USING THE

A LASER

ELECTRON

PULSE

INTERFEROMETER CONCENTRATION

DISCHARGE V . V.

TO DE T E R M I N E IN A D I S I N T E G R A T I N G

PLASMA

Tatarinov

UDC 543.46

M e a s u r e m e n t s of e l e c t r o n concentrations and their variations he(t) with time are a good means of obtaining information on p r o c e s s e s o c c u r r i n g in pulse discharge p l a s m a s . Such studies are of interest in connection with the production of inverted media in ionized g a s e s , in pinch discharge analysis, etc. Howe v e r , the m e a s u r e m e n t of ne(t ) by traditional methods of p l a s m a diagnosis (probe techniques, s p e c t r o scopic methods, superhigh frequency m e a s u r e m e n t s ) involve s e v e r a l serious difficulties. The development of l a s e r s has given rise to certain new i n t e r f e r o m e t e r setups with broad capabilities for determining p a r t i c l e concentrations in p l a s m a s [1, 2]. The l a s e r in such i n t e r f e r o m e t e r setups acts as the active e l e ment. A l a s e r i n t e r f e r o m e t e r is formed by adding a m i r r o r M 3 to a l a s e r r e s o n a t o r MiM 2 (Fig. 1). The r e f e r e n c e r e s o n a t o r M2M3 can be regarded as an efficient compound m i r r o r which conforms to the Fabry - P e r o t standard theory [3]. This means that the ratio of the intensity Ire f reflected from (or transmitted by) the compound m i r r o r to the incident intensity Io is a function of the t r a n s m i s s i o n coefficients of the m i r r o r s M 2 and M 3 and of the phase difference ~v between the incident and e m e r g i n g r a y s . When the optical length of the r e f e r e n c e r e s o n a t o r M2M3 changes by ~ / 2 the ratio I r e f / I 0 p a s s e s through an extremal value. Since the oscillation modes of l a s e r radiation are of fixed frequency, it follows that alteration of the optical length M2M3 produces amplitude modulation (AM) of the intensity I i of the l a s e r radiation and of the intensity 12 of the radiation passing through the r e f e r e n c e r e s o n a t o r . In strict analysis of the operation of a l a s e r i n t e r f e r o m e t e r it is n e c e s s a r y to consider the r e f e r e n c e and the l a s e r r e s o n a t o r s as a single s y s t e m . A d i a g r a m of our setup appears as Fig. 1. The p l a s m a was transilluminated at the 6328/k w a v e length of a H e - N e l a s e r whose discharge tube T t was filled with Ne and He 3. The use of He 3 enabled us to achieve a high l a s e r gain at the axial l a s e r modes TEMoo q. The n u m b e r of axial oscillation modes generated by the l a s e r was selected by suitable adjustment of the diaphragm D i and by selecting the power of the high-frequency oscillator; the number of axial modes was determined visually by means of a 12 cm F a b r y - P e r o t i n t e r f e r o m e t e r (FP) and c o l l i m a t o r tube (K). In o r d e r to facilitate adjustment of the optical s y s t e m the flat m i r r o r M 3 was mounted on a loudspeaker cone. When a voltage was applied to the loudspeaker, the resulting small displacement of m i r r o r M3 altered the optical length of M2M3. The resulting AM of the radiations I 1 and I z was picked up by the ,,

t

S ',

FEU2 Q L~

U~

:z

Dz ~z

r,

~

_/~ LI

J ) Ev.

.

/"

l

gFio~ []

Fig. 1. Diagram of the setup.

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 9, No. 3, pp. 369-373, September, Original article submitted October 6, 1967. 1972 Consultants Bureau , a division of Plenum PublishDig Corporation, 227 West I7th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00.

898

1968.

/

T A B L E 1. M e a s u r e d A m b i p o l a r D i f f u s i o n C o e f ficients Da Da, crrt~ 9sec -I p, m m Hg

~0,06 0,88 1,25

2,25

He

N~

m

7270 7050 5660

4~0 4520 3500

Ar

5540 2100 1600 890

l
4500 1720, 1150

J"

p h o t o m u l t i p l i e r s F E U 1 and FEU2, w h o s e s i g n a l s w e r e a p p l i e d to a n O K - 1 7 M d o u b l e - b e a m o s c i l l o g r a p h . W h e n a x i a l o s c i l l a t i o n m o d e s w e r e e x c i t e d in the r e f e r e n c e r e s o n a t o r M21V[3, the n u m b e r of p u l s e s p i k e s in the p a t t e r n a s the m i r r o r M 3 p a s s e d "dead p o i n t s " d i d not d e p e n d on the l e n g t h of M2M 3, s i n c e 2= hr - ~ A (ln) = r.hm,

(1)

w h e r e A ~ i s the t o t a l p h a s e c h a n g e c o r r e s p o n d i n g to a c h a n g e A(/n) in the o p t i c a l l e n g t h of M2M3; l is the l e n g t h of the r e f e r e n c e r e s o n a t o r M2M3; k i s the w a v e l e n g t h of the l a s e r r a d i a t i o n ; n i s the r e f r a c t i v e i n d e x of the m e d i u m b e t w e e n the m i r r o r s M 2 and M3; A m is the c h a n g e in the r e f r a c t i v e i n d e x . The p e r c e n t a g e a m p l i t u d e m o d u l a t i o n of the r e c o r d e d r a d i a t i o n s d e p e n d e d m a r k e d l y on the n u m b e r of a x i a l o s c i l l a t i o n m o d e s g e n e r a t e d by t h e l a s e r and on the r a t i o of l e n g t h s of the r e f e r e n c e and l a s e r r e s o n a t o r s . I t w a s found t h a t when M1M 2 = M2M 3 the n u m b e r of a x i a l o s c i l l a t i o n m o d e s ( f r o m one to six) w a s p r e s e r v e d w i t h the r e f e r e n c e r e s o n a t o r e i t h e r o p e r a t i n g o r shut off. In t h i s c a s e a l t e r a t i o n of the l e n g t h of M2M 3 e n s u r e d a q u i t e high p e r c e n t a g e m o d u l a t i o n of the l a s e r r a d i a t i o n . T h e i n d i c a t e d l e n g t h r a t i o (M1M 2 = M2M 3 = 135 cm) c h o s e n f o r the p l a s m a a n a l y s i s e n a b l e d us to o b v i a t e the n e e d to c a l i b r a t e the l a s e r i n t e r f e r o m e t e r by o t h e r m e t h o d s , and to a s s u m e that the a p p e a r a n c e of a s i n g l e AM s p i k e w a s due to a c h a n g e of the o p t i c a l l e n g t h by X / 2 . R e p l a c e m e n t of the f i a t m i r r o r M 3 by a s p h e r i c a l m i r r o r (R = 135 c m ) r e s u l t e d in a f o u r - to f i v e f o l d i n c r e a s e of the s e n s i t i v i t y of the s e t u p . T h i s w a s a c c o m p a n i e d by the a p p e a r a n c e of " s m a l l " s p i k e s b e t w e e n the l a r g e r s p i k e s a s s o c i a t e d w i t h the a x i a l v i b r a t i o n m o d e s ; t h e s e s m a l l s p i k e s w e r e a s s o c i a t e d w i t h n o n a x i a l m o d e s . By s u i t a b l e a d j u s t m e n t of the m i r r o r M 3 we w e r e a b l e to e q u a l i z e the s p i k e h e i g h t s . T h i s i n d i c a t e d a r e d i s t r i b u t i o n of e n e r g y o v e r the v i b r a t i o n m o d e s in the r e f e r e n c e r e s o n a t o r . If the r e f e r e n c e r e s o n a t o r c o n t a i n s a t i m e - v a r i a b l e p l a s m a m e d i u m , t h e n the v a r i a t i o n n(t) of the r e f r a c t i v e i n d e x i s r e l a t e d to the p a r t i c l e d e n s i t y in the p l a s m a by the d i s p e r s i o n f o r m u l a [4] e~ ~,~ n (t) ~ 1-- - n e (t), 2n mc2

(2)

w h e r e ~, e, e , m a r e known c o n s t a n t s and he(t) i s the e l e c t r o n c o n c e n t r a t i o n a s a function of t i m e . The c o n t r i b u t i o n of i o n s and n e u t r a l a t o m s to the r e f r a c t i v e i n d e x n(t) of the p l a s m a i s m u c h l e s s m a r k e d than the c o n t r i b u t i o n m a d e by the f r e e e l e c t r o n s . C o m p a r i n g f o r m u l a s (1) and (2), we o b t a i n the m i n i m u m v a l u e of the v a r i a t i o n s of the e l e c t r o n c o n c e n t r a t i o n (ne min) r e q u i r e d to p r o d u c e a s i n g l e s p i k e in the l a s e r r a d i a t i o n c o r r e s p o n d i n g to a c h a n g e of X / 2 (Am = 1) in the o p t i c a l l e n g t h of M2M 3. O u r p r o b e of the p l a s m a w i t h the 6328 A l i n e of Ne i n d i c a t e d t h a t the m i n i m u m e l e c t r o n d e n s i t y p e r unit l e n g t h w a s 1.76 91017 c m -3. The e l e c t r o n c o n c e n t r a t i o n s ne(t) in the d i s i n t e g r a t i n g p l a s m a w e r e d e t e r m i n e d in d i s c h a r g e tube T 2 of l e n g t h 56 c m and i n s i d e d i a m e t e r 1.75 c m . The l a s e r b e a m p a s s e d t h r o u g h l i m i t i n g d i a p h r a g m D 2 (1.9 m m in d i a m e t e r ) and t r a v e l e d a l o n g the a x i s of tube T 2. D i s c h a r g e tube T 2 w a s e v a c u a t e d to 1 0 - 5 - 1 0 -4 m m Hg and f i l l e d w i t h one of the g a s e s He 3, He 4, A r , K r , N 2 at p r e s s u r e s r a n g i n g f r o m 10 -2 to 3 m m Hg. The p r e s s u r e w e r e m e a s u r e d w i t h a n oil g a u g e and an L T - 2 t h e r m o c o u p l e l a m p , w i t h an a p p r o p r i a t e c o r r e c t i o n for each gas. B r e a k d o w n of the d i s c h a r g e g a p w i t h s i m u l t a n e o u s s t a b i l i z a t i o n of the d i s c h a r g e t h r o u g h p r e l i m i n a r y i o n i z a t i o n in tube T 2 w a s e f f e c t e d by m e a n s of a l o w - p o w e r s p a r k (V = 25 kV). The o s c i l l o g r a p h s c a n w a s t r i g g e r e d s i m u l t a n e o u s l y with the s p a r k (a 12 tzF c a p a c i t o r b a t t e r y c h a r g e d to 3 k V w a s d i s c h a r g e d at the s a m e t i m e ) . A c a r b o n shunt w a s u s e d to p r o d u c e o s c i l l o g r a m s of the d i s c h a r g e c u r r e n t a s a f u n c t i o n of t i m e . The d u r a t i o n of c u r r e n t flow w i t h a n a p e r i o d i c d i s c h a r g e m o d e d i d not e x c e e d 30 t~see. In r e c o r d i n g the A M of t h e r a d i a t i o n s I t and 12 we f i l t e r e d out t h e i n c o h e r e n t r a d i a t i o n by m e a n s of g l a s s f i l t e r s F 1 and F 2 and c h r o m a t i c l e n s e s L 1 and L 2. The n u m b e r of A M s p i k e s in the r a d i a t i o n I t w a s u s e d to c o n s t r u c t ne(t ) f r o m the i n i t i a l i n s t a n t of the c a p a c i t o r b a t t e r y d i s c h a r g e . The p e r c e n t a g e m o d u l a t i o n d e c r e a s e d w i t h i n c r e a s i n g s p i k e f r e q u e n c y , so t h a t the t o t a l n u m b e r of s p i k e s w a s c o u n t e d in i n d i v i d u a l c a s e s o n l y . The h i g h e s t r e c o r d e d s p i k e f r e q u e n c y

899

CITI

i

,

"~

i i

!

J5

0

/6#

32#

t, ~sec

Fig. 3

~0

#0

50 t, gsec

Fig. 4

Fig. 2. O s c i l l o g r a m of the emerging radiation 11 obtained by producing a disintegrating p l a s m a in the r e s o n a t o r M2M3 (initial Kr p r e s s u r e p = 0.5 m m Hg). Fig. 3. The function ne(t) for A r for several initial p r e s s u r e s p, m m I-tg: 1) 6.2 -10-2; 2) 1.4 910-2; 3) 0.25; 4) 0.58; 5) 0.88; 6) 1.0; 7) 1.26; 8) 2.1; 9) 2.27. Fig. 4. Drop of electron density in krypton (p = 2.26 m m Hg; length of discharge tube L = 86 cm; tube d i a m e t e r 1.52 cm; C = 20/zF). due to the production of a p l a s m a in the r e f e r e n c e branch of the i n t e r f e r o m e t e r setup was 500 k c / s e c . ure 2 shows a typical photograph of the AM of the I l radiation.

Fig-

The resulting values of the e l e c t r o n concentration as functions of time were piotted on s e m i l o g a r i t h m i c p a p e r . Figure 3 shows the averaged results for argon for various initial p r e s s u r e s p. Our determinations of ne(t) contained an e r r o r due to mechanical vibrations of the setup. The l a r g e s t e r r o r was associated with the last spike in theAM of the l a s e r radiation (this e r r o r amounted to 6-7% for 10 photographs). In the absence of vibrations the individual points were approximated well by a straight line in the chosen (semilog) scale. The only effect of nonidentity of the d i s c h a r g e s was to produce a slight parallel d i s p l a c e ment of the c u r v e s . Upon termination of the c u r r e n t pulse the decline in e l e c t r o n concentrations in the 1016-101~ c m -3 range was exponential. The decay constants 9 i n c r e a s e d with increasing initial p r e s s u r e and atomic weight of the gas under investigation. The same relationship was found to hold in the times of appearance of the last spikes. The l a r g e s t electron concentration decay time (over 500 psec) was noted with Kr. The functions n e (t) aiso indicated that the m a x i m u m e l e c t r o n concentrations achieved in d i s c h a r g e s i n c r e a s e d with i n c r e a s i n g initial gas p r e s s u r e . In the low p r e s s u r e range (p < exponential. This deviation was due (as a r e s u l t of m a r k e d escape of gas and also to the action of the residual

0.3 m m Hg) the decline in the electron concentrations he(t) was not to the increase in gas density during p a s s a g e of the discharge pulse f r o m the walls of the vessel and e l e c t r o d e s under the given conditions) voltage on the disintegrating p l a s m a .

The d e c r e a s e in e l e c t r o n concentrations i-n the disintegrating p l a s m a of the chosen g a s e s was due largely to p r o c e s s e s of diffusion and recombination of electrons with positive ions. The equation describing the rate of d e c r e a s e of ne(t) can be written as [5] One _ Ot

Da V ~ne ~

a ~.n ,,

(3)

where D a is the coefficient of ambipolar diffusion and ote the e l e c t r o n - i o n combination coefficient. The experimental functions ne(t) enabled us to draw certain conclusions by isolating the dominant disintegration p r o c e s s . For example, the diffusion p r o c e s s when ~- was s m a l l e r than the constant of t e m p e r a t u r e d e c r e a s e T e was c h a r a c t e r i z e d by an exponential, d e c r e a s e of ne(t); in recombination the r e l a t i o n ship between 1/n e and time was linear.

900

Comparing these regularities with our experimental results, we concluded that after cessation of the current, the decrease in electron concentration at the tube axis was due largely to ambipolar diffusion. Assuming that the effect of the upper harmonics of the decrease in n e was small, we used the slopes of the straight portions of the functions n e(t) (Fig. 3) to find the ambipolar diffusion coefficients for a given tube geometry characterized by the diffusion length A = R/2.4. For A = 0.36 cm we determined the ambipolar diffusion coefficients Da which lie in the 800-11,000 em 2 9 sec -i range under the chosen conditions. Table 1 contains some of the values of the measured coefficients. The diffusion coefficient Da decreased with increasing initial gas pressure p; however, the products pD a were not constant throughout the entire range of pressures. It appears that the measured coefficients D a were attributable to the early stage of plasma disintegration. Analysis of Eq. (3) indicated that as the initial gas pressure p increased, the relative role of recombination in the decline of the electron concentration increased as well, which resulted in deviations from a linear n e (t) on the semilog scale. In fact, under the indicated conditions the decrease in n e at the initial instants of krypton plasma disintegration was due to electron-ion recombination. Figure 4 shows the decrease of electron concentrations in krypton. Evaluation of the recombination coefficient yielded the value o~e = 6 910 -13 c m 3 - see -t. The decline in e l e c t r o n concentrations ne(t ) computed with allowance for the b e a s u r e d coefficients c~e and D a on the basis of the solution of Eq. !3), namely t --- t o = z I n

n~ ne

1 + a ~ n~ l+ue~:neo

,

(4)

a g r e e d s a t i s f a c t o r i l y with the experimental curve of ne(t). I n c r e a s e d a g r e e m e n t of the experimental and theoretical functions ne(t) could have been achieved by c o r r e c t i n g the m e a s u r e d values of the coefficient Da by means of the coefficient a e. A s i m i l a r behavior of the decline in e l e c t r o n concentrations was noted with the other g a s e s , although quantitative m e a s u r e m e n t s would have required some improvement in instrument sensitivity [6]. (We note that a deviation f r o m a linear function I n n e = f(t) indicates not only recombination. For example, a s i m i l a r deviation o c c u r s when the coefficient D a v a r i e s with the t e m p e r a t u r e of the charged particles.) In individual c a s e s we m e a s u r e d all the modulation spikes obtained by varying the r e f r a c t i v e index of the p l a s m a . This enabled us to determine the m a x i m u m e l e c t r o n concentrations in the d i s c h a r g e s . The m a x i m u m e l e c t r o n concentrations i n c r e a s e d with rising initial p r e s s u r e and reached 4 91016 cm -3. This value a g r e e s with r e s u l t s obtained for s i m i l a r d i s c h a r g e s in [7]. I am grateful to V. S. Mel'chenko for his comments on the p r e s e n t study and to L. T. Poleshchuk for a s s i s t a n c e in c a r r y i n g out the e x p e r i m e n t s . LITERATURE 1 2 3 4 5 6 7.

CITED

D. E. T. F. Ashby and D. F. Jephcott, Appl. Phys. Letters, 3, 13 (1963). J. B. G e r a r d o , J. T. Verdeyen, and M. A. Gusinow, J. Appl. P h y s . , 3_66,3526 (1965). G. V. Rozenberg, Optics of Thin Coatings [in Russian], GIFML (1958). V. L. Ginzburg, 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 in P l a s m a s [in Russian], Fizmatgiz (1960). J. Hasted, P h y s i c s of Atomic Collisions [Russian translation], Izd. Mir (1966). J. M. Quinn, P l a s m a P h y s i c s (J. Nucl. E n e r g y Pt.) C 7 , 1 1 3 (1965). Edward Thornton, J. Appl. P h y s . , 36, 3539 (1965).

901