ON THE BEHAVIOUR OF WEAKLY IONIZED PLASMA WITH NON-ZERO NEUTRALS TEMPERATURE PLACED IN EXTERNAL D.C. ELECTRIC FIELD OF MODERATE INTENSITY

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ON THE BEHAVIOUR OF WEAKLY IONIZED PLASMA WITH NON-ZERO NEUTRALS TEMPERATURE PLACED IN EXTERNAL D.C.

ELECTRIC FIELD OF MODERATE INTENSITY

V. Žigman, B. Milić

To cite this version:

V. Žigman, B. Milić. ON THE BEHAVIOUR OF WEAKLY IONIZED PLASMA WITH NON- ZERO NEUTRALS TEMPERATURE PLACED IN EXTERNAL D.C. ELECTRIC FIELD OF MODERATE INTENSITY. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-589-C7-590.

�10.1051/jphyscol:19797285�. �jpa-00219273�

JOURPiAL DE PHYSIQUE Colioque C7, suppZdment au n07, Tome 40, J u i l l e t 1979, page C7- 589

ON THE BEHAVIOUR OF WEAKLY IONIZED PLASMA WITH NON-ZERO NEUTRALS TEMPERATURE PLACED IN EXTERNAL D.C. ELECTRIC FIELD OF MODERATE INTENSmY

V.J. iigman and B.S. ~ i l i c f .

I n s t i t u t e

of

I n order t o i n v e s t i g a t e f u r t h e r above expression i s appropriate, and t h e t h e dynamically unstable modes i n weakly following form of t h e e l e c t r o n d i s t r i b - ionized plasmas placed i n t h e e x t e r n a l u t i o n function r e s u l t s :

d.c. e l e c t r i c f i e l d discussed i n 113,

we consider here t h e behaviour of t h e mo-

des analogous t o t h e ones obtained in[1,2]

assuming now t h a t t h e applied e l e c t r i c

f i e l d i n t e n s i t i e s (Eo) a r e intermediate It can be e a s i l y seen t h a t t h i s approxim- or low, and t h a t t h e e f f e c t s of t h e non- a t e form of t h e function ( 1 ) i s n o t s u i t - zero temperature of t h e n e u t r a l s (Tn) have a b l e e i t h e r f o r EODs well above t h e plas- t o be taken i n t o account. ma e l e c t r i c f i e l d , or f o r EO8s near zero.

To t h i s end, a new form of t h e e l - ectron d i s t r i b u t i o n function f o r Tn # ⁰

i s derived here. The Margenau-Davydov d i s - t r i b u t i o n was assumed a s t h e s t a r t i n g point, and only e l a s t i c electron-neutral

c o l l i s i o n s were taken i n t o account, and t h e y were described by t h e b i l l i a r d - b a l l model. The exact r e s u l t f o r t h e i s o t r o p i c p a r t of t h i s function i s obtained i n a

straightforward way, and i s of t h e follow-

=

c2G*)v' i s t h e character- where vr, *

' ,

i s t i c ~ G u ~ v e s t e i n i a n v e l o c i t y , and C i s t h e normalization f a c t o r . It is c l e a r l y seen t h a t i n t h e limits Eo- 0 and Eo*

t h e above function becomes a Maxwellian

The components of t h e plasma d i e l e c t r i c t e n s o r (PDT) were then evaluat- ed with t h e above form of t h e e l e c t r o n d i s t r i b u t i o n function

an i t e r a t i v e pro- cedure, up t o t h e second order i n VvTe.

The small terms of t h i s order of magnit- ude have already been shown t o be of i m - portance if t h e non-pokeneial (non-longi- t u d i n a l ) o s c i l l a t i o n s of t h e plasma a r e analyzed. The r e s u l t s f o r t h e components of t h e PDT generalize t h e expressions ob- t a i n e d i n l1,21 and w i l l be omitted here.

The p e r t a i n i n g d i s p e r s i o n equation f o r t h e

a

low frequency range

& and f o r t h e waves propagating a t r i g h t angles t o t h e d i r e c t i o n of Eo has been found t o be:

and a Druyvesteinian f u n c t i o n respective-

ly. For moderate f i e l d i n t e n s i t i e s , but

*d ^ga -@=%

[/- "4 ^F.+v~*-O

s t i l l below t h e c h a r a c t e r i s t i c plasma e l - e c t r i c f i e l d , Ep, (b

^{, which}

i s -1 V/m f o r t y p i c a l l a b o r a t o r y plasma, Here F, D, R, G denote dimensionless an expansion in binomial s e r i e s i n t h e f u n c t i o n a l s of f zO(v), weakly dependent on

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797285

Eo through t h e small parameter (vN/vD)

,

where vx =

ZTn/me) , ^aad B and q,e

a r e t h e e l e c t r o n e f f e c t i v e d r i f t and therm- a l v e l o c i t i e s respectively. For t h e func- t i o n

t h e s e q u a n t i t i e s a r e given by:

where

(

^Ld - E (msqj

^=w

9$(v) = .2r

,

0 ( 9 0 )

and

f o r t h e b i l l i a r d - b a l l model.

From ( 3 ) , t h e following s p e c t r a a r e obtain- ed:

( 4 4

where

e l

These two modes have been found t o be weakly damped; t h e a t t e n u a t i o n c o e f f i c i e n t a s determined from t h e

i s given by:

This i s i n accordance with t h e behaviour of t h e analogous modes i n s t r o n g e l e c t r i c f i e l d s f o r t h e d i r e c t i o n of propagation perpendicular t o Eo, Rowever, a s a r e s u l t of non-zero Tn and comparatively small i n - t e n s i t i e s of t h e e x t e r n a l l y applied elec- t r i c f i e l d Eo, i n t h e s i t u a t i o n consider- ed i n t h i s paper t h e term containing F i n eq. (11) may become very l a r g e and t h i ~ f a c t may lead t a dynamic i n s t a b i l i t y of t h e s e two modes. It i s t o be noted t h a t t h e numerical values of t h e f u n c t i o n a l s given by eqs. (4)-(7) a r e a l l of the or- der of u n i t y , a s has been shown previous- l y ll]. I n t h e case considered here, only D, R

a r e of t h i s order of magnitude.

The f u n c t i o n a l F, eq.

may become much l a r g e r , a s can be e a s i l y v e r i f i e d f o r a t m i c a l s e t of wlasma parameters

..

( T ~ ~ I O ~ K , n ...1019 ne -lo15

& e n ~ 1 0 - 2 0 m'). The p o s s i b i l i t y of t h e

development o f dynamic i n s t a b i l i t y with t h e modes considered i s , hence, a specif- i c consequence of % ^# 0 and of E o g E

P

R e f e r e n c e s

Zigman, V.J., Mili6,

Proc.o$

t h e V I I I t h Yugoslav S.P.I.G., Dub- rovnik, 1976, p. 491.

C27 iigman, V.J., Mili6, B.s., Third I n t e r n a t i o n a l Congress on Waves

and I n s t a b i l i t i e s i n Plasmas, Pa-

r i s , 1977, Book of Abstracts, p.175.