a n g u l a r dependence of the b a c k s c a t t e r e d l i g h t . The e x p e r i m e n t a l arrangement i s shown i n F i g . (2-10) on the n e x t page. T h i s setup was  chosen f o r the f o l l o w i n g  reasons:  S p h e r i c a l m i r r o r s , i f used o f f a x i s , produce a s t i g m a t i s m . additionally  tilted  I f they are  -out o f the xy p l a n e , t h i s a s t i g m a t i s m appears  r o t a t e d . The. second p l a n e m i r r o r . i n F i g . ( 2 - 1 0 ) r e c e i v i n g ; t h e b a c k s c a t t e r e d l i g h t serves to e l i m i n a t e t h i s r o t a t i o n of astigmatism.  The r e s t of  * the o p t i c s i s s e t up t o match the f number o f the monochromator , t o keep the a s t i g m a t i s m a t a minimum by imaging as l i t t l e as p o s s i b l e o f f a x i s and, image as s t i g m a t i c a l l y as p o s s i b l e . F i n a l l y , t h e c h o i c e of components was v e r y  limited.  Another problem a r i s e s due t o the s u r f a c e i r r e g u l a r i t i e s l a s e r output window.  of the  CO2  As i t had t o be used t o r e f l e c t p a r t of the back-  s c a t t e r e d l i g h t towards the d e t e c t i o n o p t i c s , the s a g i t t a l focus a t the e n t r a n c e s l i t was not v e r y sharp and much i n t e n s i t y was  l o s t there.  To measure the a n g u l a r dependence o f the b a c k s c a t t e r e d l i g h t , two of  vmasks were used on the m i r r o r i n d i c a t e d i n F i g . (2-10) >. ..  types .•  -  A S m a l l Mask o n l y r e f l e c t e d t h a t l i g h t towards the d e t e c t i o n o p t i c s A*  t h a t came back through the i n n e r p a r t of the CO2  l a s e r output  annulus.  A B i g Mask o n l y r e f l e c t e d l i g h t towards the d e t e c t i o n o p t i c s t h a t came d i r e c t l y back through the o u t e r p a r t o f the  A  see s p e c i f i c a t i o n s a t end of r e p o r t AA  see  2.2  annulus.  45a.  Figure (2-10):  Setup t o s p e c t r a l l y decompose the. b a c k s c a t t e r e d C0„ l a s e r l i g h t ( s e c t i o n 2.6).  46.  S m a l l Mask  B i g Mask Figure (2-11):  The s p e c t r a l i n t e n s i t y  B a c k s c a t t e r e d l i g h t was t r a n s m i t t e d through the. unshaded a r e a s .  distribution  o f l i g h t s c a t t e r e d back through the  b i g mask and o f l i g h t s c a t t e r e d back through t h e s m a l l mask i s shown i n F i g s . (2-12) and ( 2 - 1 3 ) .  Karb  units)  A 10.580 1  2  3  4  F i g u r e (2-12)  5  6  7  8  9  .590  1  2  S p e c t r a l d i s t r i b u t i o n of l i g h t s c a t t e r e d back through t h e b i g mask. The dashed l i n e r e p r e s e n t s t h e u n s h i f t e d CC^ l a s e r l i n e . I t s t r u e w i d t h i s s m a l l compared t o t h e instrument p r o f i l e . 100 u s l i t s . E r r o r bars denote s t a n d a r d e r r o r o f t h e mean; t h e shaded a r e a shows t h e approximate n o i s e l e v e l . Time i s 0 ± 25 nsec.  47.  K a r b units)  Figure  (2-13):  Spectral d i s t r i b u t i o n of l i g h t scattered back t h r o u g h t h e s m a l l mask. The dashed l i n e at 10.583urepresents again the u n s h i f t e d CO2 l a s e r l i n e . I t s true width i s s m a l l compared t o t h e i n s t r u m e n t p r o f i l e d e t e r m i n e d by 100 u monochromator s l i t s . E r r o r b a r s denote s t a n d a r d e r r o r o f the mean. The shaded a r e a shows t h e approximate n o i s e l e v e l . The v e r t i c a l s c a l e i s 7.9 times t h a t of F i g . (2-12). Time i s 0 ± 2 5 n s e c .  F i g . (2-13) shows t h a t l i g h t s c a t t e r e d b a c k t h r o u g h t h e i n n e r p a r t o f the CO2 l a s e r o u t p u t annulus i s n o t o n l y s h i f t e d i n w a v e l e n g t h , b u t e x h i b i t s wings on b o t h s i d e s o f t h e c e n t r a l l i n e . f o r t h i s e f f e c t i s g i v e n i n 3.24.  A possible  explanation  Karb. units)  F i g u r e ( 2 - 1 4 ) : S p e c t r a l l y r e s o l v e d b a c k s c a t t e r e d CC^ l a s e r l i g h t , no mask used. L e f t , the u n s h i f t e d CCv, l a s e r l i n e a t 10.583 u. I t s w i d t h i s the i n s t r u m e n t w i d t h . S l i t s 130 u, e r r o r b a r s denote s t a n d a r d e r r o r of the mean. Shaded a r e a i n d i c a t e s the approximate n o i s e level. These d a t a were taken a t a much e a r l i e r date than those shown i n F i g . (2-12) and (2-13).  49.  CHAPTER 3  E v a l u a t i o n of the experimental  results  3.1 The t r a n s m i t t e d CO., l a s e r l i g h t Fig.  (3-1) shows t h e t r a n s m i t t e d and b a c k s c a t t e r e d  i n t e n s i t y as a  f u n c t i o n of d e n s i t y as i t can be condensed out of F i g . (2-3) and F i g s , (2-4)  and ( 2 - 9 ) .  I [%>of Backsc.  incident  energy]  Transm.  •11 0.5-  0.4}  0.3 +  0.2 + 0.1 f •  4  •  i  •  i  i  5 6 7 891 16  X10  i  •—i—.  3  4  i  > i—i—i—i—r-  5 6 7 891  X10  17  ~I  3  !—I—r-i—• |  4  x1018  i—|—i—I  5 6 7 89  n [cm ] 3  e  F i g u r e ( 3 - 1 ) : B a c k s c a t t e r e d (b) [one f u n n e l i n s t a l l e d ] and t r a n s m i t t e d (a) [two f u n n e l s i n s t a l l e d ] energy as a f u n c t i o n of d e n s i t y o f the plasma. V e r t i c a l e r r o r b a r s a r e e x p e r i m e n t a l e r r o r s from F i g s . (2-4) and ( 2 - 9 ) , h o r i z o n t a l e r r o r b a r s are due t o d e n s i t y e s t i m a t e s from F i g . ( 2 - 3 ) .  50.  T h i s measurement t i o n due The  w i l l now  be compared w i t h the t h e o r y o f l i g h t a b s o r p -  to inverse bremsstrahlung  two f u n n e l s i n s t a l l e d  (see a l s o p . 1  ).  i n the p i n c h v e s s e l i n o r d e r t o be a b l e t o  make these l i g h t t r a n s m i s s i o n measurements (see F i g . (2-7)) l e f t 2 of plasma between them. CO2  T h i s , t h e r e f o r e , i s the l e n g t h over which the  l a s e r l i g h t i s absorbed.  bremsstrahlung  cm  For the c l a s s i c a l t h e o r y o f i n v e r s e  t o be v a l i d , the f o l l o w i n g r e q u i r e m e n t s need t o be  satisfied. CO >> ujp, e.g.  (a)  q  the plasma must be q u i t e underdense which i s  fulfilled eE 2  (b)  c  2  V  < k T, e.g. *B  2mto 2 o  the q u i v e r energy of the e l e c t r o n i n the  of the l a s e r l i g h t must be s m a l l compared t o the energy due eE o * 9 2 2 < "ft (d o 2  (c)  field  kinetic  t o t h e r m a l m o t i o n which i s f u l f i l l e d as  well.  2  m a ]  7 •'  o  > i . e . the q u i v e r energy o f the e l e c t r o n i n die  f i e l d of the l a s e r l i g h t must be so s m a l l t h a t the energy o f photons c r e a t e d by b r e m s s t r a h l u n g  i s not comparable t o the  photon energy absorbed i n i n v e r s e b r e m s s t r a h l u n g . c a s e , the two  terms a r e comparable.  In  our  M o d i f i c a t i o n s i n the  c l a s s i c a l expression for inverse bremsstrahling e2  however, o n l y become n e c e s s a r y  if  V  2 >>-n  absorption 27 co > which 0  i s not the case f o r the experiment d e s c r i b e d . I n the R a y l e i g h Jeans l i m i t f o r P l a n c k ' s . r a d i a t i o n law,  the  l i n e a r a b s o r p t i o n c o e f f i c i e n t can be w r i t t e n as  K  B  " A •  ' ^ y , */2 3/6ii c co (mkT) ' o 2  GOVO).  (III-l)  51.  * F o r  %  =  U  C0  '  2  6  u  co  2  ~k^f~  »  Z  n  e  =  n  i  a n d  G ( T  '  "CO^  *  Z  '> 5  t h i s reduces t o n -JJ 2  K  =  7.06 x 10~  3k  (IH-2)  2  T Having £ cm o f plasma, the i n t e n s i t y I o f the t r a n s m i t t e d l i g h t as a f u n c t i o n o f £ i s g i v e n by =  e" *  (III-3)  < B  o I n comparing the experiment w i t h t h e t h e o r y however, t h e f o l l o w i n g problem a r i s e s : 1(1) As — — o  2 - C -fy £ / 3  2  T  =  e  , the r e l a t i v e e r r o r i n the i n t e n s i t y  ratio i s » i(A) I  n  2  KA) I  2  c —  "  T  -An n  £  3/2  (III-4)  3 AT 2 T  where  and 4Jr a r e the r e l a t i v e e r r o r s i n d e n s i t y and temperature so n T . t h a t f o r K £ > 1, a 10% e r r o r i n — o r 4ir l e a d s t o an o r d e r o f magnitude n T  e r r o r f o r the i n t e n s i t y  ratio.  Taken however i n the form K  B  =  - j  r  * ^ r o  1  ( I I I  "  one can see from t h e r e v e r s e argument o f ( I I I - 4 ) t h a t a measurement of  a l l o w s a good d e t e r m i n a t i o n o f K- and hence o f n /T a e 2  I  o one o f t h e q u a n t i t i e s i f the o t h e r q u a n t i t y i s known.  ^  2  , or  5 )  52.  A c c o r d i n g t o t h e d e r i v a t i o n of the above e x p r e s s i o n , T i s the temperature of the plasma b e f o r e t h e a c t u a l a b s o r p t i o n p r o c e s s h e a t s the plasma. I(£) The f o l l o w i n g t a b l e shows the v a l u e s of K computed from — and the o v a l u e s o f T computed from K.and t h e d e n s i t i e s g i v e n from F i g . ( 2 - 3 ) . FT  Electron density  101  K [L — ]  [ % ]  • cm  o  e cc  J  T  e  L  [eV] J  8 x  10  1 6  10.3  1.14  2.5  9 x  10  1 6  8.9  1.21  2.8  1 x  10  1 7  7.6  1.29  3.1  1.5 x  10  1 7  3.3  1.71  4.4  2 x  10  1 7  1.5  2.10  5.7  2.5 x  10  1 7  .75  2.45  6.9  3 x  10  1 7  .30  2.90  7.8  3.5 x  10  1 7  ^3.6  ^.05  These c a l c u l a t e d v a l u e s f o r T  ^9  a r e a l s o shown as the dashed l i n e i n e  F±g°. ( 2 - 3 ) , bottom p i c t u r e , where one can see t h a t they connect w e l l w i t h the t e m p e r a t u r e c u r v e measured by Thomson s c a t t e r i n g . I t must be kept i n mind t h a t n o t a l l t h e ( X ^ l a s e r l i g h t t h a t was n o t t r a n s m i t t e d need a c t u a l l y be absorbed by inverse- b r e m s s t r a h l u n g but can 28 w e l l be r e f r a c t e d o u t of the plasma. c o e f f i c i e n t K" and as a consequence B temperature  T h i s would lower t h e a b s o r p t i o n  increase the c a l c u l a t e d  electron  T.  E v i d e n c e f o r the c o m p l e x i t y o f t h e i n t e r a c t i o n volume i s shown i n t h e p i c t u r e on the n e x t page ( F i g . 3-2).  Many thanks t o B r i a n H i l k o f o r l e t t i n g me use t h i s  picture.  53.  CC>2 l a s e r  F i g u r e ( 3 - 2 ) : T h i s photograph i s a shadowgram done i n Ruby l a s e r l i g h t w i t h the image p l a n e *v» 1 cm away from the plasma, viewed s i d e on. The p i c t u r e i s m a g n i f i e d 3.4 t i m e s . The CC^ l a s e r i s i n c i d e n t from the r i g h t . The vacuum f o c a l spot i s i n the m i d d l e o f the p i c t u r e . The two f u n n e l s (see F i g . (2-7)) a r e j u s t o u t s i d e the p i c t u r e t o the l e f t and r i g h t ; t i m e i s - 30 n s e c *  I t i s e v i d e n t t h a t some plasma i s pushed away by the CO2  l a s e r , t h a t the  beam i s somewhat fanned out and bent away from i t s o r i g i n a l and  t h a t i t l o s e s c o n s i d e r a b l y i n i n t e n s i t y as i t p e n e t r a t e s  The  t r a n s m i t t e d C0^  l a s e r l i g h t shows no s h i f t o f f the ( X ^  direction the plasma  **  frequency  o f 10.583 y. The measured spectrum i s shown i n F i g . (3-3) The  on the f o l l o w i n g page.  r e s u l t , t o some e x t e n t , r u l e s out m o d u l a t i o n a l  r e s u l t i n g i n s i d e b a n d s i n the foreward  instabilities"^'"^  '^^'^  s c a t t e r e d l i g h t . At the g i v e n s p e c t r a l  The s h a r p l i g h t l i n e s i n d i c a t e the r e g i o n where the i n c i d e n t l i g h t has d e c r e a s e d the plasma d e n s i t y .  laser  The w e l l - d e f i n e d a n n u l a r shape o f the f o c a l r e g i o n i s a l s o i n d i c a t e d T h i s f a c t w i l l be o f g r e a t i m p o r t a n c e f o r arguments p r e s e n t e d i n S e c t i o n 3.24.  54.  I [arb. unit^  10.580  10590  F i g u r e ( 3 - 3 ) : The s p e c t r a l l y r e s o l v e d t r a n s m i t t e d CC^ l a s e r l i g h t a t p i n c h times < -20 n s e c . C i r c l e s i n d i c a t e the w a v e l e n g t h r e g i o n scanned. The shaded a r e a denotes the n o i s e l e v e l . The setup used was analogous t o t h e ones shown i n F i g . (2-7) and ( 2 - 1 0 ) .  r e s o l u t i o n t h e frequency  s h i f t r e s u l t i n g from such i n s t a b i l i t i e s  would have t o be c o m p a r a t i v e l y  l a r g e t o be o b s e r v e d .  The o c c u r r e n c e  o f f i l a m e n t a t i o n can p r i n c i p a l l y n o t be r u l e d o u t ; i t i s however, u n l i k e l y t o occur a s , f o r t h e r e l e v a n t d e n s i t i e s , homogeneous plasma t h r e s h o l d s a r e o n l y j u s t exceeded. e s t i m a t e s from o t h e r t h e o r i e s  T h i s i s i n good agreement w i t h  24 25 ' w h i c h p r e d i c t f o r o u r case a maximum  d e n s i t y d e p r e s s i o n due t o f i l a m e n t a t i o n o f — n Finally,  ^ 5%.  t h e r e i s , w i t h t h e setup used, no p o s s i b i l i t y o f d i s t i n g u i s h i n g  a minor f i l a m e n t a l e f f e c t from s i m p l e l i g h t t r a n s m i s s i o n through an underdense plasma ( s e e , however, p. 76 ) . These arguments l e a d t o t h e c o n c l u s i o n t h a t t h e d e c r e a s e i n t r a n s m i t t e d C0  2  l a s e r l i g h t i n t e n s i t y - i s due t o i n c r e a s i n g i n v e r s e  a b s o r p t i o n o f a plasma o f i n c r e a s i n g d e n s i t y .  compare w i t h F i g s . (2-12) - ( 2 - 1 4 ) .  bremsstrahlung  •55.  3.2 The b a c k s c a t t e r e d CO., l a s e r  light  The r e s u l t s o f the e x p e r i m e n t s c o n c e r n i n g t h e b a c k s c a t t e r e d CC^ l a s e r l i g h t w i l l be e v a l u a t e d i n t h e f o l l o w i n g 3.21  sections:  Enhancement of the b a c k s c a t t e r e d CC^ l a s e r l i g h t - a b o v e t h e r m a l l e v e l s and t h e r e s u l t i n g i o n wave a m p l i t u d e s  3.22  D i s c u s s i o n o f t h e observed laser  3.23  wavelength s h i f t of the backscattered  light.  A n g u l a r dependence.of t h e b a c k s c a t t e r e d CO^ l a s e r l i g h t and comparison w i t h  3.24  i n t h e plasma.  theory.  The wavelength dependence o f t h e l i g h t b a c k s c a t t e r e d the - s m a l l mask .  see p. 46  through  5.6.  3.21  Enhancement of the b a c k s c a t t e r e d CO^ l e v e l s and  l a s e r l i g h t above t h e r m a l  the r e s u l t i n g i o n wave a m p l i t u d e s i n the plasma.  I n o r d e r t o determine the enhancement of s c a t t e r e d l e v e l s , the i n t e n s i t i e s s c a t t e r e d  l i g h t above t h e r m a l  from t h e r m a l d e n s i t y  fluctuations  (Thomson s c a t t e r i n g ) must be known f i r s t . The  t h e o r y of Thomson s c a t t e r i n g from plasmas  intensity I  as s c a t t e r e d . f r o m t h e r m a l f l u c t u a t i o n i s g i v e n  I (a) s Here,  =  = .66  8n  T  x 10  - 2 1 +  cm  =  by (III-6)  2  z  r  i s the Thomson s c a t t e r i n g  2  crossection.  4  • ( l + a ) [ l + a ( l + Z Y-)] 2  1 a = ——  light  I. N. -4- ( l - s i n 2 e c o s * ) xnc e r  S(a)  Za S(a)  shows t h a t the  f o r the i o n  feature  2  1  , where k i s the wave v e c t o r  of the d e n s i t y  fluctuation  D w h i c h does the s c a t t e r i n g .  I. xnc  The  i s the Debye s h i e l d i n g  =  distance. incident laser light intensity  =  number of e l e c t r o n s  J  p r e s e n t w i t h i n the s c a t t e r i n g volume.  l a s t term on the R.H.S. of e q u a t i o n ( I I I - 6 ) d e s c r i b e s the  dipole  f i e l d of the e l e c t r o n o s c i l l a t i n g i n the i n c i d e n t l a s e r f i e l d i n a c o o r d i n a t e system e x p l a i n e d  *41,  51  i n F i g . (3-4)  on the f o l l o w i n g page.  57.  F i g u r e ( 3 - 4 ) : E x p l a i n i n g t h e c o o r d i n a t e system used i n t h e c a l c u l a t i o n s i n S e c t i o n 3.21. The d i p o l e f i e l d i s r o t a t i o n a l l y symmetric w i t h r e s p e c t t o t h e x a x i s . The * c o o r d i n a t e r o t a t e s around t h e Z a x i s . " B a c k s e a t t e r i n g " means 6 -> 180 . I n o r d e r t o f i n d t h e i n t e n s i t y s c a t t e r e d back t h r o u g h t h e p i n c h (see F i g . ( 2 - 5 ) ) , e q u a t i o n t o 2ir  ( I I I - 6 ) w i l l have t o be i n t e g r a t e d from <j> = 0  and 9 = 180° - 4p- t o 180°.  the "u f/5 p i n c h lens--, A0  lens  There A6 c o r r e s p o n d s t o t h e a n g l e o f  f-number  Assuming t h a t t h e s c a t t e r i n g o c c u r s  for  f-numbers >> 1.  i n t h e underdense r e g i o n o f the  plasma, |k| * 12k | (see p. 16 ) so t h a t a =  * 2k~\ ' ° * D o D d e n s i t i e s and temperatures i n v o l v e d ( s e e F i g . (2-3)) one can see t h a t i n a l l cases a >> 1. X  2 3" " ^ e ' * t  N where n  ie  n  e  e  n u m  ^  F  r  t  ie  W i t h the plasma b e i n g a He-Plasma, S(a) then becomes e r  °f e l e c t r o n s i n t h e s c a t t e r i n g volume i s g i v e n by  h  i s the e l e c t r o n d e n s i t y , A^ t h e f o c a l a r e a o f t h e C0„ l a s e r , F 2  b e i n g ^ 1 mm  2  and I i s t h e l e n g t h o f the i n t e r a c t i o n r e g i o n .  F i n a l l y , we m u l t i p l y eq. ( I I I - 6 ) by y because o n l y the l o n g w a v e l e n g t h s i d e o f t h e Thomson s c a t t e r e d i o n f e a t u r e was observed as b e i n g enhanced. Accounting  f o r a l l these p o i n t s , one a r r i v e s a t  58.  BS  therm  =  8 . 1 3 x l 0 inc  T  _  3  0  x  n  x£ e  (III-7)  where now I,,,, i s i n J o u l e s , and I . i s i n Joules/cm . BS xnc 2  W i t h 27 J o u l e s o f i n c i d e n t CO^ l a s e r energy f o c u s s e d t o 1 mm  this  2  reduces t o therm  =  2  2  ^  1 Q  _  2 6  £  JJO  x  q  (IH-8)  e  An " e x a c t " v a l u e f o r I i s n o t known.  C o n s i d e r i n g t h e geometry  involved  i t i s , however, r e a s o n a b l e t o assume t h a t i t i s o f the o r d e r o f a few mm.  Supported by e x p e r i m e n t a l e v i d e n c e , ( F i g . (3^-2)), I ^ 1 cm was  used. Igg T  From f o r m u l a ( I I I - 8 ) and F i g . ( 3 - 1 ) , t h e enhancement V.  observed  ' BS  thermal  C a n  ,  , , , „ , , , . c a l c u l a t e d . The r e s u l t s xs p l o t t e d xn  F i g . (3-5) on the f o l l o w i n g page and shows t h a t the i n t e n s i t y enhancement drops smoothly as the d e n s i t y o f the plasma  increases.  To t r u l y u n d e r s t a n d the b e h a v i o u r shown i n F i g . (3-5) i n terms o f S t i m u l a t e d B r i l l o u i n s c a t t e r i n g i t would be n e c e s s a r y t o have d e t a i l e d i n f o r m a t i o n about the temperature s c a l e l e n g t h o f t h e plasma as a f u n c t i o n of time.  F i g u r e ( 3 - 5 ) : Showing the i n t e n s i t y enhancement above t h e r m a l l e v e l s as a f u n c t i o n of d e n s i t y i n the plasma. V e r t i c a l e r r o r b a r s are e x p e r i m e n t a l e r r o r s from F i g . ( 2 - 4 ) ; h o r i z o n t a l e r r o r b a r s are due t o the d e n s i t y e s t i m a t e s from F i g . ( 2 - 1 ) . With t h i s i n f o r m a t i o n not b e i n g a v a i l a b l e a t t h i s p o i n t , the q u a l i t a t i v e behaviour, of -I - . / I • .. enh therm  versus n e  could  perhaps be understood-by the f a c t t h a t i n c r e a s i n g d e n s i t y temperature a t d e c r e a s i n g decreasing  see  p.29  and  dimensions ( t h e plasma i s p i n c h i n g ) means  s c a l e l e n g t h s , hence i n c r e a s i n g t h r e s h o l d s .  •60.  To c a l c u l a t e t h e d e n s i t y  f l u c t u a t i o n that gives r i s e t o t h i s  enhancement, one a g a i n needs t o know t h e t h e r m a l f l u c t u a t i o n As  29 i s w e l l known,  the r e l a t i v e thermal density  fluctuation  of N p a r t i c l e s w i t h i n a g i v e n c o n t r o l volume c o n t a i n i n g  first. 6 N  therm N  on t h e average  N >>> 1 p a r t i c l e s , i s 6 N therm N  therm 6 n n  _1_  (III-9)  where n denotes t h e c o r r e s p o n d i n g p a r t i c l e d e n s i t i e s , therm i n t e n s i t y I,,,, scattered  The  from t h e s e t h e r m a l f l u c t u a t i o n i s  DO  I  therm  T  B  S  . therm ? ^<|6n |2>  (111-10)  Hence, t h e r e l a t i v e i n t e n s i t y enhancement above t h e r m a l l e v e l s , f o l l o w s from the d e n s i t y , g thermal l e v e l s :— through - therm ° o n enh enh 6 n "BS therm therm 6 n  i  Do k/l , , ' do Jib e n  t  T  i e r m  r  e  n  f l u c t u a t i o n enhancement above  n  n  (III-ll)  BS  This,  together with (III-9) y i e l d s the absolute density  fluctuation  g i v i n g r i s e t o t h e observed i n t e n s i t y enhancement as enh  enh 6 n  U  /nV LP  x  BS  therm L I  (111-12)  BS  where V^p i s t h e i n t e r a c t i o n volume, ^enh Note t h a t — depends o n l y w e a k l y on t h e i n t e r a c t i o n volume.  As we  d i s c u s s enhancements o f s e v e r a l o r d e r s o f magnitude, an i n a c c u r a t e guess i n V^p by a f a c t o r 10 does n o t change t h e c o n t e n t s o f a statement about 6 n  61.  F i g . (3-6) shows t h e observed  6 n  e n n  n  * therm as w e l l as t h e t h e o r e t i c a l -^-2 n  ^ n . The o v e r a l l enhancement above t h e r m a l  f l u c t u a t i o n s i s about f o u r  orders  of magnitude.  6 n on  ~ enh  th  n  n  -8  -4  x10 . x10 20  10 9  8  7 6  5  2 H  1 .9  .8  .7  .6  •II  •I  1  .  i  2  :  1  i  l  l  1—I—i  3 4 5 6 7 8 9 1  x10  1?  i  ——T  2  :  1  I  I—i—«—r—r-i  3 4 5 6 7 8 9 1  xld  8  i  :—>  2  njcm ]  F i g u r e ( 3 - 6 ) : Showing t h e a b s o l u t e d e n s i t y f l u c t u a t i o n s g i v i n g r i s e t o t h e enhanced b a c k s c a t t e r e d l i g h t s i g n a l as a f u n c t i o n o f plasma d e n s i t y . E r r o r b a r s l i k e i n F i g . ( 3 - 5 ) . The s t r a i g h t l i n e represents r e l a t i v e thermal d e n s i t y f l u c t u a t i o n s .  3  62.  3.22 D i s c u s s i o n of the observed w a v e l e n g t h s h i f t of the b a c k s c a t t e r e d CO^  laser  light.  The w a v e l e n g t h " s h i f t of t h e b a c k s c a t t e r e d CC^ l a s e r l i g h t was s e v e r a l independent e x p e r i m e n t s , t o be (4.7 ± .4) x 1 0  - 3  measured,:.in  um towards the  r e d end o f the spectrum. In p r i n c i p l e , t h i s i m p l i e s a net r e c e s s i o n v e l o c i t y v  of the r e f l e c t i n g  o b j e c t of  vr  =  |2f A  (111-13) o  w h i c h f o r the quoted Aa = 4.7 x 1 0 v  =  6.6  - 3  ym i s  cm/usec.  The v e r y n a t u r e of the b a c k s e a t t e r i n g experiment however does not a l l o w d i s t i n g u i s h i n g between a s h i f t a r i s i n g from b u l k plasma m o t i o n and a s h i f t a r i s i n g from the s c a t t e r i n g o f f t r a v e l l i n g i o n a c o u s t i c waves. T h e r e f o r e , t h e v e l o c i t y of the b u l k plasma m o t i o n towards t h e i n c i d e n t CC>2 l a s e r s h a l l be e s t i m a t e d . Then, t h e h e a t i n g o f t h e plasma by i n v e r s e b r e m s s t r a h l u n g under t h e g i v e n plasma parameters w i l l be c o n s i d e r e d .  From t h a t , we t r y t o c o n c l u d e  under .which, .circumstances:.-the:" enhanced b a c k s e a t t e r i n g o f C 0 " l a s e r 2  light  ?  occurs.  To e s t i m a t e t h e a x i a l escape v e l o c i t y , we proceed two ways.  Momentum  c o n s e r v a t i o n f o r an i n f i n i t e s i m a l mass element of the r a d i a l l y  collapsing  plasma shows t h a t the a x i a l escape v e l o c i t y must be o f the o r d e r of the  same f o r o t h e r e x p e r i m e n t s of t h i s t y p e , e.g.  30,31.  63.  radial collapse velocity.  From s t r e a k photography  t h i s was  measured  to be ^ 4 cm/usec. C o n s i d e r i n g , on t h e o t h e r hand, f r e e t h e r m a l e x p a n s i o n out o f the ends of a plasma column ( r a d i a l l y c o n f i n e d by a magnetic f i e l d ) , one would e s t i m a t e t h e excape v e l o c i t y t o be l a r g e r or e q u a l t o t h e i o n t h e r m a l speed w h i c h , a t T ^ 25 eV, i s about 3.5 cm/usec. W i t h b o t h e s t i m a t e s l e a d i n g t o the same r e s u l t , we assume 4 cm/usec f o r the  a x i a l escape v e l o c i t y v 1  esc  N e x t , we combine t h e a x i a l escape v e l o c i t y o f the plasma w i t h the measured w a v e l e n g t h s h i f t of the b a c k s c a t t e r e d l i g h t t o make a statement about the  temperature o f the r e g i o n from w h i c h the enhanced b a c k s c a t t e r i n g  occurs.  S c a t t e r i n g o f f i o n a c o u s t i c waves d r i v e n by the i n c i d e n t  CC^  l a s e r l i g h t w i l l r e s u l t i n a r e d s h i f t p r o p o r t i o n a l t o t h e group v e l o c i t y v . o f t h e i o n a c o u s t i c wave.  I f t h i s i o n a c o u s t i c wave t r a v e l s i n a  plasma t h a t moves as a whole towards the i n c i d e n t CC^ l a s e r l i g h t w i t h velocity v , the n e t w a v e l e n g t h s h i f t due t o both motions w i l l be esc = 2f AT  v. i a, - ve s c  (111-14)  1  o e.g. i f Vj, = v a  With v  , no s h i f t w i l l  result.  e s t i m a t e d , as 4 cm/usec and an observed w a v e l e n g t h s h i f t of AA of  £ s c  4.67 x 1 0  e s c  - 3  v. = xa  um, t h i s i s 10.6 cm/usec,  U s i n g the d i s p e r s i o n r e l a t i o n f o r i o n a c o u s t i c waves a t e q u a l i o n and e l e c t r o n temperatures and t a k i n g k x the  D  << 1 (see p. 5 7 ) , one o b t a i n s f o r  t e m p e r a t u r e of the plasma i n w h i c h the i o n wave t r a v e l s  see f o o t n o t e p. 33  64.  T = 70 eV f o r v  = 0 cm/usec  esc  T = 180 eV f o r v  esc  =4  cm/ysec  N e x t , we proceed t o make a temperature e s t i m a t e from i n v e r s e b r e m s s t r a h l u n g considerations. The i n v e r s e b r e m s s t r a h l u n g a b s o r p t i o n of n  a 2 x 10 cm 1 8  e  of  l a s e r l i g h t by a plasma  T » 25 eV, w h i c h a r e the parameters a t the time ) e  - 3  of i n t e r e s t (see F i g . (2-3) m i d d l e ) , i s found to be  K  22  -  B  cm l -  Hence, over 2 mm,  99% o f the i n c i d e n t r a d i a t i o n would be  absorbed.  Because of the f i n i t e temperature c o n d u c t i v i t y of the plasma i t i s u n r e a s o n a b l e t o assume such a l o c a l h e a t i n g o f a 17 cm l o n g plasma column and one has t o t a k e .temperature d i f f u s i o n i n t o a c c o u n t . C o n s i d e r i n g the l o s s of t h e r m a l energy out of a volume l i m i t e d by the  C0  2  l a s e r f o c a l a r e a and these 2 mm a b s o r p t i o n l e n g t h due t o temperature d i f f u s i o n o n l y , u s i n g the t h e r m a l c o n d u c t i v i t y .5/2 ** 10k^ (2k T ) °  19 32 '  / Z  K  T =  3/2 \ , TT m ^ e lnA o h  < m  4  and t y p i c a l assumed temperature s c a l e l e n t h s  of the plasma,  a r r i v e s a t a r e p r e s e n t a t i v e d i f f u s i o n time n -fy 5/2  1 5  >  one  of  2  x  T T  = £  2  T  x 4.9 x 10  2 2  (T. eV) in  9  T  For s c a l e l e n g t h s Jc m <v mm, T  n  »  2 x 10 cm 1 8  - 3  (111-16)  and T  e  > 20 eV, x m i s found 0/ T  -5/2 t o be  < 10 n s e c .  As x m i s p r o p o r t i o n a l t o T  r e s u l t i n much s m a l l e r times t ^ . *see ( I I I - l ) InA Sr' 10 i s the Coulomb l o g a r i t h m  , h i g h e r temperatures  Hence, i t must be assumed t h a t the i n t e r a c t i o n volume V  , where the J_iir  CC>2 l a s e r energy i s dumped i n t o the plasma, i s many times the 99% b r e m s s t r a h l u n g a b s o r p t i o n l e n g t h , e.g.  inverse  the e n t i r e l e n g t h of the plasma  column. The  energy c o n t e n t E = N R^T  and T  of the plasma column a t n  ^ 25 eV i s about E = 2.0  g  ^ 2  x'.AO cm 18  -3  Joules.  e Hence, a b s o r b i n g  a l l the i n c i d e n t 27 J o u l e s of l a s e r l i g h t w i t h i n the 27  plasma l e a d s t o a T = 350 eV. e  f o l d i n c r e a s e i n temperature or t o a h e a t i n g  to  I n a p p l y i n g i n v e r s e b r e m s s t r a h l u n g c o n s i d e r a t i o n however, s e v e r a l assumpt i o n s were- made, w h i c h are i n r e a l i t y not f u l f i l l e d . The  d e r i v a t i o n s l e a d i n g t o I I I - l , I I I - 3 , and 111-15 assume t h a t  h e a t i n g i s i n f i n i t e s i m a l , e.g.,  t h a t the temperature b e f o r e and a f t e r the  a b s o r p t i o n p r o c e s s i s e s s e n t i a l l y the same, t h a t k d i s t a n c e and  the  i s not a f u n c t i o n of  t h a t K„ i s n e i t h e r a f u n c t i o n of temperature nor 1  time. i  Attempts w i t h i n t h i s l a b o r a t o r y t o s o l v e the e x a c t problem n u m e r i c a l l y are under  way.  Considering  t h a t the i n v e r s e b r e m s s t r a h l u n g a b s o r p t i o n c o e f f i c i e n t d e c r e a s e s  as the plasma temperature i n c r e a s e s and i n c i d e n t CO^  t h a t most l i k e l y some of 28  l a s e r l i g h t i s r e f r a c t e d away from the plasma  the  without  being  absorbed,cone w i l l have t o c o n c l u d e t h a t the plasma i s heated to l e s s 9 than 350  eV by i n v e r s e b r e m s s t r a h l u n g a b s o r p t i o n .  An e a r l i e r experiment  however . w i t h somewhat d i f f e r e n t geometry, i n d i c a t e d h e a t i n g t o 200  eV.  There e x i s t s however a l s o the p o s s i b i l i t y t h a t the r e g i o n from where the b a c k s c a t t e r i n g o c c u r s i s a c t u a l l y a r e g i o n of lower d e n s i t y which B a r n a r d , G u l i z i a , p r i v a t e communications.  lies  66. o u t s i d e the main plasma body and f o r which the i n v e r s e b r e m s s t r a h l u n g a b s o r p t i o n c o e f f i c i e n t i s lower and t h e r e f o r e the temperature i n c r e a s e due t o h e a t i n g by i n v e r s e b r e m s s t r a h l u n g a b s o r p t i o n i s a l s o l o w e r . experiment d i s c u s s e d i n 3.24  The  seems t o s u p p o r t t h i s v i e w .  S t r i c t l y s p e a k i n g , t h e r e i s not y e t enough e x p e r i m e n t a l d a t a t o d e c i s i v e l y conclude on the c i r c u m s t a n c e s under which the observed  enhanced  s c a t t e r i n g o c c u r s but from the measurements and c o n s i d e r a t i o n s p r e s e n t e d i t can be concluded t h a t the enhanced s c a t t e r i n g o f f i o n a c o u s t i c waves ( s t i m u l a t e d B r i l l o u i n s c a t t e r i n g ) occurs' i n a r e g i o n i n f r o n t of the main c o r e of the plasma where the e l e c t r o n d e n s i t y i s some a. 1 0 temperature  i s around  o r d e r of m i l l i m e t e r s .  1 7  cm , -3  the  180 eV and the temperature s c a l e l e n g t h s are o f the The enhancement i n b a c k s c a t t e r e d i n t e n s i t y and i n  i n d u c e d d e n s i t y f l u c t u a t i o n s above t h e r m a l l e v e l s i s l i k e l y t o be somewhat h i g h e r than i n d i c a t e d by F i g s . (3-5) and  (3-6).  67.  3.23 The a n g u l a r dependence o f t h e b a c k s c a t t e r e d CO., l a s e r l i g h t and comparison w i t h t h e o r y .  The a n g u l a r dimensions of t h e setup f o r measuring t h e b a c k s c a t t e r e d C0  9  l a s e r l i g h t were as f o l l o w s .  interaction volume  F i g u r e ( 3 - 7 ) : A n g u l a r dimensions o f t h e CC^ l a s e r f o c u s s i n g o p t i c s (see a l s o p. 3 4 ) . The arrows m c i d a t e t h a t t h e l a s e r l i g h t was i n c i d e n t through t h e a n n u l a r r e g i o n ; b a c k s c a t t e r e d l i g h t was observed s e p a r a t e l y through t h e a n n u l a r r e g i o n and through t h e c e n t r a l r e g i o n o f the annulus. The spot i n t h e m i d d l e i n d i c a t e s t h e a r e a o b s c u r r e d by an o b s t a c l e p u t i n t h e way of t h e a x i a l l y e s c a p i n g plasma t o p r e v e n t s e v e r e m e c h a n i c a l damage t o the KC1 l e n s e .  By u s i n g a p p r o p r i a t e masks i n t h e b a c k s c a t t e r i n g o p t i c s (see F i g . (2-10) and  (2-11)) and comparing t h e b a c k s c a t t e r e d peak i n t e n s i t i e s i t was  found t h a t 7.9 times more l i g h t was s c a t t e r e d back through as compared t o t h e s m a l l mask ( F i g s . (2-12) and ( 2 - 1 3 ) ) . i t i s therefore reasonable  t o say t h a t t h e d i v e r g e n c e  t h e b i g mask As an e s t i m a t e  angle of the  b a c k s c a t t e r e d l i g h t i s about 3° t o 5°.  Comparison w i t h  theory  O m i t t i n g the ^ cos <j> dependence p r e d i c t e d f o r t h e b a c k s c a t t e r e d l i g h t by 2  the t h e o r y f o r i n f i n i t e , homogeneous plasmas as t o o s i m p l e , we w i l l r e s t r i c t o u r s e l v e s t o t h e comparison w i t h two more e l a b o r a t e t h e o r i e s p r e d i c t i n g the t y p i c a l laser l i g h t .  angular divergence  for Brillouin  backscattered  68.  The f i r s t  theory  14  i s the treatment of s t i m u l a t e d b a c k s c a t t e r i n g i n a  f i n i t e , inhomogeneous plasma w h i c h p r e d i c t s a t y p i c a l a n g u l a r  spread  Se__ o f (quoted i n R e f . 33) DO 6 6  BS -  7Ti  (III  There, 3£ i s t h e t o t a l g a i n . o b s e r v e d when a b a c k s c a t t e r e d  "  17)  electro-  magnetic wave t r a v e l s through a medium o f l e n g t h £ w i t h a g a i n o f 3 p e r unit  length.  The second t h e o r y  33  , was forewarded r e c e n t l y by Lehmberg.  Knowing t h a t  the f i r s t t h e o r y p r e d i c t s f o r t y p i c a l l a s e r f u s i o n e x p e r i m e n t s spreads w h i c h a r e f a r l a r g e r than o b s e r v e d , t h e second t h e o r y not o n l y t h a t a s c a t t e r e d e l e c t r o m a g n e t i c  angular assumed  wave t r a v e l s t h r o u g h a medium  w i t h g a i n , b u t a l s o , t h a t i t has t o s a t i s f y a Bragg c o n d i t i o n s e t up by the i n t e r f e r e n c e o f d i f f e r e n t a n g u l a r  p a r t s o f t h e i n c i d e n t l i g h t beam  i n t h e plasma. From t h a t , an a n g u l a r  r e s o l u t i o n f o r the backscattered  \, 9  min  Here, k  °  =  (  s T  )  4  l i g h t of  I, (  f  )  2  i  s  o  d  e  r  i  v  e  d  -  <  iri  - > 18  i s t h e wave v e c t o r o f t h e i n c i d e n t l i g h t .  The p r e d i c t i o n s o f b o t h t h e o r i e s f o r a t y p i c a l l a s e r f u s i o n experiment on one hand, and t h e e x p e r i m e n t d e s c r i b e d hand, w i l l  i n t h i s r e p o r t on t h e o t h e r  now be compared.  Typical laser fusion experiment-^  T h i s experiment parameters  k (Nd g l a s s ) = 6 x l O V c m o g£  3  o  3£ 19.  10 t o 15  £  100 ym  3  ( 1 t o 1.5) x:10 /cm  *see F i g . (3-5)  k*.(C0 l a s e r ) = 6 x 10 /cm o 2  3  £  5 mm  3  38/cm  *  Typical laser experiment  This  fusion  experiment  Theoretical Predictions  e  D  o  6e„_ ^ .93  ^ 1.2 or 60 ^ .14 or 8° min  BS  0^ . D min  or 53°  ^ .063  or  3.6°  Observed  I t i s c l e a r t h a t the f i r s t t h e o r y f a i l s i n e x p l a i n i n g b o t h types of  experiments.  The e x p e r i m e n t a l e v i d e n c e s u g g e s t s the  c o r r e c t n e s s of Lehmberg's f o r m u l a .  The a u t h o r wishes t o emphasize t h a t even though he c l a i m s t o understand the p h y s i c a l p r i n c i p l e behind 111-18 as i t i s d e s c r i b e d i n Ref. 33, he would a t t h i s p o i n t be unable to. r e d e r i v e 111-18 from f i r s t p r i n c i p l e s . The d e s c r i p t i o n of the r e s u l t s o b t a i n e d i n Ref. 33 i s however e x p l i c i t enough t h a t n u m e r i c a l v a l u e s can be o b t a i n e d from the p r e s e n t e d f o r m u l a e .  70.  3.24 The w a v e l e n g t h dependence o f t h e l i g h t b a c k s c a t t e r e d through t h e * s m a l l mask The e x p e r i m e n t a l r e s u l t ( F i g . (2-13)) shows t h a t t h e spectrum o f t h e CO^ l a s e r l i g h t s c a t t e r e d back through t h e s m a l l mask i s n o t s i m p l y a l i n e s h i f t e d by 4.7 x 1 0  - 3  ym  The c e n t e r o f t h e l i n e i s s t i l l s h i f t e d by 4.7 x 1 0  _ 3  ym b u t a d d i t i o n a l l y  wings a r e p r e s e n t , s u g g e s t i n g a m o d u l a t i o n f r e q u e n c y co^ o f co % (3.5 t o 2.9) x 1 0 M M  1 0  sec  To my knowledge, t h e a n g u l a r dependence o f s t i m u l a t e d  Brillouin  s c a t t e r i n g has n o t been measured b e f o r e w i t h t h i s t y p e o f geometry (see  F i g . (3-7)) and such a m o d u l a t i o n has n o t y e t been o b s e r v e d .  t h a t t h i s m o d u l a t i o n f r e q u e n c y i s now an a b s o l u t e l y determined t h a t i s n o t obscured by any immeasurable  Note  frequency  s h i f t s due t o b u l k m o t i o n s , :. '. ..  etc. I n t r y i n g t o p r o v i d e a p h y s i c a l e x p l a n a t i o n i t was found t h a t t h e m o d u l a t i o n c o u l d b e s t be e x p l a i n e d through t h e g y r a t i o n o f e l e c t r o n s i n the p i n c h magnetic f i e l d .  The n e c e s s a r y r e a s o n i n g s h a l l now be  presented. For a s c a t t e r e d spectrum t o be modulated,  a n o n l i n e a r c o u p l i n g between  the m o d u l a t i o n o s c i l l a t i o n and the o s c i l l a t i o n of t h e s c a t t e r i n g e l e c t r o n i n t h e e l e c t r o m a g n e t i c f i e l d s must e x i s t . I n a s t a t i o n a r y magnetic f i e l d , t h e L o r e n t z f o r c e p r o v i d e s t h i s c o u p l i n g i n a v e r y n a t u r a l way by s i m p l y m o d u l a t i n g t h e v e l o c i t y o f t h e e l e c t r o n w i t h t h e gyro f r e q u e n c y w A  see 2.6  where  71. to  = — g  (111-19) m  For these m o d u l a t i o n s t o be v i s i b l e however, the wave v e c t o r "of the d e n s i t y f l u c t u a t i o n s c a t t e r i n g the i n c i d e n t e l e c t r o m a g n e t i c wave must be v e r y near p e r p e n d i c u l a r t o the v e c t o r of the magnetic  field  4 8  '"^  (e.g. < 5 ° ) .  Other-  w i s e , the t h e r m a l motion of e l e c t r o n s moving p a r a l l e l t o the magnetic produces enough ing  Doppler b r o a d e n i n g to smear out the m o d u l a t i o n s . C o n s i d e r -  the setup i n F i g . (2-10) and the a n g u l a r dimensions of the f o c u s s i n g  and b a c k s c a t t e r i n g o p t i c s ( F i g . ( 3 - 7 ) ) , one can see .that t h i s is  field  requirement;  fulfilled.  S e c o n d l y , the spectrum of t h e r m a l e l e c t r o n d e n s i t y f l u c t u a t i o n s p e r p e n d i c u l a r to an a p p l i e d magnetic f i e l d a l r e a d y shows m o d u l a t i o n s a t m u l t i p l e s of the e l e c t r o n c y c l o t r o n frequency. Thirdly.;,^ i t w i l l be seen t h a t no o t h e r c h a r a c t e r i s t i c f r e q u e n c y i n a of a d e n s i t y o f 2 x 1 0 c m 1 8  - 3  plasma  i s i n the v i c i n i t y of the observed m o d u l a t i o n  frequency. In  o r d e r t o s u p p o r t these s t a t e m e n t s , we w i l l f i r s t use (111-19) t o  c a l c u l a t e the magnitude of the magnetic  f i e l d a t the i n t e r a c t i o n volume.  Then we w i l l e s t i m a t e t h i s magnitude from plasma dynamic c o n s i d e r a t i o n s . The observed spectrum OL,  M  =  ( F i g . (2-13)) s u g g e s t s a m o d u l a t i o n f r e q u e n c y of  co o , -, lQ rads (3.2 ± .6) x 10 sec n  *  S e t t i n g t h i s e q u a l t o the gyro f r e q u e n c y to  and u s i n g (111-19),  this  suggests a magnetic f i e l d a t the i n t e r a c t i o n volume of B  2000 Gauss  The magnitude of t h i s magnetic f i e l d w i l l now a l s o be e s t i m a t e d from the c u r r e n t f l o w and the s i z e of the i n t e r a c t i o n volume i n the plasma,  The lower l i m i t of to^ i s h a r d t o e s t i m a t e as the observed f r e q u e n c y m o d u l a t i o n i s a t the l i m i t of what can be s p e c t r a l l y r e s o l v e d .  72.  a p p l y i n g the t h e o r y of the s k i n e f f e c t i n u n i f o r m  cylindrical  conductors. A  As t h i s t h e o r y i s p r e s e n t e d it  will  not be p r e s e n t e d  i n almost any  t e s t book on e l e c t r o d y n a m i c s  h e r e t o any e x t e n t , o n l y i t s r e s u l t s w i l l  ,  be  used. A  Current  A  t r a c e s of the Z - p i n c h d i s c h a r g e  show the magnitude of  the  c u r r e n t f l o w i n g through the plasma t o v a r y on a t i m e s c a l e o f ^ 1 usee, e.g. w i t h a frequency of c rads co -'- 2TT x 10° I sec 0  i n  T  Assuming t h a t the plasma i s a u n i f o r m c o n d u c t o r o f r a d i u s r • f ++ w i t h a t e m p e r a t u r e of 180 eV , i t s r e s i s t i v i t y a a « 4 x 10  - 5  •of <5 = .33  mm  will  be  0, cm,;  or t h a t o f a m e t a l . 6 =  =2 o  From t h a t one  i„  can c a l c u l a t e a .skin depth  (c = speed of l i g h t )  C  v2irt0ja  (111-20)  mm.  As the r a d i u s o f the plasma i s r  Q  = 2 mm,  one can see t h a t the m a j o r i t y  o f the c u r r e n t f l o w o c c u r s a t r a d i i l a r g e r t h a n the r a d i u s o f the b a c k s c a t t e r i n g i n t e r a c t i o n volume ( r » .5  mm).  A p p l y i n g the r e s u l t s of the s k i n e f f e c t t h e o r y f o r a u n i f o r m conductor w i t h outer r a d i u s 6 = .33 mm,  A  one  see p a r t i c u l a r l y  49,50  see s p e c i f i c a t i o n . see p.32  and a c u r r e n t s k i n depth of  f i n d s t h a t the c u r r e n t f l o w i n g t h r o u g h a c e n t r a l p a r t  AA  AAA  = 2mm  cylindrical  f  see p. 66 ff see p.26  73.  w i t h r = .5 mm i s 6.7 x 1 0  of the t o t a l  - 3  current.  W i t h t h e t o t a l c u r r e n t measured t o be 110 k amps a t t h e time t h e backs c a t t e r i n g t a k e s p l a c e , t h i s means t h a t t h e c u r r e n t f l o w i n g through a circular  c r o s s - s e c t i o n w i t h a r a d i u s e q u a l t o t h a t o f t h e f o c a l spot i s  740 amps. To c a l c u l a t e t h e magnetic f i e l d s u r r o u n d i n g t h i s c u r r e n t , one uses Stokes theorem t o e v a l u a t e M a x w e l l ' s e q u a t i o n V x H = j f o r t h e g i v e n geometry to  obtain B(r)  =  ~ - I  (111-21)  zirr  For  r = .5 mm and I = 740 amps t h i s r e s u l t s i n a magnetic f i e l d B o f B = 3000  Gauss  I n v i e w o f t h e a p p r o x i m a t i o n s made, t h i s compares w e l l w i t h t h e measured value (p. 71). The a p p r o x i m a t i o n s made were t h e f o l l o w i n g : (1)  The plasma was c o n s i d e r e d a u n i f o r m c y l i n d r i c a l c o n d u c t o r o f r  Q  = 2 mm; i n r e a l i t y however i t has a r a d i a l temperature p r o f i l e ,  hence, a r a d i a l c o n d u c t i v i t y p r o f i l e . . . Fbr:.the assumption t o h o l d , the  temperature p r o f i l e must be r e a s o n a b l y f l a t w i t h i n t h e c e n t r a l  r e g i o n o f t h e plasma.  For t h e convenience o f measuring I i n amps, t h i s f o r m u l a i s g i v e n i n MKSA u n i t s , y _o - 7 Y_sec 2ir Am =  1  Q  x  1 0  74.  (2)  The s c a t t e r i n g volume was r = .5 mm.  considered a t h i n annular r i n g w i t h  C o n s i d e r i n g t h a t the a p e r t u r e through which t h e  CC^  l a s e r l i g h t e n t e r s the plasma i s an annulus a l r e a d y and t h a t r a y bending i n the r a d i a l d e n s i t y p r o f i l e o f the plasma i s l i k e l y t o change the a s p e c t r a t i o o f t h i s annulus t o v a l u e s c l o s e r t o 1, the assumption made seems r e a s o n a b l e and i s as w e l l s u p p o r t e d by e v i d e n c e from shadow photographs  ( F i g . (3-2 , ) ) .  F i n a l l y , we s h a l l show t h a t a t the d e n s i t y of n  g  = 2 x 10  cm ,  1 8  -3  which  i s the d e n s i t y a t the p i n c h time of i n t e r e s t , no o t h e r c h a r a c t e r i s t i c f r e q u e n c y of the plasma i s near t h e observed m o d u l a t i o n f r e q u e n c y of 10 r a d s sec  co. .= m  3 x 10  (1)  e l e c t r o n plasma f r e q u e n c y :  (2)  i o n plasma f r e q u e n c y (He i o n s )  (3)  e l e c t r o n gyro f r e q u e n c y co f o r 3000 Gauss ge 10 co = 3.x 10. ge  (4)  co pe  8 x 10  co . px  =  13 r a d s sec  1.8 x 1 0  * sec  1 2  r a c  s  rads sec  .ion gyro f r e q u e n c y co . f o r 3000 Gauss g l  (5) resonance hybrid  co . gi  i / x 10' in7 rads 1.4 sec  '  f r e q u e n c y of e l e c t r o n waves i n a magnetic  f i e l d , the upper  frequency co,, uh  (6)  =  resonance co., ih  =  /co pe  2  + C0  2  ge  > CO ;  pe  f r e q u e n c y o f i o n waves i n a magnetic =  / k . v . " + co . i la gi 2  z  z  ;  co . gi  2  field  << k . v . l la 2  2  A  These f r e q u e n c i e s are e x p l a i n e d i n any plasma p h y s i c s book (16-19).  75. (6) c o n t i n u e d Here, ^ k ^ v ^ 2  Section  2  i-  i°  st n e  n  a c o u s t i c frequency d i s c u s s e d i n  3.22.  Hence, U K ^ i s v e r y c l o s e t o the i o n a c o u s t i c f r e q u e n c y ( w i t h i n 10~ '''%) . 2  (7) I f an e l e c t r o s t a t i c i o n wave t r a v e l s e x a c t l y p e r p e n d i c u l a r t o a magnetic co... lh  f i e l d , i t has a resonance a t the lower h y b r i d f r e q u e n c y . =  I , rads vco to . = 5 x 10° ge g i sec c  I t needs t o be emphasized  n 8  t h a t the arguments p r e s e n t e d a r e not meant t o  be unique statements about the p h y s i c a l p r o c e s s g i v i n g r i s e t o the observed s p e c t r a l i n t e n s i t y modulations.  They r a t h e r a r e i n i t i a l s u g g e s t i o n s  based on the a v a i l a b l e e x p e r i m e n t a l d a t a .  More e x p e r i m e n t s ,  e.g.  b a c k s c a t t e r i n g of CC^ l a s e r l i g h t a t d i f f e r e n t c u r r e n t s i n t h e p i n c h and a genuine t h e o r e t i c a l treatment would be needed to i n t e r p r e t the described  data c o n c l u s i v e l y .  W i t h i n the scope of the d a t a and the r e a s o n i n g p r e s e n t e d however, i t can be suggested t h a t the observed m o d u l a t i o n i n the b a c k s c a t t e r e d spectrum i s most l i k e l y f i e l d of the p i n c h .  due to the g y r a t i o n of e l e c t r o n s i n the magnetic  76. CONCLUSIONS The  e x p e r i m e n t s d e s c r i b e d i n Chapter I I and e v a l u a t e d  showed which p r o c e s s e s can be observed when a 250 MW w i t h a plasma a t d e n s i t i e s from 1 0  cm  1 7  -3 t o  s o m  e 10  1 8  i n Chapter I I I C0  laser interacts  2  cm .  At  -3  low  d e n s i t i e s , the good agreement between t h e o r y and experiment shows t h a t s i g n i f i c a n t a b s o r p t i o n of CO^ takes p l a c e .  l a s e r l i g h t by i n v e r s e bremmstrahlung  At h i g h e r d e n s i t i e s , s t i m u l a t e d B r i l l o u i n s c a t t e r i n g i s 46  seen t o o c c u r , however, a t l e v e l s w e l l below s a t u r a t i o n angular divergence s c a t t e r i n g was  of l i g h t b a c k s c a t t e r e d / b y  stimulated  .  The  observed  Brillouin  seen t o agree w e l l w i t h t h e o r e t i c a l p r e d i c t i o n s . '  F i n a l l y , i f has been observed t h a t some of the B r i l l o u i n  backscattered  l i g h t i s modulated w i t h the gyro f r e q u e n c y of e l e c t r o n s i n the magnetic f i e l d i n the plasma, an e f f e c t t h a t c o u l d be of g r e a t i n t e r e s t f o r the 35-37 49 i n v e s t i g a t i o n of magnetic f i e l d s i n l a s e r f u s i o n plasmas. As f a r as o t h e r i n s t a b i l i t i e s a v a i l a b l e w i t h the C 0 Higher C0 how  2  '  l a s e r was  2  are concerned, we  '  f e e l t h a t the power  too low t o exceed t h e i r  thresholds.  l a s e r powers would make i t c o n s i d e r a b l y e a s i e r t o measure  the observed i n t e n s i t y enhancement of the b a c k s c a t t e r e d  as a f u n c t i o n of the i n c i d e n t C 0  2  l a s e r power.  I t would a l s o a l l o w the imaging of the b a c k s c a t t e r i n g r e g i o n " f o o t p r i n t " paper and  light varies  on  thus o b t a i n d i r e c t i n f o r m a t i o n about the geometry  of the i n t e r a c t i o n volume. 24 From s i m p l e , e x p e r i m e n t a l l y v e r i f i e d t h e o r i e s about f i l a m e n t a t i o n i t can be p r e d i c t e d t h a t , w i t h the parameters d e s c r i b e d a density depression  l a s e r power, t h i s d e n s i t y d e p r e s s i o n w i l l become s e v e r a l tens of observable.  '  i n Chapter I I I ,  of ^ 3% s h o u l d r e s u l t . W i t h t e n times h i g h e r  hence, s h o u l d e a s i l y be  25  C0  2  percent,  H i g h e r CC^ l a s e r powers would a l s o p r o v i d e a p o s s i b i l i t y o f making a contribution  t o the q u e s t i o n o f s t i m u l a t e d  ,. _ ,10,11,12,14,15 , predicted  t  Raman s c a t t e r i n g .  .  , 22  b u t perhaps o n l y once o b s e r v e d ,  would p r o v i d e i n t e r e s t i n g d e n s i t y  Much  our experiment  scale lengths f o r t e s t i n g the  predictions. A p p r o p r i a t e changes i n t h e d i s c h a r g e bank o f the Z - p i n c h would a l l o w the measuring o f t h e spectrum.of t h e b a c k s c a t t e r e d l i g h t a t d i f f e r e n t plasma c u r r e n t s ,  e.g. d i f f e r e n t magnetic f i e l d • s t r e n g t h s w i t h i n t h e  laser-plasma i n t e r a c t i o n region.  T h i s would make i t p o s s i b l e  to further  t e s t i f the model assumed i n 3.24 i s c o r r e c t . F i n a l l y , a change i n geometry, e.g. f o c u s s i n g  the  i n t o the plasma, w i l l have t h e advantage o f a b e t t e r r e g i o n and w i l l a l l o w d i a g n o s t i c  A  21  decay.  >  23  laser defined  access to i n v e s t i g a t e  radially interaction  two plasmon  78.  CHAPTER 4  The f a s t g a t i n g o f an O p t i c a l M u l t i c h a n n e l A n a l y s e r  (OMA)^  and a c o n t r i b u t i o n t o the d i a g n o s t i c s o f t h e Z - p i n c h plasma_ 4.1 I n t r o d u c t i o n The f i r s t measurements o f e l e c t r o n d e n s i t y and temperature o f t h e Z - p i n c h plasma were s p e c t r o s c o p i c a l measurements u s i n g t h e S t a r k b r o a d e n i n g o f the 4 6 8 6 $ l i n e o f He  II.  2 6  I n o r d e r t o have t h e s e measurements supplemented by a second method, a Thomson s c a t t e r i n g system (see F i g . ( 4 - 1 ) ) was s e t up. Ruby l a s e r was f o c u s s e d o b s e r v e d under 173°.  A3  i n t o t h e plasma and t h e b a c k s c a t t e r e d  Joule light  A t t h e d e n s i t y and temperature i n d i c a t e d by t h e  i n i t i a l s p e c t r o s c o p i c a l measurements, t h i s s h o u l d have r e s u l t e d i n a Thomson-scattered spectrum c h a r a c t e r i z e d by • a.  1.2.  79.  Ruby laser  !1 Figure (4-1):  The Ruby l a s e r Thomson s c a t t e r i n g  system.  80.  The spectrum, o b t a i n e d on a s h o t - t o - s h o t b a s i s and r e c o r d e d w i t h a photomultiplier, n  e  « 10  1 8  cm  i s shown below and y i e l d s  - 3  I Karb  ,  T  e  = 40 eV  units)  o  ;  •  F i g u r e ( 4 - 2 ) : Thomson s c a t t e r e d spectrum o b t a i n e d w i t h setup i n F i g . ( 4 - 1 ) , r e c o r d e d w i t h a p h o t o m u l t i p l i e r . The next s t e p was t o use a 500 c h a n n e l OMA i n o r d e r t o d e t e c t  this  e l e c t r o n f e a t u r e i n one s i n g l e s h o t . D e s p i t e much e f f o r t i n v e s t e d t o a r r i v e a t a t r u l y s a t i s f a c t o r y t h i s was n o t a c h i e v e d  w i t h i n t h e work d e s c r i b e d i n t h i s r e p o r t .  result, Part  of the r e a s o n can be u n d e r s t o o d by examining F i g u r e (4-3) which shows a Thomson s c a t t e r e d s i g n a l d e t e c t e d w i t h a p h o t o m u l t i p l i e r .  81.  100 n s / d i v  F i g u r e ( 4 - 3 ) : A p h o t o m u l t i p l i e r t r a c e of the Thomson s c a t t e r e d s i g n a l . The f i r s t p u l s e i s the Ruby m o n i t o r . The m i s s i n g p i e c e i n d i c a t e s the p l a c e of a foreward s c a t t e r e d s i g n a l w h i c h . i s w e l l o f f the s c r e e n and of no r e l e v a n c e h e r e . The subsequent r i s e i s the d e l a y e d s i g n a l showing the plasma l i g h t w i t h the b a c k s c a t t e r e d s i g n a l i n d i c a t e d . AX was lOoX; p i n c h t i m e was - 50 < t < 0 ns.  The  F i g u r e shows c l e a r l y t h a t the s i g n a l - t o - p i n c h l i g h t r a t i o i s about  or s m a l l e r . Fig.  .2  T h i s a l s o g i v e s r i s e t o the l a r g e s t r a y of d a t a p o i n t s i n  (4-2).  W i t h the means a v a i l a b l e a t the t i m e , i t was  found t h a t the e v a l u a t i o n  the i o n f e a t u r e of the Thomson s c a t t e r e d spectrum p r o v i d e d a v e r y measurement of plasma d e n s i t y and f e a t u r e approach was  temperature,  not pursued any  of  good  hence, the e l e c t r o n  further.  The work however d i d r e s u l t i n d e v e l o p i n g  a technique f o r s u c c e s s f u l  40 nanosecond g a t i n g of the  OMA.  I n the f o l l o w i n g s e c t i o n t h i s t e c h n i q u e s h a l l be d e s c r i b e d improved s p e c t r o s c o p i c a l measurement of d e n s i t y and plasma.  see f o o t n o t e p.  33  and  applied  temperature of  the  to  82. 4.2  Nanosecond g a t i n g of an o p t i c a l m u l t i c h a n n e l a n a l y s e r  (OMA)  Many types o f t i m e - r e s o l v e d measurements i n plasma p h y s i c s r e q u i r e s h o r t time g a t i n g o f a d e t e c t i o n system d u r i n g c o m p a r a t i v e l y light levels.  One  long duration high  such case i s the d e t e c t i o n of a Thomson s c a t t e r e d  s i g n a l of nsec d u r a t i o n  during  the h i g h b r e m s s t r a h l u n g  e m i s s i o n of a  dense plasma l a s t i n g many ysec. I f the d e t e c t e d s i g n a l s a r e weak, two r e q u i r e m e n t s must be The  fulfilled:  c o n t r a s t r a t i o of the g a t i n g system must be h i g h (e.g. > 10,000) and  the g a t i n g p r o c e s s must not r e s u l t i n d i s t o r t i o n s of the r e c o r d e d How  the OMA  can be made t o f u l f i l l b o t h c o n d i t i o n s w i l l  now  signal.  be  described. An OMA  can be used i n two modes o f o p e r a t i o n .  I n the c o n t i n u o u s  mode  ( a l s o c a l l e d " r e a l t i m e " mode), the 500 c h a n n e l s of the OMA  a r e scanned  every 32 msec w i t h an open time of 768 usee between s c a n s .  I n t h i s mode,  the OMA  can s t o r e about 5,000 counts per c h a n n e l , each count  corresponding  to ^ 20 v i s i b l e photons. I n the gated mode, the 500  c h a n n e l s a r e s e n s i t i s e d d u r i n g a d e s i r e d time  i n t e r v a l , w h i c h must be s h o r t e r than Gating i s achieved a t ^ 7 kV.  by h o l d i n g  and  w i t h i n the 768  the photocathode of the image i n t e n s i f i e r  A g a t i n g p u l s e of 1.1 kV t o 1.4  photocathode up t o the ^ 8.2  ysec open time.  kV b r i n g s the v o l t a g e o f  kV r e q u i r e d f o r f u l l s e n s i t i v i t y .  the  The  m a n u f a c t u r e r c l a i m s t h a t g a t i n g times as s h o r t as 10 nsec a r e p o s s i b l e , but i t w i l l be shown t h a t t h i s i s o n l y the case i f the s i g n a l r e c e i v e d w i t h i n the g a t i n g time i s s h o r t e r than 10 n s e c .  see  specifications  Otherwise, very  severe  distortions w i l l In  result.  o r d e r t o t e s t t h e response o f t h e OMA d e t e c t o r under v a r i o u s  c o n d i t i o n s , t h e f o l l o w i n g experiment was s e t up  "_~_~j!WMiiMiiiiiiiiitiimmuntHM  Z  Pinch  7i—• G r o u n d G l a s s j  Polarizers and PockelsCell  Screen  i  , , , , , ,  [  ,  Screened Room Extension  (inrad 261-150) Gate Pulse in  4 IT  Spectrograph  • • OMA ( P A R 12501 ISIT )  F i g u r e ( 4 - 4 ) : E x p e r i m e n t a l setup t o t e s t t h e response o f the OMA i n gated mode. The s p e c t r o g r a p h i s s e t t o z e r o o r d e r t o e l i m i n a t e s p e c t r a l dependences. The Z-pinch s e r v e s as a w h i t e l i g h t s o u r c e o f ysec d u r a t i o n .  The  d e t e c t o r i s mounted i n t h e f o c a l p l a n e o f a monochromator s e t t o z e r o order to transmit white l i g h t . c o n s i s t i n g o f 10 s l i t s  On t h e e n t r a n c e s l i t p l a n e a package  (25 thou wide, 25 thou a p a r t ) i s mounted.  The  w h i t e l i g h t image o f t h i s s l i t package i s r e g i s t e r e d by t h e d e t e c t o r .  such a s l i t package was a l r e a d y used by (26) t o o p t i m i z e t h e g a t i n g voltage.  84.  Fig.  (4-5) shows the response when the d e t e c t o r o p e r a t e s i n the r e a l  time mode.  The r e s o l u t i o n i s about 7 c h a n n e l s ; the i n t e n s i t y  a c r o s s the 500 c h a n n e l s i s r e a s o n a b l y f l a t .  response  D e f i c i e n c i e s a r e due t o  pincushion d i s t o r t i o n .  real t i m e  A*\  r\  100  Figure (4-5): Fig.  n  u u  200  U 300  u u u 400  Response o f the OMA  channel  No-  500  i n r e a l time.  (4-6) shows the response i n gated mode a t l o n g g a t i n g t i m e s .  g a t i n g was done e l e c t r o n i c a l l y o n l y ; the g a t i n g time was  1.2  i s seen t h a t some r e s o l u t i o n i s l o s t and a s t r e t c h i n g of the a c r o s s the c h a n n e l s o c c u r s .  The  ysec.  It  spectrum  These d i s t o r t i o n s , however, a r e minor  and,  as they a r e l a r g e l y i n t e n s i t y independent, can be accounted f o r . Intensity 500  W  U 400  F i g u r e ( 4 - 6 ) : Response of the OMA w i t h 1.2 y s e c .  U  channel  No.  500  when e l e c t r o n i c a l l y gated  I am i n d e b t e d t o W. Seka f o r i n f o r m a t i o n about work t h a t has been done w i t h OMAs a t the U. o f R o c h e s t e r L a b o r a t o r y f o r L a s e r E n e r g e t i c s .  85.  F i g . (4-7) and F i g . (4-8) show t h e response when t h e g a t i n g t i m e i s 50 nsec and 6 nsec r e s p e c t i v e l y .  ,I ntensity 2000 +  400  channel 500  No.  F i g u r e ( 4 - 7 ) : Response o f the OMA. when e l e c t r o n i c a l l y gated w i t h " 5 0 nsecT  .Intensity 2000 H  500  100  channel  No.  F i g u r e ( 4 - 8 ) : Response o f t h e OMA when e l e c t r o n i c a l l y gated w i t h 6 n s e c . The d i s t o r t i o n s f o r 50 nsec g a t i n g time a r e o b v i o u s l y s e v e r e and f o r 6 nsec g a t i n g time t h e d e t e c t o r becomes u s e l e s s . These d i s t o r t i o n s a r e presumably caused by an i n c o r r e c t and t i m e 42v a r y i n g v o l t a g e a p p l i e d t o t h e photocathode  d u r i n g t h e switch<on and  s w i t c h of f o f t h e g a t i n g p u l s e . F i r s t i t was t r i e d t o improve t h e o p e r a t i o n o f t h e OMA i n gated mode by i m p r o v i n g t h e e l e c t r o n i c s o f t h e g a t i n g c i r c u i t r y as suggested by i n (45)  86.  Additionally,  t h e c a b l e c a r r y i n g the HV g a t i n g p u l s e t o t h e photocathode  of t h e f i r s t i n t e n s i f i e r was removed from i n s i d e t h e OMA and f e d d i r e c t l y i n t o t h e OMA head t e r m i n a t i o n (see 4-4). I t , however, soon was e v i d e n t t h a t t h e remedy c o u l d n o t r e a d i l y be a c h i e v e d by e l e c t r o n i c a l means o n l y . To gate t h e incoming  l i g h t w i t h an e l e c t r o - o p t i c a l s w i t c h r a t h e r than  g a t i n g t h e OMA e l e c t r o n i c a l l y e l i m i n a t e d t h e d i s t o r t i o n s i n t h e r e c o r d e d spectrum, b u t c a r e f u l measurements showed t h a t a c o n t r a s t r a t i o o f about 400:1  was t h e b e s t t h a t c o u l d be a c h i e v e d w i t h t h i s method.  To combine t h e advantages o f b o t h methods, i . e . t h e d i s t o r t i o n f r e e g a t i n g by s w i t c h i n g the incoming  l i g h t and t h e good c o n t r a s t o b t a i n e d by  g a t i n g t h e OMA e l e c t r o n i c a l l y , t h e f o l l o w i n g e x p e r i m e n t a l setup was used. I n o r d e r t o l e t t h e l i g h t s i g n a l r e a c h t h e d e t e c t o r o n l y d u r i n g t h e time when the e l e c t r o n i c a l g a t i n g p u l s e v o l t a g e i s c o n s t a n t , an o p t i c a l g a t i n g p u l s e (30 nsec) was f i t t e d t e m p o r a l l y i n t o a 50 nsec e l e c t r o n i c pulse.  The v o l t a g e o f the e l e c t r o n i c .  gating  g a t i n g p u l s e was a d j u s t e d t o  g i v e t h e l e a s t d i s t o r t i o n s a c r o s s t h e whole spectrum a t l o n g g a t i n g t i m e s . The  t i m i n g o f t h e two p u l s e s can be done w i t h  synchronized  cable discharges.  F i g u r e ( 4 - 9 ) : E l e c t r o n i c a l and o p t i c a l g a t i n g p u l s e t e m p o r a l l y f i t t e d i n t o each o t h e r . P u l s e h e i g h t i s 1.2 kV.  87.  Fig.  (4—9) shows t h a t d u r i n g the time the o p t i c a l g a t i n g p u l s e i s s w i t c h e d ,  the v o l t a g e of the e l e c t r o n i c Fig.  gating pulse i s quite  (4-10) shows a g a i n the r e a l time response o f the OMA,  ( F i g . (4-4)) now i n c l u d e s the P o c k e l s a c r o s s the spectrum now  sensitive  a r e a of the  cell.  The i n t e n s i t y  but the setup distribution  a r i s e s m a i n l y from t h e f a c t t h a t the open  a p e r t u r e of the P o c k e l s , c e l l (= 15 mm)  Fig.  stable.  was o n l y s l i g h t l y l a r g e r  than the  OMA.  (4-11) shows the performance  of the OMA  i n gated mode f o r b o t h g a t i n g  p u l s e s combined.  F i g u r e s (4-10) and (4-11): Response of the OMA (a) i n r e a l time (b) f o r the i d e n t i c a l setup when e l e c t r o n i c a l l y gated w i t h 50 nsec and o p t i c a l l y gated w i t h 30 n s e c .  88. The absence o f any background  such as i n F i g . (4-7) i s i m m e d i a t e l y o b v i o u s .  The i n t e n s i t y d i s t r i b u t i o n o f t h e r e a l time spectrum i s c l o s e l y r e p r o duced.  F i g . (4-12) shows t h a t t h e r e s o l u t i o n  i s improved as compared t o t h e e l e c t r o n i c a l  i n t h i s double g a t i n g mode  gating only.  number of channels 15-  10 5  100  200  300  400  500  channel number  F i g u r e ( 4 - 1 2 ) : A comparison o f t h e f o c u s i n g p r o p e r t i e s f o r t h e i n v e s t i g a t e d c a s e s . The number o f c h a n n e l s on t h e r i s e and f a l l o f t h e s l i t image i s shown as a f u n c t i o n o f c h a n n e l number f o r t h e t h r e e c a s e s . The upper s o l i d Surve shows t h e e l e c t r o n i c a l l y gated mode, t h e lower s o l i d c u r v e s shows t h e r e a l time b e h a v i o u r and t h e dashed one shows the r e s u l t s from t h e combined g a t i n g p u l s e s .  I t f i n a l l y was observed t h a t i n t h e gated mode, t h e i n t e n s i t y of t h e OMA i s o n l y l i n e a r up t o a t most ^ 2000 c o u n t s / c h a n n e l . i l l u s t r a t e d i n F i g . (4-13).  sensitivity This i s  89.  counts  attenuation 316  100  31.6  10  3.16  factor  F i g u r e ( 4 - 1 3 ) : Shown a r e t h e number o f counts i n a g i v e n c h a n n e l as a f u n c t i o n o f i n t e n s i t y . The i n t e n s i t y was v a r i e d by i n s e r t i n g f i l t e r s of i n c r e a s i n g n e u t r a l d e n s i t y i n the l i g h t p a t h between t h e s o u r c e and t h e OMA (see F i g . ( 4 - 4 ) ) . From t h e measurements p r e s e n t e d , t h e f o l l o w i n g c o n c l u s i o n s can be drawn. The background  observed i n t h e spectrum when t h e OMA i s gated  electron-  i c a l l y o n l y ( F i g . (4-7)) a r i s e s from l e a k a g e o f p h o t o c u r r e n t due t o l i g h t r e a c h i n g t h e d e t e c t o r when o n l y 7 kV a r e a p p l i e d .  The d i s t o r t i o n i n t h e  i n t e n s i t y d i s t r i b u t i o n i s indeed due t o t h e s w i t c h o n and s w i t c h o f f p r o c e s s w i t h l i g h t f a l l i n g on t h e OMA s e n s i t i v e elements as suggested by (42) The advantages  o f t h e double g a t i n g t e c h n i q u e a r e , a p a r t from  the d i f f i c u l t i e s mentioned  removing  above, t h a t :  The c o n t r a s t r e q u i r e m e n t s f o r the o p t i c a l gate a r e n o t any more determined by t h e time t h e l i g h t s o u r c e i s a c t i v e , but by t h e e l e c t r o n i c time.  gating  Hence, t o a c h i e v e f a s t e r g a t i n g t i m e s , o n l y t h e o p t i c a l g a t i n g  p u l s e needs t o be s h o r t e n e d .  90.  The q u a l i t y r e q u i r e m e n t s  ( e . g . , squareness) f o r the e l e c t r o n i c .  (as w e l l  as o p t i c a l ) g a t i n g p u l s e a r e much r e l a x e d , as l o n g as the v o l t a g e i s s t e a d y d u r i n g the s w i t c h i n g time of the o p t i c a l g a t e . e l i m i n a t e s the need f o r e l a b o r a t e g a t i n g c i r c u i t s .  This  completely  91.  4.3 S p e c t r o s c o p i c measurements o f plasma d e n s i t y and temperature u s i n g the 4686$ l i n e o f He I I .  The double g a t i n g t e c h n i q u e d e s c r i b e d i n 4.2  will  now be a p p l i e d t o  s p e c t r o s c o p i c temperature and d e n s i t y measurements u s i n g t h e 4686$ l i n e o f He I I .  Even though t h i s type o f d i a g n o s t i c s had a l r e a d y been used,  improved measurement appeared d e s i r a b l e .  Fig.  (4-14) shows, as an  example, t h e 4686$ p r o f i l e a t p i n c h time t = + 300 n s e c , composed o f f i v e s e p a r a t e measurements.  -100A  0  •ipoA  F i g u r e ( 4 - 1 4 ) : D a t a o f e a r l i e r s p e c t r o s c o p i c a l measurements Composed l i n e p r o f i l e a t 4686$ a t t = + 300 nsec.  D e s p i t e e x c e l l e n t e x p e r i m e n t a l work, t h e means a v a i l a b l e a t t h a t s i m p l y d i d not a l l o w b e t t e r d a t a t o be o b t a i n e d .  26  time  92.  93.  F i g . (4-15) shows a s e l e c t i o n  of 4686$ p r o f i l e s o b t a i n e d w i t h the double  g a t i n g .technique (30 nsec o p t i c a l , 50 nsec e l e c t r i c a l ) and a monochromator 26 of l e s s d i s p e r s i o n than used p r e v i o u s l y .  The e x p e r i m e n t a l setup  was  e s s e n t i a l l y the same as shown i n F i g . ( 4 - 4 ) , of c o u r s e w i t h o u t ground g l a s s s c r e e n , and the plasma was v i e w e d i s i d e on.— As a comparison, the r i g h t p i c t u r e i n F i g . (4-15) shows the r e s u l t o b t a i n e d w i t h 50 nsec e l e c t r o n i c a l g a t i n g o n l y . 26 t h a t the OMA  used by Houtman  I t must be  emphasized  had o n l y one image i n t e n s i f i e r .  The  OMA  employed i n the measurements d e s c r i b e d here had two image i n t e n s i f i e r s which r e s u l t e d i n more s e v e r e d i s t o r t i o n s electronically  when the OMA  was  gated  only.  E v a l u a t i n g the w i d t h of these l i n e s t o o b t a i n the e l e c t r o n d e n s i t y and the  t o t a l l i n e t o continuum i n t e n s i t y r a t i o t o o b t a i n the e l e c t r o n  temperature » ^ J  4  o f the plasma a t a g i v e n t i m e , one o b t a i n s the d a t a  shown i n F i g . (2-1) which agree w e l l , w i t h the i o n f e a t u r e Thomson scattering  measurements, as f a r as the d e n s i t y i s concerned.  As f o r the  t e m p e r a t u r e s , the t h e o r i e s a l l o w i n g the d e t e r m i n a t i o n of temperature  from  the l i n e t o continuum r a t i o of i n t e n s i t i e s Opf) a r e t o o u n c e r t a i n f o r r a t i o s < 1. a. T h i s , and the d i s a p p e a r a n c e of the 4686A l i n e a t h i g h e r temperature 5  due  t o a d e c r e a s e i n the amount of H e l l i o n p r e s e n t , does not a l l o w f o r a good temperature measurement a t p i n c h times of i n t e r e s t .  f o r — «* 1, a t •• d e n s i t i e s o f ^ 5 x 1 0 , p r e d i c t s about 5 eV. 1 8  (46) p r e d i c t s about 40 eV,  (47)  Specifications Z-pinch D e t a i l s o f t h e Z - p i n c h a r e d e s c r i b e d i n R e f . 26 . the most i m p o r t a n t  He - f i l l i n g  Here, o n l y  c h a r a c t e r i s t i c s s h a l l be d e s c r i b e d .  pressure  1.2 T o r r  inner radius v e s s e l  5.08 cm  outer r a d i u s v e s s e l  5.72 cm  m a t e r i a l of v e s s e l  pyrex  Electrode separation  (copper)  35.6 cm  Bank  capacitance  84 yF  Bank  inductance  33 n H  Bank energy a t 11.5 kV charging  voltage  5.6 k J  T y p i c a l maximum c u r r e n t o f discharge  150 k Amp  Time o f maximum d e n s i t y and  temperature  2.0 ys a f t e r i n i t i a l breakdown  95.  Figure (5-1): Shows the c i r c u i t r y o f the Z - p i n c h d i s c h a r g e bank. Note t h e added p r e i o n i z a t i o n d i s c h a r g e a t the anode, mentioned i n 2.2.  Z-Pinch  Crytron Trigger Unit  100 M  -  300 k  5k  •Wl! Charge 100 M  HV Supply 11-5 kV  Dump  96. A typical  t r a c e as p i c k e d up by the Rogowsky c o i l i s shown i n the  f i g u r e below.  Maximum c u r r e n t I = 180 k  5V  amp.  500  ns  ,' d t  1  dI  F i g u r e (5-2) : - j ^ - as a f u n c t i o n of time; Rogowsky c o i l  (2)  C0  2  signal.  laser  Type:  Lumonix T600  Cavity:  unstable resonator c o n f i g u r a t i o n  Output geometry:  see F i g s . (2-1)  and  (2-2).  T y p i c a l o u t p u t p u l s e s a t an energy of 27 J o u l e s i s shown i n the s e c t i o n (3)  (3)  Detectors.  Detectors Au Ge:  Gold doped germanium semiconductor d e t e c t o r , l i q u i d n i t r o g e n c o o l e d , s e n s i t i v e f o r X < 11 C a l i b r a t e d s e n s i t i v i t y a t 10.6 S e n s i t i v e a r e a 16 Fig. Au Ge  u i s 6.7  V/mJ.  mm . 2  (5-3) shows the C 0 detector.  u.  2  l a s e r p u l s e as r e g i s t e r e d by  the  100 mV  Figure  100ns  (5-3):  l a s e r p u l s e , Au Ge d e t e c t o r .  Pyrd e l e c t r i c detector:  M o l e c t r o n Corp Model P3-00  50% o f maximum s e n s i t i v i t y  f o r X > 8 u.  C a l i b r a t e d s e n s i t i v i t y a t 10.6 u i s b e t t e r than 1.5 V/mJ. S e n s i t i v e area 1 Fig.  mm . 2  (5-4) shows t h e CO2 l a s e r p u l s e as r e g i s t e r e d by  the P y r o . e l e c t r i c d e t e c t o r .  5 0 mV  Figure (5-4): C0  0  100ns  l a s e r p u l s e , Pyro e l e c t r i c  detector.  Photon Drag D e t e c t o r :  O p t i c o n Corp L t d . , Model 7425  T h i s d e t e c t o r was used e x c l u s i v e l y as a t i m i n g m o n i t o r f o r the CO^ l a s e r , hence, a s e n s i t i v i t y c a l i b r a t i o n was unnecessary.  A t y p i c a l t r a c e i s shown below.  F i g u r e ( 5 - 5 ) : COv, l a s e r p u l s e , Photon Drag D e t e c t o r . Note t h e b e a t i n g o f l o n g i t u d i n a l l a s e r modes.  Gen Tech Energy M e t e r :  Gen Tech I n c . Model LED-200-C  F a s t b a l l i s t i c energy meter,  5 msec r e s p o n s e time.  C a l i b r a t e d s e n s i t i v i t y a t 10.6 ym i s 7.8  mV mJ  A t y p i c a l t r a c e i s shown below.  F i g u r e ( 5 - 6 ) : Response o f Gen Tech energy meter t o CO2 l a s e r p u l s e . A p o l l o Energy M e t e r :  A p o l l o L a s e r s I n c . , Model ACM-100  Range: 5 mJ t o 2 k J , d i g i t a l r e a d o u t .  99. (4)  Salt Optics A l l i n f r a r e d t r a n s m i t t i n g o p t i c s c o n s i s t e d of :,KCL., a l l m i r r o r s were aluminum-coated f r o n t s u r f a c e m i r r o r s . The f i g u r e b e l o w shows t h e measured  t r a n s m i s s i o n o f a 6 mm KCL s a l t  window (as used w i t h t h e Au Ge d e t e c t o r ) and o f a 12 mm  KCL f l a t  ( t h i c k n e s s o f t h e s a l t l e n s e ) as a f u n c t i o n o f w a v e l e n g t h .  °/o  Transmission  10oi  50  10  15  20  25  (5) Monochromator and Gratings" Monochromator: y m . J e r r a l A s h , 100 urn o r 130 ym s l i t s G r a t i n g s : a) Y o b i n I v o n , 50 x 50 mm,  153 lines/mm  B l a z e d a t 10.6 ym D i s p e r s i o n 110 8/:mm. b) Bausch and Lomb, 2.7" x 2.7", 60 lines/mm B l a z e d a t 16 ym D i s p e r s i o n 300 A*/mm  100.  (6)  Optical Multichannel  Analyser  S u p p l i e d by P r i n c e t o n A p p l i e d Research Corp, P r i n c e t o n N . J . The OMA used f o r t h e e x p e r i m e n t s d e s c r i b e d i n Chapter IV was type 12051.  As t h i s d e v i c e i s o f c o n s i d e r a b l e c o m p l e x i t y , i t  w i l l , - not be t r e a t e d f u r t h e r i n t h i s appendix.  For f u r t h e r  i n f o r m a t i o n r e f e r t o t h e i n s t r u c t i o n manual, a v a i l a b l e from P.A.R. c o r p .  (7)  Oscilloscopes T e k t r o n i x 7704 w i t h v e r t i c a l amps 7A16 and 7A12 T e k t r o n i x 466 f a s t s t o r a g e o s c i l l o s c o p e .  101. References  1.  Lubin, M., Goldman,. 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