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EFFECT OF COLLISIONS BETWEEN THE METASTABLE ATOMS ON THEIR RADIAL TRANSPORT IN A POSITIVE COLUMN AT
VARIOUS SPATIAL DISTRIBUTIONS OF ELECTRONS
V. Martisovits
To cite this version:
V. Martisovits. EFFECT OF COLLISIONS BETWEEN THE METASTABLE ATOMS ON THEIR RADIAL TRANSPORT IN A POSITIVE COLUMN AT VARIOUS SPATIAL DISTRI- BUTIONS OF ELECTRONS. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-183-C7-184.
�10.1051/jphyscol:1979790�. �jpa-00219496�
JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 40, ~ u i Z Z e t 7 9 7 9 , page C7- 183
EFFECT OF COLLISIONS BETWEEN THE METASTABLE ATOMS ON THEIR RADIAL TRANSPORT
M A POSKIVE COLUMN AT VARIOUS SPATIAL DISTRIBUnONS OF ELECTRONS
V. Martisovits.
I n s t i t u t e of Physics and Biophysics, Komensky-University, 816 31 Bratiszava, MZynskd DoZina, CzechosZavakia.
+he p u r p o s e o f t h e p r e s e n t c o n t r i b u t i o n is t o s t u d y t h e r a d i a l t r a n s p o r t of m e t a s t a - b l e ~ t o t h e d i s c h a r g e t u b e w a l l when c o l - l i s i o n s 'between two m e t a s t a b l e a t o m s are t a k e n i n t o c o n s i d e r a t i o n t o g e t h e r w i t h o t h e r d e s t r u c t i o n p r o c e s s e s . The number d e n s i t y d i s t r i b u t i o n of m e t a s t a b l e s a c r o s s a s e c t i o n o f t h e p o s i t i v e column and t h e i r f l u x t o t h e d i s c h a r g e t u b e w a l l a r e c a l c u - l a t e d f o r v a r i o u s s p a t i a l d i s t r i b u t i o n of e l e c t r o n s
.
INTRODUCTION
I n t h e p r e v i o u s p a p e r s [1,2] t h e t r a n s p o r t o f m e t a s t a b l e a t o m s t o t h e d i s c h a r g e t u b e w a l l was s t u d i e d when assuming t h e metas-
t a b l e s t o be produced by d i r e c t e x c i t a t i o n by e l e c t r o n i m p a c t and t h r o u g h t h e s t a t e s o p t i c a l l y c o n n e c t e d w i t h t h e m e t a s t a b l e s t a t e s , On t h e o t h e r hand o n l y two-body and three-body c o l l i s i o n s w i t h ground-sta- t e a t o m s , and c o l l i s i o n s w i t h e l e c t r o n s were assumed a s t h e most i m p o r t a n t volume p r o c e s s e s t h a t l e d t o d e s t r u c t i o n o f t h e m e t a s t a b i l i t y i n a glow d i s c h a r g e .However, a t h i g h e r c o n c e n t r a t i o n of m e t a s t a b l e par- t i c l e s t h e d e s t r u c t i o n by c o l l i s i o n s meta- s t a b l e - m e t a s t a b l e i s t o be t a k e n i n t o con- s i d e r a t i o n , The problem i s s o l v e d f o r va- r i o u s f o r m s f o r t h e s p a t i a l d i s t r i b u t i o n of e l e c t r o n s g ( y r / ~ ) s s s u m t n g t h e r a t e co- e f f i c i e n t f o r e x c i t a t i o n CC a n d d e s t r u c - t i o n of m e t a s t a b l e s
(/3
by e r e c t r o n i m p a c t e n dae
by c o l l i s i o n s w i t h atoms) t o be i n - d e p e n d e n t o f r a d i u s r. Here,p
i s t h e f i r s t zero p o i n t o f t h e B e s s e l f u n c t i o n o f t h e f i r s t k i n d of o r d e r z e r o J0 a n d R t h e i n n e r r a d i u s o f t h e d i s c h a r g e t u b e .f o r a s t e a d y s t a t e rre h a v e
-D
+
&(r = (OL ng- p n ) ne- %ngn-
6 n 2where D i s t h e d i f f u s i o n c o e f f i c i e n t of m e t a s t a b l e s a n d
dS
c o e f f i c i e n t f o r des- t r u c t i o n of m e t a s t a b l e s by m u t u a l c o l l i - s i o n s . The number d e n s i t y of e l e c t r o p s i s g i v e n by ne = ne0g(rr/R). Using t h e sym- m e t r y r e q u i r e m e n t s we f i n d t h a t dn/dr 0 a t r P 0. TO s i m p l i f y t h e a n a l y s i s t h e boundary c o n d i t i o n nW= 0 a t t h e w a l l was u s e dThe e q u a t i o n c a n be n o r m a l i z e d by p u t t i n g
g - t - ~ : p
n e 0 p 2 ~ .P
=~ ~ a c
nglP2Dp.
n / C FA
I R6~/?
5 , w h e r e C-
a n g P /i s a n e q u i l i b r i u m number d e n s i t y of metas- t a b l e s . Then w e o b t a i n t h e f o l l o w i n g e a u a t i o n
w i t h - t h e t e s p e c t ive boundary c o n d i t i o n s V,= 0 a n d (d V/dg) = 0.
RESULTS
PoO
The n u m e r i c a l s o l u t i o n was p e r f o r m e d f o r Y v a r y i n g between 0 and 104 and
A
from 0 t o 1000 f o r = 0 ( n e g l i g i b l e d e s t r u c - t i o n by c o l l i s!
o n s w i t h atoms). The spa- t i a l d i s t r i b u t i o n of e l e c t r o n s was d e s c r i -THEORETICAL MODEL Fig.1. The s p a t i a l d i s t r i b u t i o n of elec- If ng
,
n, n a r e t h e r e s p e c t i v e concen-e o t r o n s a c r o s s a s e c t i o n of t h e p o s i -
t r a t i o n s of g r o u n d - s t a t e , m e t a s t a b l e a t o m s t i v e column p l o t t e d f o r q r a n g i n g a n d t h e e l e c t r o n c o n c e n t r a t i o n on t h e a x i s from 0.01 t o 64
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b e d by t h e f u n c t i o n g ( x ) = [ J ~ ( X ) ] ~ where 0 5 q t 0 0 . The f a m i l y o f curves ne/neo a g a i n s t r / R i s shown i n f i g u r e 1, F i g u r e s 2 and 3 i l l u s t r a t e t y p i c a l shapes of t h e r a d i a l d i s t r i b u t i o n s o f metastables norma- l i z e d t o u n i t y a t the column a x i s n/no f o r v a r i o u s values o f t h e parameters q end
r.
The f l u x d e n s i t y o f metastables t o t h e w a l l i s g i v e n by a formula
f w
= -~(dn/dr),*
- ( v / ~ ) % f ( d v/d$), and i t i s shown i n f i g u r e s 4-
6 ( p l o t t e d - r ( d v / d $ ) w only).Representing t h e d i f f u s i o n e q u a t i o n i n terms o f t h e c h a r a c t e r i s t i c d i f f u s i o n l e n g t h , t h e r a t i o o f metastable number d e n s i t y a t t h e a x i s no t o t h e e q u i l i b r i u m c o n c e n t r a t i o n C can be w r i t t e n as
k r e i s a n u m e r i c a l f a c t o r which cha- r a c t e r i z e s t h e i n f l u e n c e o f t h e h i g h e r d i f f u s i o n modes. The n u m e r i c a l values of go a r e presented i n t a b l e 1.
Table 1.
-
-
r/R 1 - r/R a
F i g .2.The r a d i a l d i e t r i b u t i o n o f metastab- l e s f o r d i f f e r e n t e l e c t r o n d e n s i t y p r o f i l e s and A a 0
Fig.3.The r a d i a l d i s t r i b u t i o n o f metas- t a b l e s f o r q n 1
F i g .4.The normalized f l u x d e n s i t y o f me-
a
t a s t a b l e ~ t o t h e w a l l f o r q t 0
10
,
I I I I I 1.The normalized f l u x d e n s i t y o f me- 0 t a s t a b l e ~ t o t h e w a l l f o r q = 1
I I I I I +
-
Fig.6.The normalized f l u x d e n s i t y o f me- V
t a s t a b l e ~ t o t h e w a l l f o r q r 64
REFERENCES
[ l ] ~ a r t i 6 o v i t 6 V.,KoginBr I. and Veis
3..
Proc.12th I n t . Conf. Phenomena I n I o n i - zed Gasee, Contr. Papersr North-Holland Publ. ~omp. (~msterdam, 1975) p. 60 [ 2 ] ~ o l i n B r 1 , , ~ r t i 6 o v i t 6 V* and Veis 8..
Proc.13th I n t . Conf. Phenomena i n I o n i - zed Gases, Coat r .Papers, Phys .Soc .GDR ( ~ e r l i n , 1977) p. 233