THE INFLUENCE OF GASDYNAMIC DISTURBANCES ON STABILITY OF SELF-SUSTAINED DISCHARGE IN A HIGH-REPETITION-RATE PULSED CO2-LASER

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THE INFLUENCE OF GASDYNAMIC

DISTURBANCES ON STABILITY OF

SELF-SUSTAINED DISCHARGE IN A

HIGH-REPETITION-RATE PULSED CO2-LASER

V. Baranov, D. Malyuta, V. Mezhevov, A. Napartovich

To cite this version:

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THE INFLUENCE OF GASDYNAMIC DISTURBANCES ON STABILITY OF SELF-SUSTAINED DISCHARGE IN A HIGH-REPETITION-RATE PULSED ~ 0 ~ - L A S E R *

V.Y. Baranov, D.D. Malyuta, V.S. Mezhevov and A.P. Napartovich.

I . V . Kurchatov I n s t i t u t e of Atomic Energy, Moscow, U. S. S. R.

Abstract.- It is shown experimentally that gas densityfluctuations~l% affect strongly a plasma sta- bility in an UV-preionized self-sustained discharge. The influence of gasdynamic disturbances crea- ted in a closed gas channel of a high-repetition-rate pulsed gas laser upon output laser performan- ces was studied. The interaction between acoustic waves and a diffuse glow discharge plasma leading to appearance of the thermoacoustic instability was observed.

There a r e a d d i t i o n a l p h y s i c a l proces- s e s due t o a f a s t gas flow and t o a h i g h p u l s e r e p e t i t i o n r a t e , which a r i s e when c r e a t i n g h i g h - r e p e t i t i o n - r a t e p u l s e d g a s l a s e r , b e s i d e s phenomena c h a r a c t e r i s t i c of s i n g l e p u l s e gas l a s e r s .

1. Authors of one of t h e p i o n e e r i n g works concerning h i g h - r e p e t i t i o n - r a t e pul-

s e d gas l a s e r s (HPGL) c o n s i d e r e d t h e a d i a - b a t i c expansion of a h o t g a s p l u g i n t h e n e a r - e l e c t r o d e boundary l a y e r a s t h e main average o u t p u t power l i m i t i n g f a c t o r [I

3.

I n l a t e r works, some o t h e r l i m i t i n g f a c t o r s were c o n s i d e r e d : expansion of a d i s t u r b e d r e g i o n owing t o t h e t u r b u l e n t i n t e r m i x i n g

l.23

; h e a t i n g of t h e g a s e n t e r i n g t h e d i s - charge r e g i o n by shock waves g e n e r a t e d by r a p i d p u l s e d energy r e l e a s e i n a d i s c h a r g e ; development of t h e thermoacoustic i n s t a b i - l i t y [3]; presence of gas d e n s i t y g r a d i - e n t s i n t h e d i s c h a r g e r e g i o n due t o e i t h e r a c o u s t i c d e n s i t y o s c i l l a t i o n s c r e a t e d by t h e d i s c h a r g e o r h e a t i n g ( o r c o o l i n g ) of a g a s i n t h e n e a r - e l e c t r o d e l a y e r s by cham- b e r w a l l s

131 .

*

Post deadline paper.

The l a x g e number o f v a r i o u s processes a f f e c t i n g a c u r r e n t flow i n a glow d i s - charge l e a d s t o appearance of numerous feedbacks which make t h e d i f f u s e dischaxge u n s t a b l e . I n s t a b i l i t i e s developing i n t h e d i f f u s e glow d i s c h a r g e a t an i n c r e a s e d p r e s s u r e appear both as domains ( t h e l a y e r s i n which e l e c t r i c f i e l d d i s t r i b u t i o n does n o t c o i n c i d e w i t h t h e o u t e r one) propaga-

ting bstween the e l e c t r o d e s , and as f i l a - ments [4]

.

I n t h e s i m p l e s t c a s e of a s e l f - s u s t a i n e d discharge, when ne i s determined by d i s c h a r g e i o n i z a t i o n o n l y and all t h e energy r e l e a s e d i n t h e g a s goes i n t o h e a t , t h e time of t h e h e a t i n s t a b i l i t y growth i s a t j o E - ~ ~ 5 ~ / c r n 3 . Here W i s t h e e n t h a l p y p e r u n i t volume, t h e c o n s t a n t A d e f i n e s t h e dependence of i o n i z a t i o n r a t e c o n s t a n t Ki upon

E/N.

I n n i t r o g e n , t h e r e i s one more mecha- nism f o r t h e d i s c h a r g e f i l a m e n t a t i o n due t o presence of v i b r a t i o n a l l y e x c i t e d mole- c u l e s . E l e c t r o n s i n t h e d i s c h a r g e c o l l i d e with t h e s e molecules, t h u s g a t h e r i n g a n a d d i t i o n a l energy by t h e second kind c o l l i -

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C9-310 JOURNAL DE PHYSIQUE

sions. This a c c e l e r a t e s processes of di- ment when the next voltage pulse should be r e c t and multistaged i o n i z a t i o n (and ex- applied t o the e l e c t r o d e s ,

c i t a t i o n of metastable nitrogen molecules The energy r e l e a s e l i m i t a t i o n i n a Np

(f13

E:

) a l s o ) . s i n g l e pulse i s connected with the dischax-

I n the case of a non-self-sustained ge filamentation, The main well-known e-beam c o n t r o l l e d discharge, the acoustic reason f o r t h i s e f f e c t i s the appearance i n s t a b i l i t y increment equals of gas d e n s i t y and/or gas mixture composi-

where

I),,

and

9d

a r e t h e attachment f i anfi detachment r a t e s , respectively, and =(JQJ!!J&E),!!%~ a c o u s t i c i n s t a b i l i t y growth

time i s a l s o commensurable with the pum- ping duration. Both energy r e l e a s e times t y p i c a l f o r CO2-lasers and v-t r e l a x a t i o n times a r e about 1

o'~,

.

.l o - ~ sec, t h a t , a s a r u l e , i s much smaller than c h a r a c t e r i s - t i c gasdynamic time

t

b,/c,

10-4 sec. Therefore, pulsed energy r e l e a s e i n a CO2- l a s e r mixture l e a d s t o a generation of simple waves with a magnitude g r e a t enough,

t i o n nonuniformities i n the discharge r e - gion. The density f l u c t u a t i o n

<

0

,

with a s c a l e l e n g t h much g r e a t e r than a d i f f u s i o n l e n g t h and much smaller than e l e c t r o d e ' s minimum dimensions,results i n sharp r e l a t i v e increase of the l o c a l energy r e l e a s e because of t h e l a r g e value of i o n i z a t i o n gain i n a discharge and i t s s e n s i t i v i t y t o

E/N.

The demand f o r t h e l o c a l energy r e - l e a s e t o be l i m i t e d l e a d s t o s p e c i f i c energy r e l e a s e decrease i n o t h e r regions of a discharge and, hence, t o reduction of a t o t a l energy r e l e a s e :

a s a r e s u l t of the U-shaped i n i t i a l d i s t u r -

_SW

_,

-

S9

-p

d & ~ ;

nm

bance decay. Afterwards, these waves trans-

W

9 &?nE

n o

form i n t o weak shock waves i n a characte- where

gi

i s the gas i o n i z a t i o n r a t e , E i s r i s t i c time

T

= A X

,

where the e l e c t r i c f i e l d , nm i s the plasma den-

(~pb/p)(cs/rl

AX

i s the s c a l e length f o r t h e i n i t i a l s i t y a t the moment of maximum c u r r e n t , no pressure g r a d i e n t , A p i s t h e i n i t i a l i s the d e n s i t y of a photoplasma ( f o r an wave magnitude, CS i s the sound v e l o c i t y electrode system with a photoionization), i n the undisturbed gas, i s the adiaba-

p

i s the ga,s density.

t i c exponent. s i n c e

(denVf)/(denE)

- I O , . I ~ ;

The gas plug expansion occurs

en(nvH$-lO..

.15; then t h e density f l u c t u a - simuLtaneously with the formation of waves t i o n

Ayf

1 should r e s u l t i n the

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s p i r a l placed

7

c m up t h e flow from e l e c - trodes.

The s p a t i a l d i s t r i b u t i o n of tempera- t u r e a r i s i n g from gas h e a t i n g by t h e s p i r a l was measured. The dependence of t h e maximum energy, W O , r e l e a s e d i n a d i s c h a r - ge per pulse upon d i s t u r b e d r e g i o n tempe- r a t u r e averaged over t h e d i s t a n c e between e l e c t r o d e s was measured. One can see i n t h e Fig.1 t h a t WO begins t o a l t e r a t g a s p r e h e a t

AT 0 . 7 K.

F i g . l

The i n f l u e n c e of gas d e n s i t y f l u c t u a -

,by s u r f a c e gas h e a t i n g ( o r cooling) ought t o be summarized.

3.

The most s t r o n g gas d e n s i t y d i s t u r - bance appearing a f t e r pulsed energy r e l e - a s e - i s t h e hot gas t h a t expands and i s c a r r i e d away from the i n t e r e l e c t r o d e spa- c i n g by the gas flow, The h o t gas plug dimension along t h e flow v s time, i s p l o t - t e d i n Fig.

3.

f o r d i f f e r e n t gas flow v e l o c i t i e s . T h e two s t a g e s of expansion

a r e observed. A t the f i r s t , r a p i d stage,

t ,< t o , plug1 S l e n g t h grows l i n e a r l y vs

time. The d u r a t i o n of t h i s s t a g e c o r r e s - ponds t o t h e pressure e q u a l i z a t i o n time

and, hence, i s determined by t h e a d i a b a t i c expansion of a heated gas.

_-

t i o n s conditioned by e l e c t r o d e s ' h e a t i n g upon maximum energy r e l e a e e p e r p u l s e was

s t u d i e d a l s o . An increased energy r e l e a s e

i n near-electrode regions promotes f i e r c e

₅

warming up t h e e l e c t r o d e s , The t h i c k n e s s

of t h e heated gas l a y e r before t h e next

rooo

2 m

c u r r e n t p u l s e equals zero a t t h e f r o n t edge ( r e l a t i v e l y t o gas flow) of e l e c t r o d e and i s sT=0.59 0. 1 cm a t t h e r e a r edge, Here

8

i s subsonic boundary l a y e r t h i c k n e s s and P r i s P r a n d t l number, The r e s u l t i n g dependence of t h e m a x i m energy r e l e a s e upon e l e c t r o d e s temperatu- r e i n t h e gas flow i s presented i n Fig.2,

F i g . 3

The second s t a g e i s more slow i h d

seems t o be conditioned by h e a t conductivity.

The hot gas plug expansion (allowed f o r thermal c o n d u c t i v i t y ) should l e a d t o p u l s e r e p e t i t i o n - r a t e l i m i t a t i o n '

4

=

1.6..,1.7

( a t t h e S p e c i f i c energy r e l e a s e

~ 3 0 0 J/1* atm)

.

4. Pressure chmges and propagation Qf n e a r l y i s e n t r o p i c waves m e shown sche- Fig. 2 m a t i c a l l y

i n Pig.

4,

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I n view of a small gas temperature growth a f t e r shock wave passing, the condition f o r s t a t i o n a r y temperature d i s t r i b u t i o n i s a s follows:

This equation can be i n t e g r a t e d assu- the depen- Ding t h a t a t 0

<

d)~<

dence M ( X )

(M

i s Mach number) i s determined by t h e energy

shock, while a t

Ma-

. .

i t i s determined by the wave spreading and can be found from the shock "areaw conser- vation:

J(p-&)d~

= const. Here P i s Riman i n v a r i a n t aszd t h e i n t e g r a l is t o be

taken over t h e shock width. This method i s used o f t e n i n the theory of simple waves -

containing weak shocks

[ 5 ]

.

The experimental p l o t of the gas temperature up the flow i s presented i n Pig.

5 ;

upper curve i s the r e s u l t of c a l c u l a t i o n s . A d i s c r e - pancy between experimental and t h e o r e t i c a l

!3

curves i s explaindd by neglecting of h e a t conductivity i n calculations.

8

Y

.6

t--

3

4

2

Fig. 5

It has been assumed t h a t a l l the energy c a r r i e d by waves has d i s s i p a t e d i n a sec- t i o n of l e n g t h L of a gas channel. Suppo- s i n g t h a t t h e permissible density f l u c tua- t i o n over e l e c t r o d e s f width A J / ~ ~ , <

3 . 1 0 ~ ~

( s e e Fig. 1 ) one can obtain a t

5.

It has been pointed out i n t h e previous s e c t i o n t h a t the g r e a t e r p a r t of

the energy c a r r i e d by waves outwards the discharge region converts f i n a l l y i n t o energy of a c o u s t i c waves. If the damping decrement of the waves i s comparable with pulse r e p e t i t i o n frequency, than the next pulse i s applied t o t h e discharge region when the gas density t h e r e i n i s modulated

s p a t i a l l y by t r a v e l l i n g waves. The charac- t e r i s t i c frequency of the s t r o n g e s t a c o u s t i c mode i n t h e gas channel and i t s

damping decrement have been measured by means of a p i e z o e l e c t r i c d e t e c t o r placed near the discharge region. One-dimensional resonator c a v i t y formed by a rectangular channel with open ends and e l e c t r o d e s being placed i n the c e n t r a l region of t h e c a v i t y was s t u d i e d i n Refs

6,7.

This c a v i t y has a simple spectrum of n a t u r a l

s

frequences, \)Fn

= m

,x

,

where

L

i s r e s o n a t o r l e n g t h , m=1,2,3

...

Since the discharge being the source of disturbances takes place i n the c e n t r a l region of t h e r e s o n a t o r , then symmetry considerations

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(8)

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=1:1:5 l a s e r mixture and 4.55 f o r a n i t r o - The c r e a t e d h i g h p u l s e - r e p e t i t i o n - gen-free mixture. Maximum s p e c i f i c energy r a t e CO2-laser w i t h an energy 163 p e r r e l e a s e i n a d i s c h a r g e i s about 250 J/1. p u l s e and an average o u t p u t power up t o

a t m . The e f f i c i e n c y of conversion of 10 ECG h a s t h e o v e r a l l e f f i c i e n c y of 4.5%. e l e c t r i c a l e n e r a s t o r e d i n t h e c a p a c i t o r These h i g h v a l u e s permit u s t o hope t h a t bank i n t o l a s e r r a d i a t i o n r e a c h e s 10%. t h i s l a s e r w i l l be widely adopted,

R E F E R E N C E S

1. C.S. Dzakovic and S.A. Wutzke, J.App1. Phys.,

9,

5061 (1973).

2. V.Yu. Baranov, D.D. Malyuta, and V.S. Niezhevov, Kvantovaya E l e c t r o n , (Moscow), 2 ( 1 0 ) , 2186(1978)

[SOV, J.Quantum Electon.

g,

1234 (1978)j

3. V.Yu. Baranov e t a l , Appl.Optics,

1_9(6), 930(1980).

4. E.P. Velikhov, V,D.Pismenny, and A.T. Hakhimov, Usp. F i z . Nauk,

122,

419

(1977) [SOV. Phys. Usp. 20,586 (1977)]

.

5.

A. K a n t r o v i t c , i n "l?undamental-s of g a s

11

dynamics, fdoscow, 1963.

6. V.Yu. Baxanov, V,V. Breev, It.D.l&l.yute, e t a1

,

Kvantovaya E l e c t r o n . (Moscow)

Q

( 9 1 , 1861 (1977).

7. V.Yu. Baranov. B.Ya.Lubimov, V.G. N i s i e v e* a l , Kvantovaya E l e c t r o n . (Moscow),& ( l ) , 184 (1979).

11

8. M.L. Bhaumik, i n Gas-Flow and Chemical lasers: HPC, London, 1978,pp. 49-73.

9.

V.Yu Beranov e t a l , T e p l o f i z . Vys. Temp.

"1_5:(51

972

(1977).

10,V.Yu. Baranov, G.P, Drokov, S.A, Kaaakov e t a l

,

J. Techn, Fiz. (Leningrad) l 8 , 1039 (1978).