DIFFERENCE BETWEEN ELECTRON TEMPERATURE AND HEAVY PARTICLES TEMPERATURE IN ARC PLASMA

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DIFFERENCE BETWEEN ELECTRON TEMPERATURE AND HEAVY PARTICLES

TEMPERATURE IN ARC PLASMA

H. Kafrouni, A. Gleizes, H. Dang Duc

To cite this version:

H. Kafrouni, A. Gleizes, H. Dang Duc. DIFFERENCE BETWEEN ELECTRON TEMPERATURE

AND HEAVY PARTICLES TEMPERATURE IN ARC PLASMA. Journal de Physique Colloques,

1979, 40 (C7), pp.C7-237-C7-238. �10.1051/jphyscol:19797116�. �jpa-00219087�

CoZZoque C7, suppzkment au n07, Tome 40, ~ u i Z Z e t 1979, page C7- 237

DFFERENCE BETWEEN ELECTRON TEMPERATURE AND HEAVY PARTICLES TEMPERATURE IN ARC PLASMA

H. Kafrouni, A. Gleizes and H. Dang Duc.

Centre de Physique Atomique, Laboratoire Associl au C. N. R. S. n0277, Univensitl Paul Sabatier, 218, route de Narbome, 31077 TouZouse France.

Over several years various authors / 1 - 2 / have r e p o r t e d t h a t t h e confined-arc plasma can show l a r - ge d e v i a t i o n s from Local Thermodynamic E q u i l i b r i u m (LTE) . These discrepancies appear under various forms : d e v i a t i o n s from complete LTE i f t h e pres-

sure i s considered constant, d e v i a t i o n s from Saha' s law f o r c e r t a i n atomic l e v e l s , d i f f e r e n c e between t h e e l e c t r o n temperature (Te) and t h a t o f heavy par- t i c l e s (Th). I n t h i s paper t h e l a t t e r question (Te-Th) w i l l be t h e o r e t i c a l l y and e x p e r i m e n t a l l y i n - v e s t i g a t e d f o r a plasma produced by a w a l l - s t a b i l i - zed a r c burning i n argon a t atmospheric pressure and c u r r e n t i n t e n s i t i e s o f between 6 and 35 A.

ANALYSIS. L e t us consider a s t a t i o n a r y plasma, t h e l o c a l values o f e l e c t r o n number d e n s i t y (ne) of which a r e known. I n t h e absence of a x i a l g r a d i e n t s , t h i s plasma can be described by t h e f o l l o w i n g equa- t i o n s :

- equations o f d e n s i t y conservation -

an.

+$(r n j vj)=(-J) a t c o l f o r j = 1, 2 , . . , (1) r a d

- ambipolar d i f f u s i o n f l u x -

dne 'e 'e ⁼ - A D (-)

A d r

- e l e c t r o n energy balance -

me - I d dTe

OE' = 3n P(- h "'h veh)k(Te-Th)- *(rhe F )

- s t a t e equation -

p = (na + ^n,)kTh + ne k Te

- and -

n a = N c n . j = 1 J

Equations (1) concern t h e d e n s i t i e s o f t h e r e a l l e - v e l s o f Ar I . The number o f unknown l e v e l s was li- m i t e d t o jM = 31. It i s assumed t h a t t h e e x c i t e d l e v e l s h i g h e r than jM a r e i n Saha e q u i l i b r i u m w i t h t h e e l e c t r o n s ; n . V . i s t h e d i f f u s i o n f l u x o f

J J atoms on l e v e l j :

nlV1 = - neVe (ground s t a t e ) n V = 0 f o r j > 1 ( e x c i t e d s t a t e s )

j j

(anj/attCol i s t h e balance o f c r e a t i o n s and losses, r a d

o f t h e atoms under consideration, due t o c o l l i s i o n and r a d i a t i o n processes. The r a t e s o f a l l t h e e n v i -

t

saged r e a c t i o n s appear i n t h i s term : e x c i t a t i o n and d e - e x c i t a t i o n , i o n i z a t i o n through c o l l i s i o n w i t h e l e c t r o n s , r a d i a t i v e recombination and photo-

i o n i s a t i o n , 3-body recombination, spontaneous de- e x c i t a t i o n and p h o t o - e x c i t a t i o n . These r e a c t i o n r a - t e s a r e c a l c u l a t e d from e f f e c t i v e experimental o r t h e o r e t i c a l cross-sections/3/ by assuming t h a t the e l e c t r o n s have Maxwellian d i s t r i b u t i o n .

I n eq. ( Z ) , DA i s t h e ambipolar d i f f u s i o n c o e f f i - c i e n t given by Devoto/4/ and A i s a c o r r e c t i o n term which takes i n t o account t h e atom g r a d i e n t and which, a t a f i r s t approximation, o n l y depends on ne ( a t constant pressure). V e i s t h e d i f f u s i o n v e l o c i - t y o f t h e e l e c t r o n s .

I n eq. ( 3 ) , E i s t h e a x i a l e l e c t r i c f i e l d measured, o t h e e l e c t r i c a l c o n d u c t i v i t y / 4 / a n d ;j t h e e l e c -

eh

tron-heavy p a r t i c l e e l a s t i c c o l l i s i o n frequlencies.

- v was c a l c u l a t e d from t h e e f f e c t i v e ea

momentum t r a n s f e r cross s e c t i o n . ^{X e} i s t h e t h e r - mal c o n d u c t i v i t y o f t h e e l e c t r o n s c a l c u l a t e d by Gorse /5/;

i s t h e i o n i z a t i o n energy o f Ar I and

0

R i s t h e l o c a l power l o s t through r a d i a t i o n p e r u n i t volume. I n o r d e r t o c a l c u l a t e t h i s l a s t term, about 250 l i n e s and t h e continuum r a d i a t i o n c o n t r i b u t i o n /6/ were considered t a k i n g i n t o account theabsorb-

t i o n o f c e r t a i n r a d i a t i o n s .

Knowing n e ( r ) and E, r i g o r o u s r e s o l u t i o n (eg. Runge- K u t t a ' s method) o f t h e system ( 1 ) - ( 5 ) i s d i f f i c u l t : i n s u f f i c i e n t knowledge o f t h e l i m i t c o n d i t i o n s ( r = R) and o f t e n repeated c a l c u l a t i o n o f t h e reac- t i o n r a t e s o f eq. ( 1 ) . Since t h e r e s o l u t i o n pro- blems come from (dTe/dr), t h i s term was used as pa- rameter : t h e determination o f dTe/dr i s r e a l i z e d

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797116

by an i t e r a t i v e method w i t h 4 steps :

i ) from t h e n e ( r ) p r o f i l e , a s i m i l a r p r o f i l e T,(r) i s (hosen and t h e values o f (dTe/dr), deduced from i t ;

i i ) using equations (2) and (3), t h e r e f o r e , f o r each v a l u e o f r, t h e v a r i a t i o n s o f Th w i t h Te canbe c a l c u l a t e d Th = f (Te) ;

i i i ) u s i n g equations ( I ) , (2) (4) and (5) t h e va- r i a t i o n s o f Th = g(Te) can be c a l c u l a t e d f o r each value o f r.

i v ) curves f and g cross a t one p o i n t , t h e s o l u t i o n o f t h e whole system ( a t p o i n t r ) . Thus as a f u n c t i o n o f r, a l l t h e r e q u i r e d values can be found : Te, Th and t h e atom d e n s i t i e s .

The s o l u t i o n i s improved by using the new p r o f i l e T e ( r ) as t h e s t a r t i n g p o i n t f o r step i j .

EXPERIMENTAL METHODS AND RESULTS. The experimental set-up i s described i n r e f e r e n c e /7/. I n o r d e r t o determine Te, ne i s f i r s t measured by l a s e r i n t e r - ferometry ( a t two wavelengths) and by spectroscopy (measurement o f t h e absolute i n t e n s i t y o f t h e con- tinuum r a d i a t i o n /7/ : these two techniques g i v e i d e n t i c a l r e s u l t s . The 3pg l e v e l d e n s i t y i s o b t a i n e d by measuring t h e absolute i n t e n s i t y o f t h e l i n e a t 430 nm. I f i t i s assumed t h a t t h i s l e v e l i s i n Saha e q u i l i b r i u m , t h e value o f Te can be deduced from these two measurements.

A r e l a t i p n s h i p i s obtained between Te and Th by pro- ceeding i n t h e f o l l o w i n g way : i n t h e s t a t i o n a r y s t a t e , f o r a f i x e d f i e l d value Te > Th. I f t h e f i e l d i s c u t , examination o f t h e r e l a x a t i o n times o f t h e phenomena described i n eq. (3) shows t h a t w h i l e t h e e l e c t r o n temperature passes from Te t o Thy ne and na have n o t had t h e t i m e t o change. I f n,j i s t h e d e n s i t y o f l e v e l j i n Saha e u i l i b r i u m :

~i - f j

n = ne2 c t e T - e ~ ~ ~ p ( ~ - ~ )

j ⁽⁶⁾

AS T decreases, n increases when ne remains cons- j

t a n t . Experimentally, a t c u r r e n t i n t e n s i t i e s o f l e s s than 23 A, a sharp increase i s observed i n t h e i n - t e n s i t y o f one o f t h e l i n e s e m i t t e d by l e v e l j when t h e f i e l d E i s c u t ( f i g . 1). The r e l a t i v e value o f t h e i n t e n s i t y increase i s d i r e c t l y r e l a t e d t o Te/Th.

It should be noted t h a t t h e l e v e l s under considera- t i o n a r e i n Saha e q u i l i b r i u m f o l l o w i n g t h e r e s o l u - t i o n o f system (1) and t h a t t h e i n t e r f e r o m e t r y mea- surements confirmed t h a t d u r i n g t h e increase time

o f t h e l i g h t i n t e n s i t y t h e changes i n ne and na a r e n e g l i g i b l e .

F i g . 1 : V a r i a t i o n w i t h t i m e o f t h e 696,5 nm l i n e i n t e n s i t y ( I = 3 A ) .

COMPARISON OF THEORETICAL AND EXPERIMENTAL RESULTS.

The v a r i a t i o n s o f (Te - T,,) w i t h t h e e l e c t r o n i c den- s i t y a r e given i n f i g . 2. These r e s u l t s concern mea- surements and c a l c u l a t i o n s a t t h e a x i s o f a 6 mmdia- meter argon a r c . Under t h e c o n d i t i o n s where t h e d i f - ference (Te - Th) i s e x p e r i m e n t a l l y detectable, c a l - c u l a t i o n showed t h a t t h e r a d i a t i o n l o s s i s n e g l i g i - ble, t h e energy l o s s due t o ambipolar d i f f u s i o n i s low (10 % o f t h e t o t a l ) and t h a t t h e d i f f u s i o n o f h e a t represents about 30 % o f t h e t o t a l losses. The c a l c u l a t e d values o f (Te - Th) a r e l i g h t l y g r e a t e r than measured ones. That may be due t o a systematic e r r o r o f t r a n s p o r t c o e f f i c i e n t s . Nevertheless t h e method used would seem i n t e r e s t i n g i n t h e e v a l u a t i o n of T, i n plasmas which a r e a l o n g way o u t o f LTE.

F i g . 2 : Difference between Te and Th versus ne ; --calculated r e s u l t s , + experimental values.

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