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MOLECULAR BEAM SAMPLING OF METASTABLE ATOMS FROM A HOLLOW CATHODE ARC AS A
PROBE FOR THE ELECTRON TEMPERATURE
P. Theuws, H. Beijerinck, C. Pernot, D. Schram, N.F. Verster
To cite this version:
P. Theuws, H. Beijerinck, C. Pernot, D. Schram, N.F. Verster. MOLECULAR BEAM SAMPLING OF METASTABLE ATOMS FROM A HOLLOW CATHODE ARC AS A PROBE FOR THE ELECTRON TEMPERATURE. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-141-C7-142.
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n07, Tome 40, JuiZZet 1979, pageC7- 141
MOLECULAR BEAM SAMPUNG OF METASTABLE ATOMS FROM A HOLLOW CATHODE ARC AS A PROBE FOR ME ELECTRON TEMPERATURE
P.G.A. Theuws, H.C.W. Beijerinck, C.E.E. Pernot, D.C. Schram and N.F. Verster.
Eindhoven University of Technology, Eindhoven, The Netherlands.
I n t r o d u c t i o n . I n a hollow cathode a r c (HCA) d i s - charge i n noble g a s e s f a s t m e t a s t a b l e atoms a r e pro- duced by e l e c t r o n impact and heavy p a r t i c l e c o l l i - s i o n s . These m e t a s t a b l e s a r e sampled through an o r i f i c e i n t h e end anode. I n a t i m e - o f - f l i g h t ma- c h i n e we have measured t h e c e n t r e - l i n e i n t e n s i t y and t h e v e l o c i t y d i s t r i b u t i o n of t h e beam o f m e t a s t a b l e atoms.
Molecular beam sampling o f ground s t a t e atoms g i v e s a c c u r a t e i n f o r m a t i o n on t h e i o n v e l o c i t y d i s - t r i b u t i o n and q u a l i t a t i v e i n f o r m a t i o n on t h e i o n and n e u t r a l d e n s i t y . The f r a c t i o n a l i n t e n s i t y of t h e m e t a s t a b l e s r e l a t i v e t o t h e i n t e n s i t y of t h e ground
s t a t e atoms g i v e s i n f o r m a t i o n on t h e e l e c t r o n temperature.
The f i r s t p r o c e s s can b e r e l a t e d d i r e c t l y t o o u r model c a l c u l a t i o n s and e x p e r i m e n t a l work on t h e sam- p l i n g of ground s t a t e atoms. For f a s t ground s t a t e atoms t h e view depth A i n t o t h e plasma, i . e . t h e mean f r e e p a t h , i s determined mainly by e l a s t i c c o l l i s i o n s with ground s t a t e atoms and i o n s and i n most c a s e s i o n i s a t i o n can b e n e g l e c t e d . For meta- s t a b l e atoms, however, t h e view depth
Am = vm/ (ne<Qve>ion,m) i s f u l l y determined by t h e d e e x c i t a t i o n and i o n i s a t i o n by c o l l i s i o n s w i t h e l e c t r o n s and t h e r e l a t i o n A << An h o l d s . I n t h i s
m
model t h e c e n t r e - l i n e i n t e n s i t y I ( o ) o f m e t a s t a b l e m
atoms i s given by
iivj m d2n
-
I ( o ) ~ Pexc ( Z5
km) a2S2 !"!with I ( o ) , t h e c e n t r e - l i n e i n t e n s i t y of ground Experimental s e t up. A d e t a i l e d d e s c r i p t i o n o f t h e
s t a t e atoms and P e x c (z
2
Am) t h e p r o b a b i l i t y t h a t a p p a r a t u s i s given elsewhere I ) . F i g . 1 shows aa ground s t a t e atom w i l l b e e x c i t e d t o a m e t a s t a b l e schematic o f t h e HCA. We have measured b o t h w i t h a
s t a t e i n t h e plasma s l i c e w i t h t h i c k n e s s A i n
l o n g a r c ( a r c l e n g t h L = 20 cm) and a s h o r t a r c m
f r o n t of t h e end anod
.
We i m p l i c i t e l y assume t h a t (Lo = 1 cm). T y p i c a l e l e c t r o n d e n s i t i e s a r e= 1 r ~ ~ ~ - ~ ~ ~ ~ ~ - ~ .
e
Theory. The g e n e r a l e x p r e s s i o n f o r t h e p r o d u c t of t h e c e n t r e - l i n e i n t e n s i t y I ( 0 ) ( S - l s t e r a d - I ) and t h e normalized v e l o c i t y d i s t r i b u t i o n f u n c t i o n P ( v ) of t h e beam o f m e t a s t a b l e s i s given by
I ( o ) P ( v ) d2ndv = [ ~ m ~ ( z , ~ ) ~ ( z , v ) ~ d z ] d2n
-
dv ( 1 ) 4nw i t h A t h e a r e a of t h e sampling o r i f i c a a t z=0 and z t h e c o o r d i n a t e a l o n g t h e beam a x i s . The f u n c t i o n
;I (2.v) (m-3s-1m-1s) i s t h e p r o d u c t i o n o f m e t a s t a b l e s p e r u n i t volume, p e r u n i t of time and p e r u n i t o f v e l o c i t y and T ( z , v ) i s t h e t r a n s m i s s i o n p r o b a b i l i t y of a m e t a s t a b l e through t h e plasma s l i c e between z and z=0.
F a s t m e t a s t a b l e atoms a r e produced by charge ex- change and e l a s t i c c o l l i s i o n s w i t h i o n s . We c o n s i d e r two p r o c e s s e s : f i r s t l y a c o l l i s i o n o f a ground s t a s e atom with an i o n followed by s u c c e s s i v e e x c i - t a t i o n by a c o l l i s i o n w i t h an e l e c t r o n and secondly
T ( z ,v ) =I f o r z - < X and z e r o elsewhere. The pro- m
b a b i l i t y Pexc ( Z
5
Am) i s e q u a l t o t h e p r o d u c t of t h e e x c i t a t i o n r a t e v and t h e t r a n s i t timeexc
-c = Am/vn of t h e ground s t a t e atom i n t h i s plasma s l i c e . With v = n <Qv > we w r i t e Eq. ( 2 ) a s
e x c e e e x c
where we have used v = vn, i . e . we n e g l e c t t h e m
momentum t r a n s f e r of t h e e l e c t r o n . The r a t i o of t h e r e a c t i o n c o n s t a n t s f o r e x c i t a t i o n and i o n i s a t i o n depends s t r o n g l y on t h e e l e c t r o n temperature. For argon t h i s r a t i o 2, i s g i v e n i n f i g . 2 . For
<QV > we o n l y c o n s i d e r d i r e c t e x c i t a t i o n t o a e exc
m e t a s t a b l e s t a t e . For <Qv z
e ion,m we have i n c l u d e d t h e 4s-4p e x c i t a t i o n p r o c e s s because f o r e l e c t r o n temperatures T e - > 2 eV and e l e c t r o n d e n s i t i e s
n > 1 0 ~ ~ m - ~ t h e i o n i s a t i o n r a t e of t h e 4p l e v e l s
e -
i s much l a r g e r t h a n t h e r a t e of spontaneous r a d i a - t i v e decay t o t h e 4s l e v e l s .
a c o l l i s i o n of a m e t a s t a b l e w i t h an i o n w i t h charge
The second p r o c e s s , i . e . charge and e x c i t a t i o n and e x c i t a t i o n t r a n s f e r .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979769
t r a n s f e r of a m e t a s t a b l e w i t h an i o n , h a s a very l a r g e c r o s s - s e c t i o n Q No q u a n t i t a t i v e d a t a a r e
exch '
a v a i l a b l e , however, and we use an e s t i m a t e Q = exch 500
a2
i n analogy t o t h e charge t r a n s f e r cross-sec- t i o n f o r CS+ on Cs 3 ) . We assume a homogeneous plasma with T ( z , v ) = 1 f o r z5
A and z e r o e l s e -m where. Equation ( 1 ) i s t h e n w r i t t e n a s
w i t h n and n t h e number d e n s i t y of t h e m e t a s t a b l e s
m i
and t h e i o n s , r e s p e c t i v e l y . S u b s t i t u t i o n o f t h e ex- p r e s s i o n f o r A r e s u l t s i n
m
which i s t h e c e n t r e - l i n e i n t e n s i t y of a n e f f u s i v e s o u r c e of f a s t m e t a s t a b l e s m u l t i p l i e d by t h e e x t r a f a c t o r i n square b r a c k e t s . The d e n s i t y nm i n t a b l e I h a s been c a l c u l a t e d with a c o l l i s i o n a l r a d i a t i v e model 41 f o r t h e plasma c o n d i t i o n s i n t h e upper p a r t of t a b l e I.
I n t a b l e I numerical v a l u e s o f t h e c e n t r e - l i n e i n t e n s i t y I ( o ) a r e given ?or t h e two models d l s -
m
cussed, showing t h a t e x c i t a t i o n o f f a s t ground s t a t e atoms i s t h e dominant p r o c e s s of beam forma- t i o n . Of c o u r s e , t h e models used a r e s i m p l i f i e d t o a l a r g e e x t e n t . With t h e s m a l l v a l u e o f ,Arn= 2 lod4m
?r -4
a s compared t o t h e diameter (4/w) A =5-10 m of t h e sampling o r i f i c e , t h e assumption of a homogeneous plasma i s n o t v e r y r e a l i s t i c . To e x p l a i n o u r expe- r i m e n t a l r e s u l t s we a l s o have t o assume a f a i r l y h i g h e l e c t r o n temperature a t t h i s very c l o s e d i s - t a n c e t o t h e end anode. However, t h e models used do g i v e a q u a l i t a t i v e p i c t u r e of t h e p r o d u c t i o n and d e s t r u c t i o n p r o c e s s e s involved.
Experimental r e s u l t s . Measurements have been per- formed f o r A r and Kr f o r b o t h a r c c o n f i g u r a t i o n s . I n t h i s s e c t i o n we w i l l o n l y d i s c u s s t h e r e s u l t s f o r A r i n t h e l o n g a r c c o n f i g u r a t i o n . I n f i g . 3 t h e measured i n t e n s i t i e s and t e m p e r a t u r e s a r e given f o r A r i n t h e long a r c c o n f i g u r a t i o n a s a f u n c t i o n of t h e d e n s i t y i n t h e s o u r c e chamber nn. The measured t e m p e r a t u r e s f o r t h e m e t a s t a b l e s a r e a f a c t o r 3 h i g h e r t h a n t h e temperature of t h e f a s t ground
s t a t e atoms I ) . Our models do n o t e x p l a i n t h i s d i f - f e r e n c e . The h i g h e s t i n t e n s i t i e s a r e measured i n c a s e o f low d e n s i t y , high a r c c u r r e n t and h i g h magnetic f i e l d . For f a s t ground s t a t e atoms t h e i n t e n s i t y i s p r o p a t i o n a l t o n I n f i g . 4 we
n'
g i v e t h e i n t e n s i t y of m e t a s t a b l e s r e l a t i v e t o t h e i n t e n s i t y of t h e ground s t a t e atoms a s a f u n c t i o n o f nn. Comparing t h i s w i t h f i g . 2 r e s u l t s i n e l e c - t r o n t e m p e r a t u r e s v a r y i n g from 2-5 eV.
For t h e s h o r t a r c c o n f i g u r a t i o n we f i n d e l e c t r o n t e m p e r a t u r e s v a r y i n g from 3 (high d e n s i t y ) t o 7 eV
(low d e n s i t y ) . Within t h e assumptions of o u r very simple model we have developed a s e n s i t i v e probe f o r t h e e l e c t r o n temperature i n f r o n t of t h e end anode.
For f u r t h e r i n s i g h t i n t h e p r o d u c t i o n , a b e t t e r des- c r i p t i o n of t h e plasma n e a r t h e end anode i s n e c e s s a r y .
References
1 ) P.G.A. Theuws e t a l . , J . Appl. Phys. 48,2261 - - (1977).
2 ) J.J.A.M. v.d. Mullen, A t . Phys. Group, Rep.
NT 78-01, Eindhoven U n i v e r s i t y of Technology.
3) R.N. B u l l i s , a s c i t e d i n " P a r t i a l l y i o n i z e d g a s e s " , e d i t e d by M. Mitchener and C.H. Kruger
(Wiley i n t e r s c i e n c e , New York, 1 9 7 3 ) , p. 109.
4 ) B.F.M. P o t s and B. v.d. S i j d e , p r i v a t e commu- n i c a t i o n .
3 4 5 6
Fig.
1Schematic o f Fig.
2The r a t i o o f the e z e i - the HCA t a t i o n and d e e z e i t a t i o n r a t e s
as a function o f T,.
Fig.
3Experimental re- s u l t s for Ar (Lo=20cml.
Fig.
4The r a t i o of t h e measured i n t e n s i t i e s for metastab Ze and ground s t a t e atoms (Ar,
Lo = 20ern).
Table 1 Plasma p a r a m e t e r s
19 -3
n 2 10 m <Qve>exc 1 , 7 l ~ - ~ ~a ) m ~ ~ - ~
ne 2 l ~ < ~~ v~~ >~~10-13 3 -1 ~- ~ ,~ ~
n m s a )
Te 3 . 5 e V
Am 2 10-*m
model 1 model 2
I ( o ) , 1.3 1015 b ) I ( o ) , 2.1 10 12
n m 2 1 0 ~ C ) ~ ~ - ~
I ( o ) , 6 10'' a ) Ref. 2. b) Ref. 1. C ) Ref. 4.
