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ELECTROPHYSICAL PROPERTIES OF NON-EQUILIBRIUM AEROSOL PLASMA
A. Gorbatov, E. Samuilov
To cite this version:
A. Gorbatov, E. Samuilov. ELECTROPHYSICAL PROPERTIES OF NON-EQUILIBRIUM AEROSOL PLASMA. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-519-C7-520.
�10.1051/jphyscol:19797251�. �jpa-00219236�
J0URNA.L DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 40, JuiZZet 1979, page C7- 519
ELECTROPHYSICM PROPERTIES OF NON-EQUILIBRIUM AEROSOL PLASMA
A.V. Gorbatov and E.V. Samuilov.
f i e Krizhizhanovsky Power, Engineering I s t i t u t e , Moscow U.S.S.R.
S t ~ d i e s on e l e c t r o p h y s i c a l p r o p e r t i e s of a e r o s o l plasma (LIP) with e l e c t r o n den- s i t y , ne, c o n t r o l l e d e x c l u s i v e l ~ by t h e r - mionic o r p h o t o e l e c t r i c emission from ae- r o s o l p a r t i c l e s , have been o f i n t e r e s t f o r s p a c e c r a f t development1, ?lKD energy con- v e r s i o n 2 , plaslsa c h e m i s t r y and p l ~ m a - b a s -
ed m e t a l l u r g y 3
.
The n o n - e ~ u i l i b r i m p l a s - m z wlzose e f f e c t i v e e l e c t r o n t e m p e r a t u r eexceeds t h a t of t h e c a r r y i n g g a s , Te7T,, can be sroduced ( i ) i n r a p i d l y expanding s u p e r s o n i c a e r o s o l flows whose p z r t i c l e t e m p e r a t u r e , Tp ( T ~ =(0.13-0.3 )eV), due t o t h e t i m e d e l a y i n t h e i n t e r Q h a s e h e a t t r a n s f e r , i s h i g h e r t h a n t h a t o f t h e c a r - r y i n g g a s , Tm, ( i i ) t:wough t h e e l e c t r o n h e a t i n g up by t h e a p p l i e d e l e c t r i c f i e l d , o r ( i i i ) t h r o u g h t h e exposure o f t h e aero- s o l t o photons o f s u f f i c i e n t l y h i g h ener- gy. I n o u r paper t h e d e t e r m i n a t i o n o f
AP
p a r a m e t e r s i s d i s c u s s e d t a k i n g i n t o accoY a n t t h e n o n - e ~ u i l i b r i u m mentioned.Considered i s t h e c a s e o f an i n f i n i - t e
AP
c o n s i s t i n g o f i d e n t i c a l s p h e r i c a l p a r t i c l e s o f R1 r a d i u s d i s t r i b u t e d i n s p a ce. randomly b u t u n i f o r m l y w i t h t h e concen- t r z t i o n , N p , and s u b j e c t e d t o i d e n t i c a l c o n d i t i o n s . For s i m p l i c i t y i t i s assumed t h a t t h e p a r t i c l e s emit o n l y thermoelectcc.r o n s having t h e Maxwell v e l o c i t y d i s t r i b u - t i o n c o r r e s p o n d i n g t o t h e q u a s i - s t a t i o n a r y t e m p e r a t u r e T ( T B 7 Tm). The p a r t i c l e s ab-
P
s o r b i n c i d e n t i n g e l e c t r o n s . Also, t h e as- sumption w a s made t h a t e l e c t r o n - e l e c t r o n c o l l i s i o n s c o u l d b e n e g l e c t e d . To s o l v e t h e problem, two approzches were employed, t h e approach s e l e c t e d b e i n g determined by t h e r a t i o betmeen t h e mean-free-path f o r
e l e c tron-molecule c o l l i s i o n s and t h e a c t i o n r a d i u s o f a e r o s o l p a r t i c l e s .
If r
h * ~ ,
t h e boundary problem s h o u l d b e s o l v e d t o determine ne and Te. I n t h i s problem i t i s assumed5 t h a t any a e r o s o l p a r t i c l e i s l o c a t e d i n t h e c e n t r e o f a n e l e c t r i c a l l y n e u t r a l s p h e r e of R2 r a d i u s (I?;' = 4XR2/3) end t h e e l e c t r o n d i s t r i b u - 3 t i o n f u n c t i o n (f (?) ) s h o u l d b e found from t h e s e l f - c o n s i s t e n t problem, thet i s , from t h e Boltzman k i n e t i c e q u a t i o n and P o i s s o n e q u a t i o n w r i t t e n for t h e e l e c t r i c poten- tial w i t h c o r r e s p o n d i n g boundary c o n d i t i - ons a t Rl and R2* F o r t h e c a s e s when t h e e l e c t r i c f i e l d n e a r a p a r t i c l e may b e con- s i d e r e d t o b e Coulombian o r when i t s i n f - l u e n c e on e l e c t r o n s motion i s n e g l i g i b l e( & = R1), t h e s o l u t i o n s c a n b e found by t h e momentum method i n i t s l i n e a r approxi-
13 mation ( (Tp
-
T, )/T,<< 1 ) w i t h t h e a l l o -Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797251
wance made f o r t h e ~ u a s i - s t a t i o n a r y c h a r g e of a e r o s o l p a r t i c l e s . The a n a l y s i s o f so- l u t i o n i n d i c a t e s t h a t t h e n o n - i s o t h e r m a l AP (Tp7!Pm) h a s t h e g r e e t e r e l e c t r o n con- c e n t r a t i o n ne t h a n t h e i s o t h e r m a l AP(T
-
)p-lfn a t t h e same p a r t i c l e t e m ~ e r a t u r e , th e oth- e r c o n d i t i o n s b e i n g e q u a l .
When =R1 and
1 >>
RL, t h e a e r o s o l p a r t i c l e s may b e t r e a t e d as g i g a n t i c mo- l e c u l e s e m i t t i n g and a b s o r b i n g e l e c t r o n s .I n t h e framework o f e l e m e n t a r y t h e o - r y 4
,
c o n t i n u i t y , m o t i o n , and e n e r g y equa- t i o n s a r e u s e d t o c l a r i f y t h e i n f l u e n c e o f a l t e r n a t e u n i f o r m e l e c t r i c f i e l d , E = E ~ C O S ~ ~on iQ p a r a m e t e r s . It i s assumed t h a t f i e l d does n o t h e a t u p a e r o s o l p a r t i c l e s s i g n i f i c a n t l y . The s i m u l t a n e o u s s o l u t i o n of t h e e q u a t i o n s was found f o r two extreme c a s e s :
-i ( i ) q U d < l and ( i i ) q O s i
[%=(FeJpJ,
sm=4v/.J, $ , = P ~ ~ R ; ~ ~ / J I
where f7 LT-
r e l a x a t i o n t i m e f o r t h e e l e c t r o n tempera- t u r e ;
-
V-
mean e l e c t r o n v e l o c i t y ; $-aver*g e r e l a t i v e s h a r e o f energy l o s t by e l e c t - r o n h a v i n g c o l l i d e d w i t h a m o l e c u l a r . The s o l u t i o n o b t z i n e d . s u g g e s t s t h a t t h e f i e l d i n f l u e n c e on e l e c t r o p h y s i c a l p r o p e r t i e s of
AP
may b e n e g l e c t e d ( t h e when Eo<<xc
=c q0 3m (a
+On t h e c o n t r a r y , when EoZ,Ec ( t h e s t r o n g f i e l d ) , this i n f l u e n c e i s p r o - nounced. Here Ec i s a c h a r a c t e r i s t i c f i e l d f o r t h e
AP;
I,,,, ? m , O ,yT,o
a r e Te,?,,
d
'CT
c o r r e s p o n d i n g l y a t Eo = 0; e a n d m a r e t h e e l e c t r o n c h a r g e and mass. If p a r a - m e t e r s of N? a r e t h o s e g i v e n i n Ref .5, t h a t i s , N - 1 0 7 ~ r n - ~ ; ~ ~ - 1 0 ' ~ c m ;P
T,,,=T P =T m - 2 . 1 0 3 ~ , g - l . 2 . 1 0 - ~ ;
0,
5.9.-10' s-l and
a
=23.10'
s-l i s t a k e n from Ref.6, t h e n Ec=5.2 ~ / c m . These v a l u e s o f Ec do n o t a p p e a r t o be e x c e s s i v e l y h i g h a s compared t o f i e l d s produced b y t h e modern r a d i o t r a n s m i t t e r s . T h i s a l o n g v,$th o t h e r examples i n d i c a t e t h a t t h e c o n c l u s i o n of Ref. 7 ( l a c k i n g , u n f o r t u n a t e l y,
a f f i r m a t i o n by n u m e r i c a l e s t i m a t e s ) a c c o r d i n g t o which I, and ,T c o u l d n o t d i f f e r s i g n i f i c a n t l y , i s n o t s u f f i c i e n t l y g e n e r a l . H e a t i n g u p o f e l e c t r o n s i n t h e AP i s f o l l o w e d by t h e de- C r e a s e i n n, and change of5,.
These t w of a c t o r s a r e r e s p o n s i b l e f o r t h e a p p e a r a n c e of h e a t i n g n o n - l i n e a r i t y a t which t h e ele*
t r i c a l c o n d u c t i v i t y ,
,
becomes dependentREFERENCES
1. M.S.Sodha, S.Guha. Adv. Plasmz Phys.,
N 4 , p.219, 1 9 7 1
2 . D.T.Helfritch, '#.A.Gustafson, J.Eng.
Power, T r a n s . ASME, S e r i e s A,
96,
N 3 , p.113, 19743 V.A.Legasov, e t a l . , I n l P l a s m a Chemist- r y t , A t o m i z d a t , i s s u e 5 , p.116, 1 9 7 8 4. V.L.Ginzburg, The P r o p a g a t i o n o f E l e c t -
r o m a g n e t i c Vaves i n P l a s m a s ,Pergamon P r e s s , 1 9 7 0 .
5. E.G.Gibson, Phys. F l u i d s ,
-
9, N 1 2 ,p.2389, 1966
6 . R.I.Fante, R.G.Gamache, f .M.Yos. A I A A
J *
-
1 0 , N 3 , p.352, 19727. S.Guha, A.K.Arora, A p p l . S c i . R e s . , g ,