PULSED CURRENT VOLTAGE CHARACTERISTICS OF A THERMALLY PRODUCED PLASMA

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PULSED CURRENT VOLTAGE CHARACTERISTICS OF A THERMALLY PRODUCED PLASMA

N. Braithwaite, J. Allen

To cite this version:

N. Braithwaite, J. Allen. PULSED CURRENT VOLTAGE CHARACTERISTICS OF A THER- MALLY PRODUCED PLASMA. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-491-C7-492.

�10.1051/jphyscol:19797238�. �jpa-00219221�

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JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 40, JuiZZet 1979, page C7- 49 1

PULSED CURRENT VOLTAGE CHARACTERISTICS OF A THERMALLY PRODUCED PLASMA

N. St. J. Braithwaite and J.E. Allen.

Department o f ~ n g i n e e r i n g Science, Oxford University, Oxford, England.

INTRODUCTION

The p r e s e n t work employs t h e same a p p a r a t u s a s t h a t used e a r l i e r [ I 1 - ^{[ 7 1}i n d . c . and plasma o s c i l l a t i o n s t u d i e s of c o l l i s i o n l e s s and h i g h l y i o n i s e d plasmas produced by s u r f a c e i o n i s a t i o n i n s i d e a heated c a v i t y . D.c. a n a l y s i s of t h e plasma [ I 1 has shown t h a t when a v o l t a g e i s a p p l i e d between t h e e l e c t r o d e s which form t h e c a v i t y a f i e l d f r e e plasma r e g i o n i s formed bounded by a monotonic s h e a t h a t one e l e c t r o d e and a double s h e a t h a t t h e o t h e r e l e c t r o d e ; most of t h e a p p l i e d p o t e n t i a l i s dropped a c r o s s

t h e monotonic s h e a t h . I f t h e b i a s v o l t a g e i s a p p l i e d a s a v o l t a g e s t e p t h e r e w i l l be an i n t e r - v a l of time d u r i n g which e l e c t r o n s s e e s t a t i o n - a r y e l e c t r i c f i e l d s w h i l e t h e i o n s a r e v i r t u a l l y f r o z e n , t h e l a t t e r responding t o f i e l d s a f t e r a few i o n plasma p e r i o d s . T h i s time i n t e r v a l i s i n v e s t i g a t e d h e r e f o r t h e c a s e when t h e un- p e r t u r b e d plasma i s bounded by e l e c t r o n r i c h s h e a t h s : r a p i d l y a p p l i e d v o l t a g e s a r e t h e n s c r e e - ned from t h e plasma by s h e a t h s formed a s a r e s u l t of e l e c t r o n motion o n l y , t h e plasma i o n s not moving a p p r e c i a b l y on a time s c a l e s h o r t e r t h a n t h e i o n i n e r t i a l r e s p o n s e time.

EXPERIMENTS

P r o d u c t i o n of t h e t h e r m a l l y i o n i s e d plasma, measurement of i t s temperature and a d . c . measurement of i t s d e n s i t y have been d e s c r i b e d p r e v i o u s l y [ I ] , 161. A caesium plasma i s formed i n an annular c a v i t y between two c o n c e n t r i c tantalum c y l i n d e r s , t h e o u t e r one being heated by e l e c t r o n bombardment t o around 2200K; s e e

ag. 01. The c y l i n d e r s , which a r e i n r a d i a - t i v e thermal e q u i l i b r i u m w i t h each o t h e r , a c t a s e l e c t r o d e s f o r e l e c t r i c a l measurements. One e l e c t r o d e was e a r t h e d w h i l e s q u a r e wave v o l t a g e p u l s e s were a p p l i e d t o t h e o t h e r . A square wave w i t h a r i s e time l e s s t h a n 0.5 n s e c , was o b t a i n e d by d i s c h a r g i n g a t r a n s m i s s i o n l i n e through t h e plasma, which a c t e d a s t h e load;

c u r r e n t flowing through t h e plasma was monitored using an i n d u c t i v e l y coupled measuring c i r c u i t . P u l s e d u r a t i o n s were up t o one microsecond and had a r e p e t i t i o n r a t e of one k i l o h e r t z so t h a t c u r r e n t s and v o l t a g e s could be d i s p l a y e d on a double beam o s c i l l o s c o p e . The i o n plasma p e r i o d f o r t h e plasmas i n v e s t i g a t e d was between one t h i r d and one microsecond.

THEORY

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The a n a l y s i s i s c a r r i e d o u t i n p l a n a r geom- e t r y which i s a r e a s o n a b l e appmximation t o t h e plasma c a v i t y . The s e l f - c o n s i s t e n t d . c . aria-

l y s i s I11 assumes t h a t h a l f llaxwellian d i s t r i b u t i o n s of e l e c t r o n s and of i o n s a r e em2tted from each e l e c t r o d e . The d i s t r i b u t i o n of p o t e n t i a l between t h e e l e c t r o d e s i s t h e n e s t - a b l i s h e d by f i n d i n g which of t h e many p o s s i b l e p o t e n t i a l d i s t r i b u t i o n s i s c o n s i s t e n t w i t h t h e half-Maxwellian input's a t t h e boundaries. Poten-

t i a l s between t h e e l e c t r o d e s f o r t h e c a s e con- s i d e r e d h e r e of e l e c t r o n r i c h s h e a t h s f o r no a p p l i e d b i a s and l a r g e b i a s a r e shown i n c u r v e s

( a ) and (b) r e s p e c t i v e l y i n f i g u r e 2. The p o t e n t i a l minimum, ( p o t e n t i a l normalised t o kT/e) r e g u l a t e s n l t h e f l o w of current' a c r o s s t h e d e v i c e w h i l e t h e double l a y e r . d r o p ,

n n - n l , - - a d j u s t s t h e e l e c t r o n v e l o c i t y so t h a t t h e d e n s i t y of t h e e l e c t r o n s i s e q u a l t o t h a t o f . t h e i o n s i n t h e plasma r e g i o n ( n o ) . For a g i v e n plasma d e n s i t y , no, and e l e c t r o n

e m h s i o n d e n s i t y , n eo (a f u n c t i o n of T and 4) t h e v a l u e s of n 1 and no-" a r e n o t u n i q u e l y determined, b u t must be r e l a t e d such t h a t t h e e l e c t r o n and i o n d e n s i t i e s i n t h e plasma a r e e q u a l . The a b s o l u t e v a l u e s of t h e poten- t i a l d i f f e r e n c e s n I and no-nl, a r e determined by t h e v a r i a t i o n of i o n d e n s i t y w i t h p o t e n t i a l I n t h e d.c. c a s e , r e d i s t r i b u t i o n of t h e i o n s Leads t o s a t u r a t i o n of t h e v a l u e s of n 1 and q n - n l , - - f o r l a r g e a p p l i e d v o l t a g e s , and hence t h e c u r r e n t c r o s s i n g t h e d e v i c e a l s o s a t u r a t e s . The i o n s w i l l n o t respond f o r a t l e a s t a few i o n plasma periods,. so t h a t f o r f a s t r i s i n g v o l t a g e p u l s e s t h e i o n s a r e assumed t o have a uniform d e n s i t y between t h e e l e c t r o d e s , e q u a l t o t h e unperturbed plasma d e n s i t y . The s e l f - c o n s i s t e n t potenti'al d i s t r i b u t i o n f o r a con- s t a n t uniform i o n d e n s i t y , independent of poten- t i a l i s shown on curve ( c ) of f i g u r e 2. The double s h e a t h i s formed i n a r e g i o n f o r m e r l y occupied by n e u t r a l plasma s o t h e uniform den- s i t y assumption i s r e a s o n a b l e . The v a l u e of t h e p o t e n t i a l d i f f e r e n c e no-n, i s o b t a i n e d by r e q u i r i n g t h a t t h e r e b e - two z e r o s of e l e c t r i c f i e l d , one a t n l and one a t no. S t a r t i n g from

a k i t integration .of Poisson's e q . d ~ o ~ - .

5 i s t h e d i s t a n c e co-ordinate normalised t o a Debye l e n g t h d e f i n e d i n terms of e l e c t r o n

= e,kT/n&,e2, ne(n) emission d e n s i t y neA XDeo

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797238

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i s d i s c u s s e d below; n, i s t h e u n p e r t u r b e d plasma d e n s i t y ; l i m i t s a r e f o r t h e z e r o s of t h i s e l e c t r i c f i e l d e q u a t i o n . The e l e c t r o n d i s - t r i b u t i o n f u n c t i o n t o t h e r i g h t of t h e minimiim i n f i g u r e 1 ( c ) o r ( b ) i s t h e sum of two truncated Maxwellian d i s t r i b u t i o n s and h a s been d i s c u s s e d i n e a r l i e r work [ 11 . The r e s u l t i n g e x p r e s s i o n f o r e l e c t r o n d e n s i t y , o b t a i n e d by i n t e g r a t i n g over a l l v e l o c i t i e s , a s a f u n c t i o n of p o t e n t i a l i s t h e same i n d . c . and p u l s e c a s e s because of t h e t o p o l o g i c a l equivalence,

qo = p o t e n t i a l of t h e p l a t e a u

q I = p o t e n t i a l of t h e minimum

( a ) z e r o b i a s (b) d.c. b i a s (c) p u l s e d b i a s

F i g u r e 1 . Schematic P o t e n t i a l D i s t r i b u t i o n s .

s e e f i g u r e I (b) and ( c ) .

3'71 e x p h - v p ) . ( t + ~ ( 1 - 7 $ + ~ p ( ~ ) . ~ f ~ h - ? . ) l '/

n ,

where x (2,

= c - ^edc* ⁼ - 5 i ~ y ~ k t ~ ) d

X

S u b s t i t u t i n g (2) f o r ne(n)/neo and u s i n g no = ne(no) i n ( 1 ) g i v e s no-ql = A a s t h e s o l - u t i o n of :-

2 ( 1 - d ) e x ~ ( ~ - 7 ~ ) + (~-e*p(-~~))((l - A ) ~(11) + ²^B⁾(3)

- ⁽' ⁺4 x ~ ( - 7 ~ ) = ⁰

where E ( 4 ) s expCB).et&(~'*).

Approximate s o l u t i o n of (3) shows A t o be a l m o s t l i n e a r l y p r o p o r t i o n a l t o rl f o r n >5. Thus f o r

P P

t h e p u l s e d plasma, t h e p o t e n t i a l i s mainly deve-- lop'ec' a c r o s s t h e d o u b l e l a y e r i n c o n t r a s t t o t h e d.c. e q u i l i ' b r i u m c a s e d e s c r i b e d above. T h i s d o u b l e l a y e r i s formed by r e t r e a t of plasma e l e c - t r o n s i n r e s p o n s e t o t h e a p p l i e d p o t e n t i a l and i s s i m i l ? r r t o i o n m a t r i x s h e a t h expansion i n plasmas bounded b y i o n s h e a t h s , a l t h o u g h h e r e t h e s h e a t h s a r e e l e c t r o n r i c h .

The c u r r e n t c r o s s i n g t h e d e v i c e i s found by c o n s i d e r i n g t h e n e t e l e c t r o n f l u x i n t h e poten- t i a l d i s t r i b u t i o n :

Using (2), t h i s c u r r e n t may b e e x p r e s s e d i n terms of t h e plasma d e n s i t y , n and s h e a t h d r o p

no-n1 = A , and i s g i v e n i n normalised form by 0'

I n t h e l i m i t of l a r g e q and hence l a r g e Ao, (3)

P c a n b e used t o show:

J % $ J q % k G

F i g u r e 2 shows t h e p u l s e d c u r r e n t v o l t a g e c h a r a c t e r i s t i c c a l c u l a t e d e x a c t l y from (3) and ( 4 ) .

RESULTS AND DISCUSSION

F i g u r e 2 shows t h r e e s e t s of d a t a o b t a i n e d f o r d i f f e r e n t v a l u e s of plasma d e n s i t y and t e m p e r a t u r e , f i t t e d a t one p o i n t t o t h e

t h e o r e t i c a l c u r v e of normalised c u r r e n t a g a i n s t n o r m a l i s e d v o l t a g e . The c u r r e n t t r a c e s f o r s h o r t time s c a l e s were n e a r l y f l a t topped e x c e p t f o r t h e e f f e c t s of s t r a y c a p a c i t a n c e which l e a d t o a s l i g h t o v e r s h o o t . The v a l u e s of c u r r e n t and v o l t a g e p l o t t e d on f i g u r e z were r e a d o f f o s c i ' l l o s c o p e t r a c e s i n t h e f l a t p o r t i o n a f t e r any o v e r s h o o t and p r i o r t o any decay of c u r r e n t , observed a t t i m e s a p p r o a c h i n g a n i o n plasma p e r i o d . I n p r a c t i c e f l a t topped p o r t i o n s were s e e n between 0.01 and 0.1 p s e c . There i s good agreement between t h e o r y and experiment f o r t h e plasma c o n d i t i o n s s t u d i e d .

e

F i g u r e 2. Normalised C u r r e n t V o l t a g e r'

f lLl

fr 4 n W

rT) 3 2

9

2

- C h a r a c t e r i s t i c . - ^Theory

T = 2030K = 0.175 eV x n = 8 x 1 0 14 m -3 ,

T = 2050K A

14 -3

o no= 2 x 10 m >o-

T = 1950K ?A"

- .NA'k

&A* - - - - - d . c .

8 / saturation

1 1 1 1 I 1 1 & I 1

I n c o n c l u s i o n , i t h a s been shown t h a t c u r r e n t s i n e x c e s s of d . c . e q u i l i b r i u m v a l u e s can b e drawn t h r o u g h t h e plasma i n a p u l s e d mode. T h i s i s p o s s i b l e because of t h e f i n i t e r e s p o n s e time of t h e i o n s which a r e e s s e n t i a l l y f r o z e n d u r i n g t h e e a r l y s t a g e s of t h e p u l s e . Agree- ment between t h e o r y and experiment i s good.

4 8 12 16

NORMALISED VOLTAGE ( q a )

1 . Fang, M.T.C., F r a s e r , D.A. and A l l e n , J . E . , (1969), J. Phys. D 2, 229.

2. Ward, J . C . and A l l e n , J . E . , (1970), J . Phys.

E 3, 535. -

3. A l l e n , J . E . , Fang, M.T.C. and F r a s e r , D.A., (1971), P r o c . R. Soc. Lond. E , 63..

4. Phelps. A.D.R. and A l l e n , J.E., (1975), Proc.

xII I.C.P.I.G., 128.

5 . P h e l p s , A.D.R. and A l l e n , J.E., (1976), P r o c .

R. Soc. Lond. e, 221.

6. Powers, S.R., (1976), M.Sc. D i s s e r t a t i o n , Oxford U n i v e r s i t y .

7. P h e l p s , A.D.R. and A l l e n J.E., (1978), Proc.

R. Soc. Lond. E , 541.

-