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HAL Id: jpa-00219853

https://hal.archives-ouvertes.fr/jpa-00219853

Submitted on 1 Jan 1980

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

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THE STATE OF THE ELECTRICAL ARC PLASMA

J. Richter

To cite this version:

J. Richter. THE STATE OF THE ELECTRICAL ARC PLASMA. Journal de Physique Colloques, 1980, 41 (C3), pp.C3-217-C3-223. �10.1051/jphyscol:1980334�. �jpa-00219853�

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JOURNAL DE PHYSIQUE Colloque C3, supplkment au n o 4 , Tome 41, avril 1980, page C3-217

THE ST.4TE OF THE ELECTRICAL ARC PLASMA

J . R i c h t e r

I n s t i t u t fur E x p e r i m e n t a l p h y s i k d e r U n i v e r s i t d t K i e l , O l s h a u s e n s t r . 4 0 - 6 0 , 2300 K i e l I , Germany

A b s t r a c t .- The plasma s t a t e o f ? a r t i a l t h e r m o d y n m i c e q u i l i b r i u m (PLTE) i s d i s c u s - s e d f o r a r c g a s e s . Plethods t o d e t e r m i n e t h e nlasma p a r a m e t e r s i n h i g h l y s t a b i l i - zed c a s c a d e a r c s u n d e r t h e a s s u m n t i o n o f PLTE a r e summarized and d i s c u s s e d . Some m e a s u r i n g r e s u l t s c o n c e r n i n g a r g o n a r c s a t low e l e c t r o n d e n s i t i e s a r e ? r e s e n t e d .

1 . I n t r o d u c t i o n . - The t e c h n i q u e o f e l e c t r i - c a l a r c s h a s been d e v e l o p e d a f t e r t h e i n v e n - t i o n o f t h e c a s c a d e a r c by Maecker /1/ t o a n h i g h d e g r e e o f ? e r f o r m a n c e . C a s c a d e a r c s r u n - n i n g i n i n e r t g a s e s a r e v e r y s t a b l e and r e - o r o d u c i b l e plasma l i g h t s o u r c e s . S t a b i l i t y and r e p r o d u c i b i l i t y c a n b e k e u t below o r i n t h e o r d e r o f 1 % . The plasma s t a t e i n t h e a x i s o f s u c h s t a b i l i z e d a r c s i s w e l l known compared w i t h many o t h e r - e s p e c i a l l y t r a n s i - - e n t - p l a s m a s o u r c e s . T h i s q u a l i t y o f a r c s o u r c e s i s t h e r e a s o n f o r t h e i n t e r e s t o f a number o f n a t i o n a l ? h y s i c a l l a b o r a t o r i e s

( P a r i s , Washington, T e d d i n g t o n , B e r l i n ) enga- ged i n t h e i n v e s t i g a t i o n o f a r c r a d i a t i o n under t h e a s p e c t o f UV and vacuum UV r a d i a t - i o n s t a n d a r d s . O t t e t a 1 . / 2 / , / 3 / B r i d g e s and O t t /4/,Key and P r e s t o n / 5 / , E i n i e l d e t a 1 . / 5 / . But t h e i n c r e a s i n g a c c u r a c y o f measurement r e v e a l s new p r o b l e m s which h a v e t o be s o l v e d when t h e q u a n t i t a t i v e o l a s m a s p e c t r o s c o p y w a n t s t o e n t e r a new d i m e n s i o n o f ? r e c i s i o n . Here, t h e p r o b l e m s a r e : b e t t e r r a d i a t i o n s t a n d a r d s and a b e t t e r !cno~.i2ed7e o f t h e d e v i a - t i o n from e q u i l i b r i u m s t a t e LTE. T h i s a r t i - c l e i s d e a l i n g w i t h tine plasma s t a t e model PLTE and a 5ew-mainly e x > e r i m e n t a l - i n v e s t i - g a t i o n s c o n c e r n i n g t h e a r c plasma a t l o w e r e l e c t r o n d e n s i t i e s .

2 . P a r t i a l L o c a l Thermod:7namic E q u i l i b r i u m (PLTE) .- A l a r g e number o f t h e o r e t i c a l and e x p e r i m e n t a l i n v e s t i g a t i o n s o f t h e l a s t t e n y e a r s i n d i c a t e t h a t t h e p l a s m a i n t h e a x i s of a c y l i n d r i c a l and s t a t i o n a r y & l e c t r i c a l a r c b u r n i n g a t normal p r e s s u r e i s n o t n e c e s - s a r i l y i n t h e s t a t e of l o c a l thermodynamic e q u i l i b r i u m (LTE) . Pogenoe and Shumaker /7/, PJiese e t a l . /8/, Garz /9/, Uhlenbusch / l o /

a n d B a c r j e t a l . /11/, / 1 2 / .

The plasma oE s u c h h i g h c u r r e n t a r c i s c o n t r o l l e d by7 t h e e l e c L ~ o n s which h a v e un- d e r t h o s e c o n d i t i o n s a veil e s t a b l i s h e d '!axweLlian v e l o c i t y d i s t r i b u t i o n . The elec- t r o n s n i c k u ~ t h e e n e r g y i n t h e e l e c t r i c a l f i e l d , t r a n s f e r i t 3 a r t i a l l . 1 t o t h e n e u L a a l s and i o n s , a n d c o ? u l a t e and d e - k 2 o ~ u l a t e ex- c i t e d l e v e l s by7 i n e l a s t i c c o l l i s i o n s . I t seems t h a t i n e l a s t i c c o l l i s i o n s o f heavy p a r t i c l e s p l a y a s u b o r d i n a t e r o l l w i t h t h e e x c e c t i o n oE t h e a r c e d g e ( B a c r i e t a1./13/).

I n t h i s s i m n l e p i c t u r e o f a c o l l i s i o n a l dominated p l a s m a , LTE i s o b t a i n e d i f t h e

i n e l a s t i c d e - e x c i t a t i o n c o l l i s i o n s v ~ i l l exceed t h e r a d i a t i o n and d i E f u s i o n l o s s e s . I n c a s e 04 a two l e v e l model atom, t h i s g r o - c e e d i n y c a n b e d e s c r i b e d by7 a sc:lematic r a t e e q u a t i o n

H e r e n and n 2 a r e t h e c o p u l a t i o n d e n s i t i e s 1

o f t h e l o w e r and u p p e r l e v e l , n t h e e l e c - e t r o n d e n s i t y , < Q l + 2 . v e > and < Q 2 4 1 . ~ e > t h e r a t e c o e f f i c i e n t s f o r e x c i t a t i o n a n d d e - e x c i t a t i o n by e l e c t r o n c o l l i s i o n , A2+1 t h e s p o n t a n e o u s t r a n s i t i o n p r o b a b i l i t y t o t h e g r o u n d s t a t e , y a d i m e n s i o n l e s s f a c t o r a c - c o u n t i n g f o r r e a b s o r p t i o n ( O < y < l ) , and V .

( n .v + ) a t e r m d e s c r i b i n g t h e e x c i t a t i o n

2 2

l o s s e s by d i f f u s i o n o f p a r t i c l e s .

F o r a w e l l d e f i n e d k i n e t i c t e m p e r a t u r e Te of t h e e l e c t r o n s , o n e o b t a i n s by a p p l i - c a t i o n o f t h e p r i n c i g l e o f d e t a i l e d b a l a n - c i n g o n e x c i t a t i o n and d e - e x c i t a t i o n a n e x - c r e s s i o n which t a l t e s t h e ? l a c e of t h e Boltzmann f a c t o r e x 9 ( -E/kT) :

n 2 / n l = b ( n e ) . ex?(-E 1 2 /kTe) ( 2

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980334

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C3-2 18 JOURNAL DE PHYSIQUE

w i t h

b ( n e ) = I 1 + n e . < ? 2 + 1 . ~ e > A 2 * ~ - Y

s t a t e may b e a c c o n n a n i e d by t h i s d i f f e r e n c e . ( 3 ) F o r a l o n g p e r i o d of t i m e , o n e h a s b e l i e v e d

t h a t t h e d e c r e a s i n g g a s t e m ? e r a t u r e i s t h e

V. ( n 2 . v 2 m a i n r e a s o n f o r d e ? a r t u r e from LTE.

+ n 2 . n e . <Q2*1 ' V > 3 . E l e c t r o n d e n s i t y . - T h i s q u a n t i t y may b e

e m e a s u r e d i n PLTE d i r e c t l y from t h e h a l f

Llith i n c r e a s i n g d e n s i t y ne, i n c r e a s i n g r e a b -

w i d t h o f S t a r k - b r o a d e n e d s p e c t r a l l i n e s , s o r p t i o n (y,O) , and d e c r e a s i n g d i f c u s i o n o n e

f r o m t h e c o n t i n u o u s r a d i a t i o n i n t e n s i t y , o r o b t a i n s b = 1 o r LTE.

by i n t e r f e r o m e t r y . The a c c u r a c y o f t h e f i r s t I t h a s b e e n shown b y many a u t h o r s ( I l e n z e l

two m e t h o d s i s l i m i t e d by o u r k n o w l e d g e o f /14/, B a t e s A t a1 . A 5 / 1 Drawin /16/. u h l e n b u s c h

entering t h e concerning e t a l . / l 7 / ) w h o h a v e s o l v e d s u c h r a t e e q u a -

f o r m u l a s . -

t i o n s y s t e m s f o r m o r e r e a l i s t i c m u l t i - l e v e l

I n t e r f e r c m e t r y y i e l d s t h e r e f r a c t i v i t y s y s t e m s , t h a t 2 t s u f f i c i e n t l y l a r g e e l e c t r o n

w h i c h i s i n c a s e o f s l i g h t l y i o n i z e d p l a s m 2 d e n s i t i e s , a l l e x c i t e d l e v e l s - t h e f r e e elec-

m a i n l y d e t e r m i n e d by t h e e l e c t r o n d e n s i t y t r o n i c s t a t e s i n c l u d e d - a r e m u t u a l l y i n a

( i n d e ? e n d e n t o n t h e p l a s m a s t a t e ) : v e r y good Saha-Boltzmann e q u i l i b r i u m w h i l e

t h e g r o u n d s t a t e may s t i l l b e o v e r p o ? u l a t e d .

e 2 X 2 . n + 2nc( . n

T h i s ;>lasma s t a t e i s c a l l e d p a r t i a l l o c a l e o o

thermod:lnamic e q u i l i b r i u m o r PLTE.

F o r a t o m i c s y s t e m s a s H , N,O, C , C l a n d t h e + ( 4 )

n o b l e g a s e s o n e o b s e r v e s a l a r g e e n e r g y ga.3 w h e r e a a n d a+ a r e t h e c o e Z f i c i e n t s o f b e t w e e n t h e g r o u n d s t a t e and t h e f i r s t e x c i - p o l a r i z a t i o n o f n e u t r a l s and i o n s . The f i r s t t e d e n e r g y l e v e l a n d a r e l a t i v e l y s m a l l e n e r - term o n t h e r i g h t hand s i d e o f e q . ( 4 ) domi-

gy d i s t a n c e b e t w e e n t h e f o l l o w i n g e x c i t a t i o n n a t e s u n d e r a r c c o n d i t i o n s . R e f e r a l s o t o s t e p s . T h o s e a t o m i c s y s t e m s c a n b e d e s c r i b e d f i g u r e 1 . The m e a s u r e m e n t o I e l e c t r o n d e n - e x c e l l e n t l y by a two l e v e l m o d e l and t h e s i t i e s w i t h i n t e r f e r o m e t e r s u s i n g e q . ( d ) i s PLTE s t a t e by o n e p a r a m e t e r b < 1 . F u r t h e r - a v e r y w e l l known t e c h n i q u e .

m o r e , e q . ( 3 ) c a n b e a p p l i e d f o r a n d i s c u s - s i o n o f t h e b f a c t o r v e r y w e l l .

R a t e e q u a t i o n c a l c u l a t i o n s w h i c h i n c l u d e 10"

t h e r e a b s o r p t i o n ( y < 1 ) a n d t h e d i f f u s i o n o f p a r t : . c l e s r u n i n t o e x t r e m m a t h e m a t i c d i f f i - c u l t i e s , b e c a u s e a b s o r p t i o n and d i f f u s i o n c a n n o t b e d e s c r i b e d a s l o c a l p r o c e s s e s . The t o t a l a r c p l a s m a w i t h a l l i n h o m o g e n e i t i e s

n

h a s t o b e t a k e n i n t o c o n s i d e r a t i o n . I n a d d i - t i o n , t h e p o o r k n o w l e d g e o f a t o m i c c o n s t a n t s

(absorgtion.coe?ficients, l i n e p r o f i l e s , d i E -

I

0

f u s i o n c o n s t a n t s and s o o n ) d i m i n i s h s t h e v a l u e o f t h o s e c a l c u , l a t i o n s . N e v e r t h e l e s s a number 05 i n v e s t i g a t i o n s h a s b r o u g h t c o n s i - d e r a b l e i m p r o v e m e n t s i n t h i s r e s p e c t ( U h l e n -

b u s c h a n d F i s c h e r / 1 8 / , Hermann /19/, r e f e r v

a l s o t o Drawin /16/ ) .

The PLTE s t a t e n o r m a l l y o c c u r s a t d e c r e a -

s i n g e l e c t r o n d e n s i t y w h i c h i s c o n n e c t e d - 10' J&L

w i t h a d e c r e a s i n g d e g r e e o f i o n i z a t i o n . T h i s 0 5000 10000 K

0 TEMPERATURE

l e e d s t o a s m a l l e r c o l l i s i o n r a t e b e t w e e n

t h e e l e c t r o n s a n d t h e h e a v y p a t i c l e s a n d t o Fig. 1 . - Refractivity of an argon plasma a t I atm.

a d i f f e r e n c e b e t w e e n t h e e l e c t r o n a n d t h e as a function of temperature.

g a s t e m p e r a t u r e Te< Tgas. T h u s , t h e PLTE

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The d i f f i c u l t y o f a p p l i c a t i o n t o h i g h p r e s - s u r e arcs - e s p e c i a l l y end-on o b s e r v a t i o n -

l i e s i n t h e f a c t , t h a t t h e r e f r a c t i v i t y of t h e plasma i n t e g r a t e d o v e r t n e o p t i c a l p a t h

( l a s e r - p l a s m a - d e t e c t o r ) i s m a i n l y d e t e r m i - ned by tine c o l d l a y e r s o u t s i d e t h e p l a s m a . F i g u r e 1 shows t h a t t h e r e f r a c t i v i t y b e c a n e s e x t r e m e l y l a r g e a t low t e m p e r a t u r e , c l o s e t o z e r o f o r a v e r y weakly i o n i z e d p l a s m a , and n e g a t i v e f o r i n c r e a s i n g e l e c t r o n d e n s i t y .

A f t e r f i r s t i n t e r f e r o m e t r i c measurements of Hearn and K o n j e v i c /20/ and Baum e t a l . /21/, who measured s i d e - o n , Briinger a n d Kock /22/, B S s s l e r /23/, X a f r o u n i e t a1./24/, H e l b i g and co-workers /25/, /26/ have d e v e - l o p e d and a p p l i e d a n e x p e r i m e n t a l method which b y - p a s s e s t h e above m e n t i o n e d d i f f i c u -

l t i e s : S w i t c h i n g o f f t h e a r c c u r r e n t w i t h i n a v e r y s h o r t t i m e , t h e a r c p l a s m a w i l l d e c a y and t h e c h a n g e o f r e f r a c t i v i t y c a n be o b s e r - ved d u r i n g t h e p h a s e o f r e c o m b i n a t i o n , which

i s c l o s e t o 0.1 m s .

P l a c i n g t h e a r c end-on i n t o o n e arm of an t l i c h e l s o n i n t e r f e r o m e t e r which o p e r a t e s a t two d i f f e r e n t w a v e l e n g t h s , t h e t i m e o f ccan- p l e t e r e c a n b i n a t i o n c a n be a s c e r t a i n e d by o b s e r v i n g a n i d e n t i c a l c h a n g e o f r e f r a c t i - v i t y a t b o t h w a v e l e n g t h s . Thus t h e e l e c t r o n d e n s i t y b e f o r e t h e s h o r t c i r c u i t c a n b e re- c a l c u l a t e d by c o u n t i n g t h e f r i n g e s i n t h e two w a v e l e n g t h c h a n n e l s . The v x p e r i m e n t a l s e t - u p o f t h e a u t h o r s q u - t e d above i s n e a r l y i d e n t i c a l . I t i s shown i n F i g u r e 2 .

The r e s u l t of t h e i n t e r f e r o m e t r i c m e a s u r e - q n t i s t h e q u a n t i t y

I R e f e r e n c e q ~ h o t o d l o d e l beam

L a s e r 1.1 P Arc d ~ s c h o r q e

TWO W A V E L E N G T H S M I C H E L S O N I N T E R F E R O M E T E R

Photo d ~ o d e

N ~ e r e s i s a c o o r d i n a t e a l o n g t h e a r c a x i s . I t c a n b e measured w i t h a n e r r o r i n t h e o r - d e r 0 5 m a g n i t u d e o f o n l y 1%, which e x c e e d s t h e a c c u r a c y o f a l l c o n v e n t i o n a l methods t o measure n by a f a c t o r o f 5 50 10. e

F o r a n a p p r o x i m a t e l y homogeneous l a y e r , o n e c a n w r i t e

I n e ( s ) . d s = n e s s e f f ( 6 ) To p r e s e r v e t h i s e x c e l l e n t a c c u r a c y , i t i s n e c e s s a r y t o m e a s u r e t h e e f f e c t i v e l e n g t h seff o f t h e a r c column w i t h a s i m i l a r s m a l l e r r o r . seff i s w i t h i n a b o u t 5% t h e l e n g t h o f t h e a r c c h a n n e l . B z s s l e r /23/ and Nick /26/ h a v e d e t e r m i n e d J n e . d s f o r i d e n t i c a l a r c s w i t h d i f f e r e n t l e n g t h s o f t h e a r c c h a n n e l . So, t h e y o b t a i n e d t h e l ~ n g t h o f t h e inhomogeneous p a r t of t h e l a y e r and c o u l d d e t e r m i n e t h e e l e c t r o n d e n s i t y i n a n a r g o n c a s c a d e a r c a t o n e a t m o s 3 h e r e and d i f f e r e n t c u r r e n t s and c h a n n e l d i a m e t e r s w i t h a n a c c u r a c y i n t h e o r d e r o f 2%

T a b l e

Accuracy o f e l e c t r o n d e n s i t y , measured by two w a v e l e n g t h s i n t e r f e r o m e t r y (Nick ,/26/)

4 . E l e c t r o n t e m ~ e r a t u r e . - An a c c u r a t e d e t e r - m i n a t i o n o f t h e e l e c t r o n t e m p e r a t u r e T i n

e PLTE p l a s m a s i s ~ r o b l e m a t i c . The numerous p r o c e d u r e s t o o b t a i n t!le t e m p e r a t u r e ( b e t - t e r t h e e l e c t r o n t e m p e r a t u r e ) s p e c t r o s c o p i - c a l l y a r e r e s t r i c t e d i n PLTE t o t h o s e i n which t h e ground s t a t e p o p u l a t i o n i s n o t i n v o l v e d .

The r e a s o n t h a t i t i s p o s s i b l e t o g e t t e m p e r a t u r e e r r o r s i n t h e o r d e r of 1% i n LTE a r c g l a s m a s , l i e s i n t h e f a c t t h a t h i g h l y e x c i t e d s ? e c t r a l l i n e s c a n ' b e c h o s e n a n d t h a t t h e ground s t a t e p o ? u l a t i o n d e n s i - t y c a n b e computed from t h e t o t a l g a s p r e s - s u r e v i a D a l t o n ' s law. The i n t e n s i t y o f a n e m i s s i o n l i n e i n LTE i s g i v e n by

1 I I I

arc c u r r e n t ( A ) 135 550 ; 65 , 30

Fig.2.- Two wavelengths interferometer f o r the deter- mination plasma r e f r a c t i v i t y (schematically).

plasma l e n g t h 5 1 . 5 1.5% 1 1 . 5 %

1 . 7 % 0.8%

0.3%

2.5%

2 x ( s t a n d a r d d e v . ) s t a r t i n g p h a s e f i n a l p h a s e

!El A l 2

1.1%

0.6%

1.9%

1 . 9 1 . 9 %

1.4%

0.5%

2.C%

0 . 4 % 1.54, 0.2%

1 . 6 %

(5)

C3-220 J O U R N A L DE PHYSIQUE

The d e n s i t y o f n e u t r a l p a r t i c l e s n o d e n e n d s oE i n t e n s i t y m e a s u r e m e n t s s u f f e r s by t h e o n l y w e a k l y o n t h e t e m ? e r a t u r e w h i l e t h e e x - l a c k o f good r a d i a t i o n s t a n d a r d s .

p o n e n t i a l f a c t o r i n c r e a s e s r a ~ ~ i d e l ? ; w i t h '7 5. Gas t e m n e r a t u r e .- A d e c r e a s e d g a s temge- i

LC E/kT > 1 . E/kT 1 0 o r more m e a n s t h a t r a t u r e i s i n ~ r i n c i 1 7 l e a l ~ ~ a y s t o b e e x y e c t e d w i t h a p o o r l y known t r a n s i t i o n p r o b a b i l i t y i n a r c p l a s m a s . An o l d s e m i - e m n i r i c a l m e - A and a n i n a c c u r a t e m e a s u r e d i n t e n s i t l r J a t h o d t o o b t a i n t h e g a s t e m p e r a t u r e i s b a s e d t e m p e r a t u r e w i t h a n a c c e p t a b l e a c c u r a c y n a y o n t h e e n e r g v b a l a n c e of t h e e l e c t r o n g a s b e o b t a i n e d . ( F i n k e l n b u r g a n d I l a e c k e r , / 2 9 / ) .

To m e a s u r e T i n t h e PLTE s t a t e , o n e i s t J e g l e c t i n g i n e l a s t i c c o l l i s i o n s a n d e n e r g y e

c o n f i n e d t o e x p r e s s i o n s c o n t a i n i n g B o l t z m a n n d i s s i n a t i o n b y e l e c t r o n d i f f u s i o n , o n e f i n d s C a c t o r s w i t h E / ~ T = 1 : t h e known r e l a t i o n

e

2 M i s t h e m a s s 05 t h e a t o m s , P t h e e l e c t r i c a l

- -

n 1 'I2 .exp(-(Eion-Ei)/*Te) f i e l d s t r e n g t h ( t o b e m e a s u r e d ) , A t h e me+n i g i

( 9 ) Eree n a t h o: t h e e l e c t r o n s ( t o b e c a l c u l a t e d ) Here n . a n d n d e n o t e p o n u l a t i o n d e n s i t i e s 05 and a a f a c t o r n e a r u n i t y ( B e b r i n g e r e t a l .

j

e x c i t e d l e v e l s , r r h i c h c a n b e m e a s u r e d v i a / 3 0 / , Hermann a n d rlonterde-Gs.rcj a , ,/3 1/ ) .

l i n e i n t e n s i t i e s A m r e e x p e r i m e n t a l w r o c e d u r e t o m e a s u r e t h e g a s t e m p e r a t u r e h a s b e e n p r o p o s e d by J = hcs . ~ . n .

4 n X 1

( l o )

G u r e v i c h e t a 1 . ( / 3 2 / , / 3 3 / ) a n d l a t e r o n i n - v e s t i g a t e d a n d a 2 p l i e d b y o t h e r a u t h o r s ( v . w i t h a known t r a n s i t i o n p r o b a b i l i t y A . !Tit11

Bergmann / 3 4 / , 4 i c h t e r / 3 5 / ) . G u r e v i c h a n r e a l i s t i c u n c e r t a i n t y o f 1 0 % f o r t h e t r a n - o b s e r v e d a s u d d e n r i s e o f t h e l i n e i n t e n s i - s i t i o n p r o b a b i l i t y a n d o f 5% f o r a n i n t e n s i - t y a f t e r s h o r t e n i n g t h e a r c d i s c h a r g e . P h i s t y m e a s u r e m e n t , o n e o b t a i n s t e m p e r a t u r e er- i n t e n s i t y j u m n c a n be understood b:, a coo- r o r s i n t h e same o r d e r o f m a g n i t u d e ! l i n g o f t h e e l e c t r o n g a s down t o t h e g a s

A somewhat h i g h e r a c c u r a c y o f e l e c t r o n t e m l > e r a t u r e , w h i c h n e e d s a f e w m i c r o s e c o n d s . t e m p e r a t u r e m e a s u r e m e n t may b e a t t a i n e d by R e f e r to Tilure 3 .

o b s e r v a t i o n o f o p t i c a l l y n o n - t h i n r a d i a t i o n T h i s c o n s i d e r a t i o n i s c o r r e c t f o r a n h i g h a l o n g t h e a r c a x i s . ( r l e i n e r s a n d rreiss / 2 7 / , heat capacity the heavy ?articles rrhich B a c r i e t a 1 . / 1 3 / , L e c l a i r e a n d Schram / 2 8 / ) . corresponds to a small degree of

w i t h t h e b l a c k b o d y i n t e n s i t y B X (Te) a n d t h e ess. ( 8 ) and ( 9 ) , one obtains a a b s o r p t i o n c o e f f i c i e n t K a l o n g t h e p a t h - s l i g h t l y d i f - r e n t Eormula ? o r t h e i n t e n s i - l e n g t h o n e m e a s u r e s t h e i n t e n s i t y t y o f a l i n e

I f a s p h e r i c a l m i r r o r w i t h t h e r e f l e c t i v i t y e x ? ( ( 3

i o n - E ) /kTe) / ~ y . ( 1 5 )

R f o c u s s e s t h e r a d i a t i o n b a c k i n t o t h e a r c , Inserting the gas temperature into e q . ( 1 5 ) , o n e m e a s u r e s t h e i n t e n s i t y w i l l i n c r e a s e . T h i s i s c o r r e c t

K c a n e v a l u a t e d f r o m b o t h e q u a t i o n s a n d o n e o b t a i n s

2 2 5

J 1 . R 2 h c / X B X We) = -

J . (1 + R ) - J 2 e x p (hc/XkTe) -1 1

( 1 3 ) The s e n s i t i v i t y o f t h i s method i n c r e a s e s a t

low w a v e l e n g t h s , b u t i n t h e W t h e a c c u r a c y

a s l o n g a s t h e e l e c t r o n d e n s i t y r e m a i n s con- s t a n t . T h i s c o n d i t i o n is f u l f i l l e d , b e c a u s e t h e r e c o m b i n a t i o n r e q u i r e s a b o u t 1 0 0 m i c r o s e c o n d s . T h u s , o n e o b t a i n s f r o m e q . ( 1 5 ) J / J o = J ( n e f T g a s ) / J ( n e , T e ) 1 (16) and T f o l l o v ~ s , when T h a s b e e n measu-

g a s e

r e d e l s e w h e r e .

The e x p e r i m e n t a l e q u i p m e n t f o r t h e o b s e r - v a t i o n o f t h e i n t e n s i t y jump a n d t h e s h o r t

(6)

600 V

ni/nl = b.exp(-Ei/kTe) w i t h b = c o n s t . < 1 ( 1 7 ) n l i s t h e g r o u n d s t a t e n o ? u l a t i o n d e n s i t y and b t h e same f o r a l l e x c i t e d l e v e l s .

F o r t h e d e t e r m i n a t i o n o f b , t h e q u a n t i t i e s n l , n i l and Te h a v e t o b e m e a s u r e d . The measurement of Te h a s b e e n d e s c r i b e d a b o v e ,

Short Circuit of t h e Arc t h e d e n s i t y ni may be t a k e n from a n i n t e n - s i t y measurement a c c o r d i n g e q . (1) . The mea- s u r e m e n t o f t h e g r o u n d s t a t e p o p u l a t i o n may

4 I b e p e r f o r m e d a s R e h r i n g e r /3S/ d i d , by t h e

1

I

1 'I I! --- Current --- . PC=-

0 20 LO us

- t i m e - I

Intensity a n d Current

(Schematically)

o b s e r v a t i o n of t h e r e s o n a n c e l i n e o r a n o t h e r p r i n c i ? a l l i n e ( r e f e r t o e q . (13)).

T h i s d i r e c t method h a s t h e d i E f i c u l t y e t h a t t h o s e l i n e s l i e m o s t l y i n t h e vacuum W and t h a t c o l d l a y e r s i n t h e d i r e c t i o n o f o b s e r v a t i o n ? r e v a i l e m i s s i o n and a b s o r p t i o n i n t i e plasma.

A second way t o g e t i n f o r n a t i o n a b o u t t h e g r o u n d l e v e l p o p u l a t i o n i s v i a t i e t o t a l F i g . 3 . - Upper part : schematic diagram of the argon g a s p r e s s u r e and t h e g a s t e m p e r a t u r e . A t a arc c i r c u i t f o r current i n t e r r u p t i o n . Lower part :

intensity of an spectral line and arc current S m a l l d e g r e e of i o n i z a t i o n and a t o m i c s y s - -

a s a f u n c t i o n of time. tems w i t h a l a r g e e n e r g y g a p between t h e c i r c u i t o f t h e a r c i s s i m p l e ( F i g . 3 ) . Both g r o u n d s t a t e and t h e f i r s t e x c i t e d o n e , t h e methods f o r t h e d e t e r m i n a t i o n o f T y i e l d f o l l o v r i n g a ? y r o x i m a t i o n s y i e l d

q a s t h e same r e s u l t s w i t h i n t h e e r r o r i i m i t s ,

n < < n o , n l n + p = n .IcT

e x c . o g a s . ( 1 8 )

when Te/T < 2 . R e f e r t o f i g u r e 4

g a s Combining b o t h e q u a t i o n s and i n s e r t i n g n l

L i n t o eq. ( 1 7 ) , o n e o b t a i n s

Because o f t h e f a c t t h a t Ei/kTe i s i n t h e o r d e r o f m a g n i t u d e of 1 0 and t h e a c c u r a c y o f t h e Te measurement b e t w e e n 5 and l o % ,

t h e a c c u r a c y o f b i s v e r y p o o r . B u t w i t h d e c r e a s i n g a r c c u r r e n t d e v i a t i o n f r o m LTE

i n c r e a s e r a p i d e l y . F i g u r e 5 shows some ex-

~ e r i m e n t a l r e s u l t s o b t a i n e d w i t h a 4mm a r - gon arc.

log b 0 RICYTER . HELBIG 0 N I C K

I I I _ I I

I I

0 L 8 1 2 A

- a r c c u r r e n t ---c

1 !

F i g . 4 . - Gas temperature i n an argon arc JRichter, / 3 5 / l , o p e n c i r c l e s : measured v i a the sound v e l o c i t y , s o l i d c i r c l e s : measured v i a the e l e c t r i c a l f i e l d

strength, c r o s s e s : measured v i a the i n t e n s i t y jump. i

6. Under ~ o p u l a t i o n f a c t o r .- A c c o r d i n g t o e q . I I /r. 1 I ARGON A R C 1 otm , Lmm ,$

( 2 ) , t h e u n d e r p o p u l a t i o n o f a l l e x c i t e d - 2

15.5 16.0 16.5 17.0 i

17.5

l e v e l s i n t h e PLTE s t a t e i s g i v e n by

D log n,Imeasured) n, I n cm3 F i g . 5 . - Keasured underpopulation f a c t o r b f o r an argon arc plasma.

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C3-222 JOURNAL DE PHYSIQUE

'3 s;?ov~s n s i g n j < ? . c a n t dev!-ation Crom u n i t y b e l o w a n e l e c t r o n d e n s i t y of 1 . 5 x 1 0 ' 6cm- 3 .

N i c k , / 2 6 / , h a s f o u n d t h a t t h i s l i m i t w i l l d e c r e a s e w i t h a l a r g e r d i a m e t e r o f t h e a r c c h a n n e l .

L p r g e d e v i a t i o n s Crom LTE - c o n c e r n i n g t h e g r o u n d s t a t e o v e r p o p u l a t i o n - h a v e a much w e a k e r i n f l u e n c e o n t h e m e a s u r e d e l e c t r o n t e m ? e r a t u r e . T h i s i s d e m o n s t r a t e d i n f i g u r e 6.

A T E M P E R A T U R E

I K l

L v ,, , , , 7 -

L 10 20 LO A

ARC CURRENT

Fig.6.- Temperatures in an argon arc obtained with LTE and PLTE diagnostics (Richter, /36/).

The s p e c t r o s c o p i c d a t a o n w h i c h t h e t e m p e r a - ture.: i n F i g u r e 6 a r e b a s e d , a r e t a k e n f r o m R i c h t e r /3 6 / .

L l i t h t h e a s s u m p t i o n o f LTE i n a n a r g o n c a s - c a d e a r c , o n e o b t a i n s w i t h d e c r e a s i n g a r c c u r r e n t a continuous1:r d r o p p i n g t e m p e r a t u r e . Assuming PLTE, t h e e l e c t r o n t e m p e r a t u r e becomes c o n s t a n t a t low c u r r e n t s . T h e s e mea- s u r e m e n t s h a v e b e e n p e r f o r m e d i n t h e a r c a x i s . T h u s , o n e h a s t o c o n c l u d e t h a t i n e l a s - t i c c o l l i s i o n s o f h e a v y p a r t i c l e s h a v e a much l o w e r t e m p e r a t u r e i n t h e c u r r e n t r a n g e b e l o w 20 A and d o n o t e s t a b l i s h t h e Boltzmann

d i s t r i b u t i o n o f t h e e x c i t e d l e v e l s . 7 . C o n c l u s i o n . - The p l a s m a i n t h e a x i s o f c a s c a d e arcs i s i n t h e LTE o r a t l e a s t i n t h e PLTE s t a t e . G a s e s w i t h v e r y h i g h e x c i t a - t i o n e n e r g i e s (He,Ne) c a n n o t b e b r o u g h t t o

t h e h y d r o g e n arc w i t h hig11 m e a s u r i n g p r e c i - s i o n i n d i c a t e some d e v i a t i o n s f r o m LTE tow- a r d s PLTE (Viese e t a l . /37/) . S p e c t r o s c o - p i c m e a s u r e m e n t s , r e p o r t e d i n t h i s a r t i c l e , show t h a t l a r g e d e v i a t i o n s from LTE o c c u r a t e l e c t r o n d e n s i t i e s b e l o w 1016cm-3 i n a n a r g o n arc. I n a d d i t i o n , i t h a s b e e n p o i n t e d o u t , t h a t t h e o v e r p o p u l a t i o n Z a c t o r b w h i c h i s a n i m p o r t a n t p a r a m e t e r i n ?LTE, c a n n o t b e m e a s u r e d w i t h a n a c c e p t a b l e a c c u r a c y .

T h u s , i t t u r n s o u t t h a t t h e a c c u r a c y w h i c h c a n b e a c h i e v e d a t t h e moment t o m e a s u r e t h e e l e c t r o n t e m p e r a t u r e u n d e r PLTE assump- t i o n i s n o t s u f f i c i e n t . An h i g h e r a c c u r a c y c a n b e o b t a i n e d p a r t i a l l y b y b e t t e r o s c i l - l a t o r s t r e n g t h s ; i n a n y c a s e b y r a d i a t i o n s t a n d a r d s w i t h a n i n c r e a s e d a c c u r a c y ( 1 % ) .

T h e p l a s m a s t a t e o u t s i d e t h e a r c a x i s -

n o t d e l t i n t h i s a r t i c l e - i s more p r o b l e m a - t i c a l l y . The s p e c t r o s c o p i c m e a s u r e m e n t s re- q u i r e a much h i g h e r s p a t i a l r e s o l u t i o n and h a v e t o b e p e r f o r m e d s i d e - o n , w h i c h means a s loss oZ a c c u r a c y . The u n d e r s t a n d i n g o f t h e ~3lasrna s t a t e i n t h i s r e g i o n i s more d i . ~ ~ ~ - i c u l t b e c a u s e h i g h c u r r e n t s o f h e a t , r a d i a t i o n a n d d i f F u s i o n o c c u r u n d e r t h e i n - f l u e n c e 02 e x t r e m e l y h i g h t e m p e r a t u r e g r a - d i e n t s ( 1 051</cm o r m o r e ) .

R e f e r e n c e s

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/ 2 / O t t , I!.!?., F i e f f e - P r e v o s t , P . , a n d

? ? i e s e , b!.L., A p p l . O ~ t . l _ l ( 1 9 7 3 ) 1 6 1 8 . /3/ O t t , !!.R., B e h r i n g e r , K . , a n d G i e r e s , G . ,

A p ~ 1 . O p t . fi ( 1 9 7 5 ) 2121.

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-

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( 1 9 7 6 ) 1 1 3 1 .

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Nat.Bur.Stand.7LA ( 1 9 7 2 ) 7 1 .

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( 1 9 7 7 ) 2165.

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(8)

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