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Submitted on 1 Jan 1979
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TO THE THEORY OF ELECTRONIZED DISCHARGE
V. Alexandrov, V. Danilychev, V. Koterov, V. Pustovalov, A. Soroka
To cite this version:
V. Alexandrov, V. Danilychev, V. Koterov, V. Pustovalov, A. Soroka. TO THE THEORY OF ELECTRONIZED DISCHARGE. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-357-C7-358.
�10.1051/jphyscol:19797176�. �jpa-00219153�
JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment a u n07, Tome 40, J u i Z Z e t 2979, page C7- 357
TO THE THEORY ff ELECTROIOMZED DISCHARGE
V.V. Alexandrov, V.A. Danilychev, V.N. Koterov, V.V. Pustovalov and A.M. Soroka.
P. N. Lebedev PhysicaZ I n s t i t u t e , U.S. S . R. Academy o f S c i e n c e s , L e n i n s k y p r o s p e c t 53, 117924, Moscow, U. S. S.R. -0omputer C e n t r e o f t h e U . S.S. R. Academy o f S c i e n c e s V m i Zov s t r e e t 40, Moscow 127333, U.S.S.R.
The r e s u l t s of t h e o r e t i c a l atudy of e l e c t r o i o n i z e d discharges a r e presented, which a r e based on the following equations 11 921:
L
je(o?+t=tji(O,t), j i ( ~ , t ) = ~ , 1
0Edr = U
(11
This study g i v e s a p o s s i b i l i t y t o substan- t i a t e a simple method of averaging (1 )
over f a s t time, which i s determined by e l e c t r o n motion, i n s t e a d of
relationjifi~,
E t h e following e q u a l i t y i s valid:Averaged equations a r e v a l i d both i n t h e volume and i n t h e layers.
A change of quasi-neutral plasma densi- t y n=ne=ni i n t h e discharge volume i a pre- sented by equation
2 , at 9-B
h2 .The t y p i c a l formation time f o r p o s i t i v e column reaul- t i n g from t h i s equation i~f'=
i/&$@ ~ u m e r i c a l c a l c u l a t i o n s /2/ of cathode l a y e r formation have revealed f o u r t y p e s of t r a n s i t i o n p r e c e s s e s (Big. 1 ;
U c
is We cathode f a l l ) . ~ t th e first s t a g e (Fig.1;t$0.03p$) plasma i s p o l a r i s e d near t h e ca- thQde (IB.6628;
p
=hi-n,) .'Phis l e a d s t o an i n c r e a s e i n t h e f i e l d i n t e n s i t y , andNitrogen L = i o m , n=5.4.rafd U / L p
=iOV,em.brr0
t ,
paec Big. 1.big. 2.
t h e i n i t i a t i o n of shock i o n i s a t i o n wave.
At t h e eecond s t a g e (Fig. 1 ; O.O$d$f & O . i ~ 6 ) t h e i o n i z a t i o n wave i s moving toward t h e cathode (Fig.2b), and forms near it a lay- e r of posf t i v e space charge( emitting layer) where t h e major e l e c t r o n c u r r e n t amplifi-
c a t i o n t a k e s place due t o impact gaa ioni- zation.The e m i t t i n g l a y e r i s s e t t l e d a t t h e t h i r d s t a g e (Fig.1; O . l ~ . s ( , t 5 ' 0 . 5 ~ 1 3 A t t h e aame time t h e r e begins t h e charge r e - d i s t r i b u t i o n i n t h e o u t e r oathode layer.
!Phe f o u r t h moat prolonged atage determi- nea t h e t o t a l time of t h e cathode l a y e r
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797176
f o r m a t i o n (Fig.1; t Y O . 1 ~ 5 ). a p p e a r r e p e a t e d l y . The wave i s d e s c r i b e d 'P'he f i r s t two f a s t s t a g e s a r e d e f i n e d by t h e changes i n t h e automodel form
by n o n - s t a t i o n a r y e l e c t r o n motion*The la&
p - p ' c ~ ) / . t , E - ~ E ' ( E ) , 5 -
s / t 2 ( F i g 3 1 two slow s t a g e s a r e connected w i t h i o nmotion,Below a r e l i s t e d t h e b a s i c r e s u l t s ,0, of an a s y m p t o t i c a n a l y s i s of t h e s e s t a g e s
/3,4/ : t y p i c a l t i m e s and space s c a l e s ,
@
The space c h a r g e i n t h e e m i t t i n g l a y e r i s formed mainly by t h e i o n s , t h e impact i o n i z a t i o n i s s i g n i f i c a n t l y more i n t e n s e t h e n t h e e x t e r n a l i o n i z a t i o n and recombi- n a t i o n , and t h e e l e c t r o n motion i s q u a s i - s t a t i o n a r y . E m i t t i n g l a y e r f o r m a t i o n i s ac- companied by i t s space charge o s c i l l a t i -ons /2/, and t h e i r p e r i o d and decrement Pig. 3.
may be q u i t e w e l l determined by a simple A f t e r damping of t h e space charge wave model /3/. The t h i c k n e s s of t h e e m i t t i n g t h e plasma c h a r a c t e r i s determined by t h e l a y e r n X , a n d t h e t y p i c a l time%, f o r t h e s e e x t e r n a l i o n i z a t i o n source and t h e recom- p r o c e s s e s a r e e q u a l : bination,With a n a c c u r a c y
p/n - a
t h e plasma becomes q u a s i - n e u t r a l i n t h e e x t e r n a l cathode l a y e r , and t h e t y p i c a l
-
m iX
=L ( : ~ - ~ d ~ )"
( 3 ) t h i c k n e s s 4 x E and t h e t y p i c a l time 2, j y = l e l y e h-
L P '
f o r t h i s s t a g e i s( a t
d=Ap(E/p- approximationfor for
t h e impact i o n i z a t i o n f a c t o r ) .
AXr=- je&=h2(4<:k
- T ~ = q
1 = T v@
The impact i o n i z a t i o n i n t h e e x t e r n a l ( 4 )p a r t of t h e l a y e r i s n o t s i g n i f i c a n t .The If CSml t h e n t h e time 2;-TC and space c h a r dynamics of f o r m a t i o n of t h e e x t e r n a l ca- ge wave a r e n o t e v i d e n t l y expressed.
thode l a y e r depends on t h e parameter @ A l l r e s u l t s d e s c r i b e d a r e i n good a g r e e 1
a
1 ( 0.2 i n i t - ment w i t h n u m e r i c a l l y c a l c u l a t e d ones /2/.a = (
4nle1yc;
gen plasma a t p-10 t o r r ) t h e p r o c e s s h a s 3 Asymptotic s o l u t i o n f o r s t e a d y - s t a t e d i s -
a two-stage c h a r a c t e r . F i r s t l y a wave of charge /4/ l e a d s t o t h e same space s c a l e s . p o s i t i v e space charge i s moving from t h e The same r e s u l t s a r e o b t a i n e d from ave
-
cathode w i t h t h e damping time Tw=
-
m g e d e q u a t i o n s (1,2) t h a t confirms t h e i r 4mel n)(i( ~ i g . 3 a ) . T h e i n f l u e n c e of t h e e x t e r n a l v a l i d i t y . i o n i z a t i o n and recombination i s n e g l i g i b - R e f e r e n c e s
1 .Ii.G.Basov e t al.Usp.fiz.nauk,ll 213 l e a t t h i s stage.The space charge wave ( 1 974) ;2. V. V.Blexandrov e t al&intovaya
e l e k t r o n i k a , r , I , 114 ( 1 978) ;3.V.V,Alex- is induced by t h e e m i t t i n g l a y e r and may androv e t a l * D o k l *Ak*Nauk, 241
,
5,1050( 1978)4.V.V,Alexandrov e t al.Zh.vychislit.math.
i math.phys.,s, 5, 1214 (1978).