PLASMA INSTABILITY IN HIGH-POWER CO2 LASER AMPLIFIERS

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PLASMA INSTABILITY IN HIGH-POWER CO2

LASER AMPLIFIERS

R. Bruzzese, S. Solimeno, G. Braglia, S. Martelluci, J. Quartieri

To cite this version:

JOURNAL DE PHYSIQUE CoZZoque C9, suppZdment au n u l l , Tome 41, novembre 1980, page C9-363

PLASMA INSTABILITY IN HIGH-POWER C02 LASER AMPLIFIERS

**

**

R. Bruzzese, S. Solimeno, G.L. ~ r a ~ l i a * , S. Martellucci and J. Quartieri Gruppo NazionaZe d i EZettronica Qtmntistica e PZasmi deZ C.N.R.

Abstract.- In the present paper a general modelaof plasma instabilities in high-power e-beam sustaL- ned Cop laser amplifiers is illustrated. This model improves the Nighan-Haas one by allowing expli- citly for the various degrees of vibrational freedom and-taking into account the stabilizing effect of the laser field intensity. Two numerical codes, which have been used to calculate the steady-sta- te plasma properties needed to carry out the stability analysis, are also presented. The model has been used to test the degree of thermal and ionic instability of an EDCL device using four-component gas mixture (Cop

-

N2

-

He-CO)

.

I . I n t r o d u c t i o n

The o b j e c t i v e o f t h i s paper i s t o e l u - c i d a t e t h e mechanism l e a d i n g t o i o n i c and t h e r m a l i n s t a b i l i t i e s i n EDCL d e v i c e s u s i n g four-component g a s mixturespnd p r e s e n t and d i s c u s s t h e growth t i m e s o f t h e most dange- r o u s i n s t a b i l i t y modes c a l c u l a t e d f o r a C O - N -He-CO system.

*

~ 6 e s e p a r a t i o n o f plasma i o n i z a t i o n from t h e e l e c t r o n t e m p e r a t u r e i s g e n e r a l l y a c h i e v e d i n high-power e l e c t r i c d i s c h a r g e c o n v e c t i o n l a s e r s , b y u s i n g a beam o f h i g h - energy e l e c t r o n s t o c r e a t e a uniform i o n i - ₁ z a t i o n t h r o u g h o u t t h e volume o f t h e plasma. The iligil-energy e l e c t r o n s a r e used t o pro- v i d e t h e i o n i z a t i o n , t h e e l e c t r o n t e m p e r a t u - r e b e i n g c o n t r o l l e d by a d j u s t i n g t h e e l e c - t r i c f i e l d . The e l e c t r i c a l power i s l i m i t e d by t h e o n s e t o f i n s t a b i l i t i e s which mani- f e s t t h e m s e l v e s i n t h e form o f a d i s c h a r g e c o l l a p s e from a u n i f o r m d i f f u s e glow i n t o a c o n s t r i c t e d a r c . I n f a c t , p l a s m a c o n s t r i c -

-

t i o n a n d / o r glow c o l l a p s e i s always fqund t o depend on e l e c t r i c a l power d e n s i t y

.

I n p a r t i c u l a r , i t i s t h e purpose o f t h i s paper t o a n a l y z e a l a s e r - s y s t e m model con- t a i n i n g a l a r g e enough number o f s t a t e pa- r a m e t e r s t o a c c o u n t f o r t h e main t y p e s o f . i n s t a b i l i t y . P a r t i c u l a r a t t e n t i o n h a s been p a i d t o t h e s t a b i l i z i n g e f f e c t o f t h e l a s e r beam. A plasm3 model s i m i a r t o t h a t c o n s i -

₄

d e r e d by Haas and Nighan h a s been used.

The s t e a d y - s t a t e plasma p a r a m e t e r s ( s e - condary i o n i z a t i o n and a t t a c h m e n t c o e f f i - cients,electronic,translational and v i b r a - t i o n a l t e m p e r a t u r e s a l o n g t h e l a s e r c h a n n e l e t c . ) have been c a l c l a t e d by u s i n g a B o l t -

_t

zmann n u m e r i c a l code ,which h a s been t e s t e d by a Monte-Carlo s i m u l a t i o n o f . t h e d i s c h a r - i

ge ,and a n u m e r i c a l code L E B I N T ~ ,which h a s been developed f o r a four-component e-beam p e i o n i z e d l a s e r m i x t u r e .

I n c o n t r a s t t o H a a s , t h e p r e s e n t model a l l o w s f o r t h e v a r i o u s d e g r e e s o f v i b r a t i o - n a l freedom e x p l i c i t l y . By c o n s i d e r i n g a system whose o n l y components a r e atoms and d i a t o m i c m o l e c u l e s of a s i n g l e t y p e , t h e Haas-Nighan model h a s o n l y one v i b r a t i o n a l t e m p e r a t u r e . I n t h e C02 system,however, t h e r e a r e a t l e a s t two v i b r a t i o n a l tempera- t u r e s l y i n g between 300 and 500 O X ( l o w e r l a s e r l e v e l ) and 3000

OK

( u p p e r L e v e l ) . I n t h e p r e s e n t model both t h e s e v i b r a t i o n a l t e m p e r a t u r e s have be.en c o n s i d e r e d .

F i n a l l y , t h e Nighan model has a l s o been extended by t a k i n g i n t o a c c o u n t t h e p r e s e n - c e o f t h e r a d i a t i o n f l u x i n t h e l a s e r c a v i - t y . When t h e e l e c t r i c a l power t r a n s f e r t o v i b r a t i o n i s l a r g e , l o c a l h e a t i n g o f t h e g a s because o f a s u r g e i n V-T r e l a x a t i o n may be s u f f i c i e n t t o overcome t h e s t a b i l i z i n g e f f e c t o f t h e r m a l c o n d u c t i o n w i t h t h e r e - s u l t t h a t t h e i n i t i a l i n c r e a s e i n T i s am- p l i f i e d ( p o s i t i v e f e e d ~ b a c k which can l e a d t o thermal i n s t a b i l i t y '

1.

The lase^ beam, however,depopulates by s t i m u l a t e d e m i s s i o n t h e upper l a s e r l e v e 1 , s o p r o v i d i n g a n a d d i - t i o n a l c h a n n e l f o r t h e d i s p o s a l o f t h e v i r b r a t i o n a l e n e r g y s t o r e d i n t h e C02 asymme: t r i c s t r e t c h i n g mode w i t h o u t h e a t l n g t h e gas. The s t a b i l i z i n g e f f e c t of t h e l a s e r beam h a s been s t u d i e d by i n t r o d u c i n g i n t h e e q u a t i o n s f o r t h e a m p l i t u d e s o f t h e p e r t u r - bed plasma p r o p e r t i e s , a r a d i a t i o n beam of c o n s t a n t i n t e n s i t y .

11. T h e o r e t i c a l a n a l y s i s

A s a l r e a d y m e n t i o n e d , t h e p r e s e n t ana- I S t i t u t o d i EZettrotecnica, FacoZtd d i ~ ~ e ~ ? l e r i a " _{, l}

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i n t o t h r e e m a j o r p a r t s : f l u i d dynamics ,mo-- l e c u l a r k i n e t i c s and d i s c h a r g e c h a r a c t e r i s - t i c s . The a t t e n t i o n w i l l be f o c u s e d o n t h e second p a r t where t h e complex e v o l u t i o n o f t h e C02 :N2:He:C0 s y s t e m comes i n t o p l a y t h u s making more s t r i k i n g t h e d e p a r t u r e from t,he Haas model.

The f l u i d dynamics o f t h e s y s t e m i s d e s c r i b e d by a s e t o f d e n s i t y e q u a t i o n s f o r t h e main e l e c t r i c a l l y a c t i v e s p e c i e s , i . e . , t h e e l e c t r o n s ( n and t h e p o s i t i v e ( n ) and n e g a t i v e ( n n ? i o n s ( f o r t h e compleee s e t o f e q u a t i o n s s e e R e f . 7 ) . I n t h i s s e t of e q u a t i o n s t h e f o l l o w i n g e l e m e n t a r y p r o - c e s s e s h a v e b e e n c o n s i d e r e d : e l e c t r o n - i m p a - c t i o n i z a t i o n o f m o l e c u l e s ( r a t e c o e f f i c i - e n t k . ) , e l e c t r o n - m o l e c u l e a t t a c h m e n t ( k 1, two-b&dy e l e c t r o n - i o n r e c o m b i n a t i o n ( k z y ,

.

p o s i t i v e i o n - n e g a t i v e i o n r e c o m b i n a t i o n (kl) r and d e t a c h m e n t by n e u t r a l i m p a c t ( k ) . An i n d e p e n d e n t l y c o n t r o l l a b l e s o u r c e

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i o n i - z a t i o n ( S e x t ) i n t h e form o f a n e-beam h a s a l s o been c o n s i d e r e d . Due t o t h e f a s t e l e c - t r o n r e l a x a t i o n p r o c e s s e s , t h e plasma h a s been assumed n e u t r a l 3 o n t h e t i m e s c a l e o f t h e i n s t a b i l i t i e s d i s c u s s e d i n t h i s p a p e r . T h i s i n t u r n i m p l i e s V . E = O . CO l a s e r k i n e t i c s h a s been , d i s c u s s e d 2 by many a u t h o r s 8 . The L a n d a u - T e l l e r e q u a - t i o n s h a v e been u s e d f o r d e s c r i b i n g t h e e - n e r g y s t o r e d i n t h e v i b r a t i o n a l d e g r e e s of f r e e d o m o f C O

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a n d C O . I m p l i c i t i n t h e s e 2 e q u a t i o n s i s 2 t h e a s s u m p t i o n o f p a & i a l t h e r m a l e q u i l i b r i u m f o r t h e r o t a t i o n a l a n d v i b r a t i o n a l d e g r e e s of f r e e d o m . E s s e n t i a l t o t h e mechanism o f e n e r g y r e l a x a t i o n a n d e x c h a n g e i s t h e p h o t o n ' d e a c t i v a c t i o n o f t h e u p p e r l a s e r l e v e l t o t h e l o w e r one: I n t h i s s e t of k i n e t i c e q u a t i o n s t h e r a t e o f c h a n - ge o f t h e e n e r g y o f t h e v i b r a t i o n a l modes by c o l l i s i o n a l r e l a x a t i o n ( V - T ) , e n e r g y e x - ghange (V-V) a n d photon e m i s s i o n o r a h s o r - p t i o n h a s been c o n s i d e r e d ( a s r e g a r d s t h e c o m p l e t e s e t o f e q u a t i o n s s e e R e f . 9 ) .

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' t h e r a t e f i x e d by h e e l e c t r i c a l power JE d e p o s i t e d i n t h e plasma,cp i s t h e s p e c i f i c h e a t a t c o n s t a n t p r e s s u r e and

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t r a n s l a t i o n - r o t a t i o n e x ~ i t a t i o n , F ~ ~ = Z , ~ ' $ ~ F ~ ~ - = ~ F ; ~ and F ~ ~ ~ =I i s t h e l a s e r z ~ F ~ ~ ~ . . . f i e l d i n t e n s i t y . F i n a l l y , ~ l and ~3 a r e t h e v i b r a t i o n a l t h e r m a l c o n d u c t i v i t i e s o f t h e s e t s l a b e l l e d 1 and 3 r e s p e c t i v e l y .

The l a s t e q u a t i o n o f t h e above system h a s been o b t a i n e d by Haas and Nighan under t h e assumption o f a n i n s t a n t a n e o u s r e s p o n s e o f t h e e l e c t r o n energy t o a l o c a l d i s t m - bance . ' I n t h i s e q u a t i o n v '

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_{v ~ , T ~} u,Te - v ~ ~ , ~ ~ c o s 2 $ , w h e r e v u i s t h e t o t a l e l e c t r o n energy-exchange c o l l i s i o n f r e q u e n - cy and VTR i s t h e momentum-transfer c o l l i - s i o n f ~ e q u e n c y

.

It i s worth n o t i n g t h a t t h e d e n s i t y f l u c t u a t i o n nk h a s been e l i m i n a t e d from t h e above system i n v i r t u e o f t h e r e l a t i o n , n k = - T k , which h o l d s i n t h e i n i t i a l phase o f disturbance growthywhen t h e p r e s s u r e f l u c - t u a t i o n s a r e n e g l i g i b l e .

JOURNAL DE PHYSIQUE

p r o p e r t i e s . To c a l c u l a t e t r a n s p o r t p r o p e r - t i e s and plasma p a r a m e t e r s a Boltzmann nu-

5 m e r i c a l code h a s been used

.

The e l e c t r o n motion i n t h e l a s e r mixtu- r e s 6:34:54:6 (C02:N2:He:CO) ( 1 ) and

7.5:23:63:7.5 ( 2 1 , a c t e d upon by a d . c . e l - e c t r i c f i e 1 E,has been s t u d i e d under con- d i t i o n s of s p e c i a l i n t e r e s t f o r t h e s t a b i - l i t y a n a l y s i s . T r a n s p o r t coefficients,i.e.,electron d r i f t v e l o c i t y W , l o n g i t u d i n a l and t r a n s v e r - s e d i f f u s i o n c o e f f i c i e n t s D L and DTyand i o n i z a t i o n and a t t a c h m e n t c o e f f i c i e n t s ki and ka ( s e e F i g . 1 ) have been o b t a i n e d a s a f u n c t i o n o f E/n. The o p e r a t i n g c h a r a c t e r i s t i c s o f t h e m i x t u r e s have a l s o been s t u d i e d by c a l c u - l a t i n g t h e f r a c t i o n o f e l e c t r o n energy which

i s

l o s t by: 1) e l a s t i c c o l l i s i o n s , c i a t i v e p r o c e s s

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+

C a y CO

+

0 - ) . The e l e c t r o n s have a l s o been p e r m i t t e d t o under- go r o t a t i o n a l c o l l i s i o n s , f o r which t h e con- t i n u o u s a p p r o x i m a t i o n h a s been u s e d . The e l e c t r o n - e n e r g y d i s t r i b u t i o n s were f i r s t o b t a i n e d by s o l v i n g t h e Boltzmann e - q u a t i o n f o r t h e g i v e n c r o s s - s e c t i o n s . The "two-term expansion1' o f t h e e l e c t r o n v e l o - c i t y d i s r i b u t i o n f u n c t i o n was assumed t o be v a l i d r o and n u m e r i c a l s o l u t i o n o f t h e Boltzmann e q u a t i o n was o b t a i n e d by t h e backward p r o l a n a t i o n t e c h n i q u e o f Phelps 1

f

and co-workers

.

The v a l i d i t y o f t h i s procedure i s known t o be based on some b a s i c a s s u m p t i o n s w h i c h , a t t h e e n d , r e q u i r e t h e t o t a l i n e l a s - t i c c o l l i s i o n f r e q u e n c y t o be s m a l l w i t h r e s p e c t t o t h e t o z a l e l a s t i c c o l l i s i o n F i g . 1 . C a l c u l a t e d v a l u e s o f k. and k f o r m i x t u r e (1) a s a f u n c t i o n of ~ 7 n . r o t a t i o n a l e x c i t a t i o n o f C02,N2,C0 and ex- c i t a t i o n

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o f t h e mixed modes o f t h e C02 ( b e n d i n g and symmetric s t r e t c h i n g ) ; $3 2) e x c i t a t i o n (FeV) o f t h e asymmetric s t r e - t c h i n g mode o f t h e C02 and t h e f i r s t e i g h t v i b r a t i o n a l l e v e l s of N 2 ; 3 ) e x c i t a t i o n o f t h e f i r s t t e v i b r a t i o n a l l e v e l s o f C O

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t h e m i x t u r e s and m o l e c u l a r d i s s o c i a t i o n - o f C09; 5 ) i o n i z a t i o n o f t h e g a s e s ok t h e m ' x t u r e s . The c a l c u l a t e d f u n - c t i o n s F~$',F,C$O

. .

.

, a r e r e p r e s e n t e d i n F i g . 2 .

The e l e c t r o n s .have been a l l o w e d t o un- d e r g o 4 d i f f e r e n t k i n d s o f e l a s t i c c o l l i - s i o n s (26 v i b r a t i o n a l l e v e l s , l 7 e l e c t r o n i c l e v e l s , 4 i o n i z i n g p r o c e s s e s and t h e d i s s o - F i g . 2 . C a l c u l a t e d n e t ower i n u t

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a s a u n c t l o n o f E/n. f r e q u e n c y . But i n t h e g a s m i x t u r e s we a r e i n t e r e s t e d i n , t h i s c o n d i t i o n i s s y s t e m a t i - c a l l y v i o l a t e d ( s e e Ref. 5 ) . T h e r e f o r e it i s o f p a r t i c u l a r i n t e r e s t t o t e s t t h e li- m i t s o f t h e c o n v e n t i o n a l t h e o r y and s e e i f it i s a b l e t o s u c c e s s f u l l y p r e d i c t t h e c o r - r e c t macroscopic c o e f f i c i e n t s and t h e va- r i o u s r a t e s of e x c i t a t i o n . The s t u d y o f t h e l i m i t s o f t h e c o n v e n t i o n a l t h e o r y , i . e . o f ' t h e d a t a used i n t h e s t a b i l i t y a n a l y s i s , h a s been made by t h e Monte-Carlo t e c h n i q u e

( t h e d e t a i l s o f t h e c a l c u l a t i o n s a r e d i s - c u s s e d i n Ref - 5

1.

r e s t f o r l a s e r s and t o e l s s t i c c o l l i s i o n s . The macroscopic c o e f f i c i e n t s W,DT,and DL o b t a i n e d from t h e s o l u t i o n o f t h e B o l t z - mann e q u a t i o n a l s o a g r e e w i t h i n a v e r y few p e r c e n t w i t h t h e Monte-Carlo r e s u l t s f o r E/n=15 Td.

The

electronic,translational

and v i - b r a t i o n a l t e m p e r a t u r e s a l o n g t h e l a s e r c h a n n e 1 , a l s o needed i n t h e s t a b i l i t y a n a - l y s i s , h a v e been c a l c u l a t e d by u s i n g a nu- m e r i c a l code-LEBINT which h a s been d e v e l o - ped f o r a four-component e-beam p r e i o n i z e d l a s e r m i x t u r e . A d e t a i l e d a c c o u n t o f t h i s :code c a n be found i n R e f . 6 .

The r e s u l t s o f t h i s s i m u l a t i o n a r e p l o t t e d i n F i g . 3 f o r t h e l a s e r m i x t u r e ( 1 ) .

'L

The t i m e - c o n s t a n t s T ~

?:

, and T $ have been c a l c u l a t e d ( s e e F i g . 4 ) by u s i n g t h e s e t e m p e r a t u r e p r o f i l e s a l o n g t h e l a s e r c h a n n e l . a l s o been v e r i f i e d t h a t f o r k-1>0.3 cm t h e r o o t s a r e p r a c t i c a l l y i n d e p e n d e n t of k a s p o i n t e d o u t by Nighan. I n g e n e r a 1 , o n l y one p o s i t i v e r o o t h a s been found. The u n s t a b l e node h a s r e s u l t e d t o be i o n i c f o r t h e two m i x t u r e s (1) and

( 2 ) under t h e r e f e r r e d c o n d i t i o n s . The r e - ,

l a t i v e growth r a t e h a s been shown t o be s t o n g l y dependend on t h e c o n c e n t r a t i o n o f n e g a t i v e i o n s . T h i s i s c l e a r l y d i s p l a y e d i n F i g . 5 where c a l c u l a t e d v a l u e s o f v k f o r d i f - f e r e n t r a t i o s n n / n e have been p l o t t e d .

r

I!

[ S G C ~

f

F i g . 4 C a l c u l a t e d t i m e - c o n s t a n t s r T ,

::

2r3 and .rV F i g . 3 . C a l c u l a t e d e l e c t r o n s c ( T ) , v i b r a - t i o n a l ( T 1 , T

9

and t r a n s l a t ~ o n a f ( 2 . ) tem- p e r a t u r e s a l o n g t h e l a s e r c h a n n e l V . R e s u l t s

The i n s t a b i l i t y system h a s been used t o a n a l y z e t h e s t a b i l i t y r e g i o n s o f a plasma produced i n a n e-beam p r e i o n i z e d l a s e r chan-

2 n e l having

a

c r o s s s e c T i o n o f 10x10 cm

.

Two g a s m i x t u r e s ( 1 ) 6:34:54:6 (C02:N2:He: C O ) and ( 2 ) 7 . 5 : 2 3 : 6 2 : 7 . 5 , e n t e r i n g t h e chan- n e l a t a p r e s s u r e o f 66 T o r r a t 280 OK,have been examined. A power J E = 8.7 w/cm3 h a s been assumed a s t h e f a c t o r producing t h e r e q u e s t e d pumping o f t h e p r e i o n i z e d medium.

The r o o t s o f t h e i n s t a b i l i t y d i s p e r s i o n e q u a t i o n D(vk)=O have been c a l c u l a t e d f o r d i f f e r e n t v a l u e s o f k . I n s o d o i n g , i t h a s p i g . 5 . C a l c u l a t e d growth r a t e s o f ' o n i c ' k t a b i l i t y a l o n g t h e l a e r c h a ~ n e l t o r

di*c-

f e r e n t c n e n t r $ t l o n

08

n e g a t z v e i o n s I n t n l x t u r e

817.

The f l u c t u a c t i o n s Tik o f t h e v i b r a t i o - n a l t e m p e r a t u r e s and o f t h e e l e c t r o n i c den-

JOURNAL DE PHYSIQUE

t h e . $C+5e o w a s b . e ~ ef the

$n$e&biif'ty

which

has

Been

a 6 n f i ~ m ~ d

by

ffidiving

fss

t h e

approximate dispersion equation Dion( v k > = O .

I n f a c t , t h e above approximate d i s p e r s i o n e - q u a t i o n g i v e s t h e same u n s t a b l e r o o t o f t h e

f i r m t h e r e l a t i v e h i g h 'value o f t h e e l e c t r o -

VI.

C o n c l u s i o n s rlic f l u c t u a c t i o n s w i t h r e s p e c t t o t h e t r a n -

s l a t i o n a l t e m p e r a t u r e , a s r e q u e s t e d by t h e I n t h e p r e s e n t p a p e r a g e n e r a l model o f i o n i c c h a r a c t e r o f t h e i n s t a b i l i t y mode. On plasma i n s t a b i l i t y in high-power e-beam t h e o t h e r hand,'the r e l a t i v e l y h i g h Value of s u s t a i n e d C02 l a s e r a m p l i f i e r s i s p r e s e n t e d Tlk p r o v e s t h e need f o r d e c o u p l i n g t h e flue- t o g e t h e r w i t h

a

d e t a i l e d d i s c u s s i o n o f some t u a t l o n d s o f t h e lower l a s e r l e v e l tempera- e x p e r i m e n t a l c a s e s . Our model improves t u r e from t h e t r a n s l a t i o n a l o n e . T h i s Pro- t h a t of Haas and Nighan a s t h e v a r i o u s de- v i d e s c l e a r e v i d e n c e t o t h e 0 p p o r t u n i t Y o f g r e e s o f v i b r a t i o n a l freedom and t h e l a s e r improving t h e v i b r a t i o n a l k i n e t i c model of f i e l d a r e c o n s i d e r e d . <

t h e Haas-Nighan t h e o r y . Due t o t h e r a p i d The model h a s been used t o t e s t t h e de- i n c r e a s e o f T1 w i t h r e s p e c t t o T d u r i n g t h e V (seC1) i ,

-

-

-

Q Q P r e c t e q u a t i a n '

D(vk)zO.

For m i x t u r e ( 1 ) t h e appro.ximat$.

,disger-

s i o n e q u a t i o n Dth(vk)=O has a l s o been Yes- t e d . The r e l a t i v e v a l u e s o f v k a r e p r e s e n - t e d i n F i g . 7 f o r d i f f e r e n t l a s e r i n t e n s i - l o 2 = t i e s . The o b s e r v e d d r a s t i c r e d u c t i o n ' o f v k

for

Fph=O.l c o n f i r m s t h e c o n j e c t u r e t h a t l a s i n g o f t h e a c t i v e plasma p r a d u c e s

a

&a- b i l i z i n g e f f e c t on t h e t h e ~ m a l

modes.

A s

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

-

₁₀

-

-

-

arow w i t h t h e e l e c t r i c power d e p o s i t e d i n

the

p l a s m a , t h e t h e r m a l c o l l a p s e

of t h e

d i s - -&ge

can

be e f

f

i b i e n t l y c o n t r b S t 8 d :

-

4 I I I 0 2 4 6 8 F i g . 6 . C a l c u l a t e d f l u c t u a t i o n s o f t h e v i b - r a t i o n a l t e m p e r a t u r e s ( T l k and T S k ) , a n d of

t h e e l e c t r o n i c d e n s i t y nek f o r nn/ne=lO-1.

o

2 6 CIII

F i g . 7 . C a l c u l a t e d ~ r o w t h r a t e s b f t h e r m a l i n s t a b i l i t y a l o n g t h e l a s e r chann6l f o r d i f -

i n s t a b i i i t y

a n s e t , t h e f l u c t u a t i o n

of

t h e - f a - f e r e n t i n t e n s i t i e s ( F p h ) o f l a s e r beam.Note

s ~ p

u ~ ~ a r

i g v e l t e m p e r a t u r e can grow s o t h e d r a m a t i c d e c r e a s e o f

v

hen Fph r i s e s

g6nsng

nw

Qa Q V $ % ? C , Q ~ ~ t h a t

o f

the

e l s c t r o - t o

10% of SE.

SF

$enpixyt

T h i ~ , h o w a v e r , d o e s n o t d e s t r o y

$r&aa

&

t h s ~ a a l

arid

h h i a

i n s t a b i l i t i e s

an

Ebet

device u ~ i n g

four-rorilpbneat

9&8

MIX-

t u r e s

< c o 2

:N2

:He

:C-V). The m i ? t u r e s

(13

,6134

.-

:54:6 and ( 2 ' ) 7 . 5 : 2 3 : 6 2 : 7 . 5 have been exa-

mined. ₃₆₈

with respect to the formation of moving was performed under C.N.R. contract

N.

80.

s-triations in EDCL e-beam sustained lasers. 01828.98 ( ~ i ~ ~ l i ~ ~ d project on ~ i power ~ h

Lasers). Acknowledgements

The research work leading to this paper

References.

1)

J

.D .Daugherty

,

"Electron Beam Ionized Ga-

sesU,in 'Principles of Laser Plasmas',(ed. G.Bekefi), New York (1976).

2)

E.P.Velikov,Sov.J.P1asma

Phys.,L,463 (1975).

3) R.Haas,Phys.Rev.,A~,1017 (1973). 4) W.L.Nighan,Phys.Rev.,A~,1701 (1977). 5) G.L.Braglia,R.Bruzzese and G.L.Caraffinj

Lettere a1 Nuovo C i m e n t o , ~ , 1 3 9 , (1979).

6 ) S.Martellucci,J.Quartieri,G.Mastrocinque

and S.Solimeno,Il Nuovo Cimento,*,99 (1979).

7) W.L.Nighan and W.J.Wiegand,Phys.Rev.,A~

922, (1974).

8 )

K.

Smith and

R .M

.Thornson, 'Computer Mode-

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9)

R.Bruzzese,S.Solimeno,G.L.Braglia

and S.Martellucci,"Ionic and Thermal Instabili- ties in E-beam Preionized C02 EDCL Devices in the Presence of a Laser BearnW,(to be published).

10) L.G.H.Huxley and R.W.CromptonYtThe Dif-

fusion ans Drift of Electrons in Gases', New York (1974).