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TRANSPORT OF METASTABLE ATOMS IN A POSITIVE COLUMN INCLUDING RADIAL
VARIATION OF THE EXCITATION RATE
V. Martisovits
To cite this version:
V. Martisovits. TRANSPORT OF METASTABLE ATOMS IN A POSITIVE COLUMN INCLUDING RADIAL VARIATION OF THE EXCITATION RATE. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-185-C7-186. �10.1051/jphyscol:1979791�. �jpa-00219497�
JOURNAL DE PHYSIQUE CoZZoque C7, suppZdment au n07, Tome 40, JuiZZet 1979, page C7- 185
TRANSPORT OF METASTABLE ATOMS IN A POSITIVE COL,UMN INCLUDING RADIAL VARIATION OF THE EXCITATION RATE
V. Martisovits.
Institute of Physics and Biophysics, Komenshy-University 816 31 BratisZave, MZynskd DoZina, CzechosZovakia.
The e f f e c t of r a d i a l v a r i a t i o n of t h e r a t e c o e f f i c i e n t f o r e x c i t a t i o n on s p a t i a l d i s - t r i b u t i o n o f 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 of t h e p o s i t i v e column and on 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 i s c a l c u l a t e d .
INTRODUCTION
Recent i n v e s t i g a t i o n s [l] of t h e r a d i a l d i s t r i b u t i o n o f m e t a s t a b l e a t o m s i n t h e p o s i t i v e column have s u g g e s t e d t h a t t h e e n e r g y d i e t r i b u t i o n f u n c t i o n f o r e l e c t r o n s is i n f l u e n c e d by a l o n g i t u d i n a l magnetic f i e l d . A s a r e s u l t of t h i s , t h e e x c i t a t i o n r a t e C& f o r p r o d u c t i o n o f t h e m e t a s t a b l e s t a t e s i s dependent on r a d i u s , I n o r d e r t o s t u d y t h i s problem t h e f o l l o w i n g model f o r e x c i t a t i o n r a t e v a r i a t i o n is used :
%/ao
o. w(pr/~) - [ 3 , @ r / g P where p i s a nume-
r i c a l f a c t o r , Jo t h e B e s s e l f u n c t i o n of
t h e f i r s t k i n d of o r d e r z e r o , (u i t s f i r s t
z e r o p o i n t , R t h e i n n e r r a d i u s of t h e d i s -
c h a r g e t u b e , and d o t h e e x c i t a t i o n r a t e
a t r o o. The f a m i l y of c u r v e s &/ao
a g a i n s t r/R i s shown i n f i g u r e 1 f o r -0.8 ,C P S 0.8
THEORY OF THE TRANSPORT
The 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 atoms c a n be d e s c r i b e d by t h e d i f f u s i o n e q u a t i o n
f o r a s t e a d y s t a t e C2]
where ng, ne and n a r e t h e r e s p e c t i v e con- c e n t r a t i o n e of g r o u n d - s t a t e atoms, e l e c - t r o n s and m e t a s t a b l e atoms. Here 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 and
P
c o e f f i c i e n t f o r d e s t r u c t i o n of metar- t a b l e atoms by e l e c t r o n impact. A s a f i r s t a p p r o x i m a t i o n , t h e d e s t r u c t i o n of metes- t a b l e s by m u t u a l c o l l i s i o n s and by c o l l i - s i o n s w i t h g r o u n d - s t a t e atoms i s n e g l e c t e d . A s i m p l e boundary c o n d i t i o n a t t h e w a l l n, P 0 and t h e e l e c t r o n d e n e i t y p r o f i l e g i v e n by t h e z e r o - o r d e r Sessel f u n c t i o na r e a l s o supposed.
By i n t r o d u c i n g t h e d i m e n s i o n l e s s v a r i a b l e s - n / c r . ~ -
9
= p r / ~ .f - ~~p
neO/p DI V= aon$/3
,
where neo i s t h e e l e c t r o n con- c e n t r a t i o n on t h e a x i s , w e o b t a i n t h e f o l l o w i n g e q u a t i o nw i t h 2 t h < b o u i d a r y c o n d i t i o n s V =, 0 and
-
RESULTS
The n u m e r i c a l s o l u t i o n was performed f o r
'd
v a r y i n g between 0 and lo4. F i g u r e 2 i l u s t r a t e s t h e s h a p e s o f t h e r a d i e l d i s - t r i b u t i o n s of m e t a s t a b l e s n o r m a l i z e d t o u n i t y a t t h e column a x i s n/no. The r a t i o of m e t a s t a b l e 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 i s p l o t t e d a s a f u n c t i o n of r i n f i g u r e 3, The f l u x d e n e i t y o f m e t a s t a b l e s t o t h e w a l l i s gi&ven by a formulaF i g . l e t h e r a d i a l v a r i a t i o n of t b e e x c i t a - t i o n r a t e f o r p r o d u c t i o n o f t h e me- t a s t a b l e a t o m s
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979791
Jw
"
and i t
-
'6(d-o(dn/dr), = - ( p / ~ ) o ~ f ( d p / d g I w i s shown i n f i g u r e 4 ( p l o t t e d Y o n l y
1
When comparing t h e r e s u l t s presented i n f i g u r e s 2
-
4 i t can be concluded t h a t t h e r a d i a l v a r i a t i o n o f t h e e x c i t a t i o n r a t e has o n l y a s m a l l i n f l u e n c e on t h e concen- t r a t i o n of metastables no, On t h e o t h e r hand t h e metastable f l u x d e n s i t y t o t h e w a l l and t h e r a d i a l d i s t r i b u t i o n o f meta-s t a b l e s a r e s e r i o u s l y changed a t t h e same c o n d i t i o n e .
Fig.4.The normalized f l u x densYty o f meta- s t a b l e s t o t h e w a l l
REFERENCES
[ l ] ~ e u t s c h H.,Pfau S. and Klagge S O , Proc.
1 3 t h I n t . Conf. Phenomena i n I o n i z e d Gases, Contr. Papers, Phys, Soc, GDR
( ~ e r l i n , 1977) p. 239
[Z!]MartiSovitS V.,Paper a t t h i s conference
Fig.2.The r a d i a l d i s t r i b u t i o n of metasta- b l e ~ f o r d i f f e r e n t p r o f i l e s o f t h e e x c i t a t i o n r a t e
F i g .3.The r e l a t i v e concent r a t io n o f meta- s t a b l e s a t t h e a x i s
