THEORY OF HOLLOW CATHODE IN ATMOSPHERIC ARC IN NOBLE GAS

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THEORY OF HOLLOW CATHODE IN ATMOSPHERIC ARC IN NOBLE GAS

F. Baksht, A. Rybakov

To cite this version:

F. Baksht, A. Rybakov. THEORY OF HOLLOW CATHODE IN ATMOSPHERIC ARC IN NOBLE GAS. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-341-C7-342. �10.1051/jphyscol:19797168�.

�jpa-00219144�

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JOURNAL DE PPHYSIQUE

THEORY OF =LOW CATHODE IN ATMOSPHERIC ARC IN NOBLE GAS

F.G. Baksht, A.B. Rybakov.

A. F. I o f f e PhysieaZ TeehnieaZ I n s t i t u t e , Aeadew of Seienees of the U. S . S. R., Leningrad K. 21 U. S. S. R.

1. The hollow a r c d i s c h a r g e i n c y l i n d r i c a l hollow cathode (IiC) with s l i g h t l y ionized noble gas plasma i s considered t h e o r e t i c a l - ly. The erpproach, t h a t was Used i n /1-3/, i s u t i l i z e d below. The following unequali- t i e s a r e supposed t o be v a l i d : 1L4<k;<c

<<b <<R&Lo( 1; is a Langmuir s h e a t h d i - mension, 4* ^{i s}^ani o n mean f r e e path, fi i s an l o n i s a t i o n l e n g t h , 4

-

^{0 , l}^cm ^{i s a}

11C r a d i u s , Lo i s a l e n g t h of HC plasma column

-

s e e Fig.1). The main p o t e n t i a l and c o n c e n t r a t i o n v a r i a t i o n along t h e ^HC r a d i u s Is l o c a l i z e d i n comparatively narrow pre-electrod e l a y e r s , which dimensions

a r e lL a& l i

.

I n t h e o t h e r p a r t of plasma column t h e i o n i z a t i o n equilibrium e s t a b l i s h e s . I n t h i s p a r t of plasma column plasma p a r m e t e r s a r e supposed t o be inde- pendent on r a d i u s 2

.

Numerical c a l c u l a - t i o n s were performed f o r

xe

plasma a t p e s s u r e s p (0.3-1) atm., R = 0.15 cm,

0.1 eV ( i s cathode w a l l tempera- t u r e ) . R e s u l t s of c a l c u l a t i o n s a r e d e p i c t - e d a t Fig.2-4 f o r P = ¹atm.

2. Plasma i n the c a v i t y is d i s c r i b e d by following s e t of squat ions:

P = ~ x T ^J fi)

temperatsure &

.

^I i s a whole e l e c t r i c cur- r e n t . d. ^{i s}^anemission c u r r e n t from cavi- t y wall.

/a

^azxi

8;

are e l e c t r o n an2 i o n

. f

c u r r e n t s from plasma t o w a l l . d ~ $ 4 2 .

J-exp6gV~t). Be, ^l/r,

krn

^{m e}

e l e c t r o n d i f f u s i o n c o e f f i c i e n t , lnobility and thsrmodiff usion r a t i o . p o t e n t i a l is counted &om t h e cavr t y wall.

9e i s an ele- c t r o n power d e n s i t y l o s s e s , t h a t c o n s i s t of r a d i a t ion l o s s e s i n s p e c t r a l l i n e s and continuum and energy l o s s e s because of electron-ion

ge; , and electron-aWm c o l l i s i o n s .

3, 'l'he Baha equation becoues unvalid f o r plasma c o n c e n t r a t i o n d e t e r a i n a t i on a t low

6 ^an&^{l 2} ^,when Che conversion r a t e 03 atomic i o n s i n t o molecular ones is compa- r a b l e with o r l a r g e r t h a n t h e r a t e of three p a r t i c l e c o l l i s i o n a l recombination. The h i g h r a t e of molecular i o n recornbination c a u s e s t h e d e p l e t i o n of whole plasma con- c e n t r a t i o n &

.

^Iti s n o t i c e b l e t h a t plas- m a remains. i n t h e i o n i z a t i o n equilibrium, 1.e. t h e whole r a t e of atomic and molecu- l a r i o n c r e a t i o n i s equal t o t h e whole ra- t e of atoinic and rooleculer i o n recombina- t i o n /4/. A t Fig.2 degree of i o n i z a t i o n f i and Yaha degree of i o n i z a t i o n pe (5) a r e shown ^ast u n c t i o n s of

.

^lt^is^evident

t h a t sharp d e p l e t i o n of plasma concentra- t i o n t a k e s p l a c e i n very narrow i n t e r v a l o r v a r i a t i o n . T h e r e f m e ^thec r i t i a a l e l e c t r o n Selugerature v a l u e To uay be de- f inecl. The degree of i o n i z a t i o n may be suf- f i c i e n t l y l a r g e r o r p r a c t i c a l a p p l i c a t i o n s

(4' o n l y i f & > b

.

Pe regarded t h e p o i n t

) S = 0 , where

5

'

&,,

⁹ a s t h e Hc plasma column boundary.

4-

2 2 7 4 2 ~ - j , 2x$-.@+.j# .Ya4z(5) ^4. ^hepre-electr*e i o n i z a t i o n ~ w e r ( L

df 9 ^e ^L ⁴ - ~ = d ; ) must be considered s e p a r a t e l y f o r

i s an _{M i}e e c t r o n temperature. fl and

4

₄d e t e r m i n a t i o n . T h i s l a y e r i s d i s c r i b - are plasmavneutral atom conc entratio-, 4 ed by t h e equations t h a t t a k e i n t o account calculated by Saha e q u a t i o n a t e l e c t r o n atomic i o n genaration, t h e i r d i f f u s i o n sad

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797168

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c o n v e r s i o n l n t o i ~ o l e c u l a r ones. The mole-

1

-

^cathode, ²

-

Langmuir s h e a t h ,

~ u l a r i o n s a r e d i s c r i b e d by bhe i o n i z a t i o n

e q u i l i b r i u m e q u a t i o n s . T h e i r c o n c e n t r a t i o n 3

-

plasma ~ o l u m n .

i s s m a l l because of l a r g e r e c o m b i n a t i o n co- A

e f f i c i e n t v a l u e . R e s u l t ? of c ? l c u l a t i o n a r e shown a t Fig.3. G=d/da( di0 i s t h e atomic i o n c u r r e n t v a l u e , c a l c u l a t e d with- o u t c o n v e r s i o n ) 4; (0) i s p l a s n a concen- t r a t i o n a t t h e boundary betxeen t h e h n g u - i r s h e a t h and i o n i z a t i o n s h e a t h . -plas- m a c o n c e n t r a t i o n a t t h e boundary of t h e plasma column, where i o n i z a t i o n u q u i l i b r i - um e x i s t s , - c o i n c i d e s w i t h Saha c o z e n - t r a t i o n fiS a t s u i i i c i e n t l y h i g h ( 4

and fiS a r e c a l c u l a t e d a t atom t e u p e r a t u r r e 7 " ).

5. Atoa and i o n tenlljerature T i n t h e plasma c o l u ~ n n mas found froiil L e a t b a l a n c e e q u a t i o n :

r a

- - -

_{( 6 )}

w i t h boundarv c o n d i t i o n s

iiut.;erically f r o n Z = O , wllere T - T e- eerdat '

= 0. The ti:irC boundary c o n c i t i o n a l o n g 3 a x i s was f o r m u l a t e d a t che e x i t of t h e ca- v i t y :[.lG] 2F i f - f . = 0 , a c c o r d i n g t o e r p e r i a e n t a l s i t u a t i o n /5,6/. A t Fig.4 t t e c a l c u l a t e d d i s t r i b u t i o n s of & * . ! ? , , I . ^ra-

d i a l c u r r e n t bomponents 4 _z _d

9 di ^are

shown a t n i l o l e v o l t a g e d r o p '

&CJ

^6.2 ^Y

( p = 1 atm, ds ⁼10 4 / c m 2 , R = 0 , 1 5 am).

1. ~ . ~ . ~ a f i s h t , - d .B .rIybakov. "&-c t h e o r y f o r a hollow c a t h o d e U i s c h a r g e i n a f u l l y i o n i z e d d e n s e plasma" XI11 I n t . Conf. on Phenomena i n l o n i a e d Gases

.519-320 ( ~ e r l i n , 1977).

2. F.C.Baksht, A.3.zybakov. J o u r n a l of t h e T e c h n i c a l Phys (JTP) 48, 234 (1978).

3

.

F.G.Baksht , A .B.Rybakov.JTP 48,700(1978) 4. F.G.Balcsht, V.G.l;vanov "Theory of Low-

V o l t a g e Arc i n Noble Gas" ( r e p o r t a t p r e s e n t c o n f e r e n c e ) ; JTP 48, 688 (1978) 5, G.A.DJUZ~~V, N.li&itroPanov, $ . A . S t a r t -

s ev, S . ~ . S h k o l n i k , V .G.Yuriev "Experi- a e n t a l Study of Arc Hollow Cathodeii

( ~ . F . i o f f e P h y s i c a l - T e o h n i c a l l n s t i t u - t e, Leningrad ( 1978) )

.

6. G.A.Djuzhev, N.K.Mitrofanov. JTP 4 8 , 1 2 ( 1978)