ON CHARGE-EXCHANGE OF IONS IN PLASMA

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Submitted on 1 Jan 1979

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ON CHARGE-EXCHANGE OF IONS IN PLASMA

A. Grigoriady, O. Fisun

To cite this version:

A. Grigoriady, O. Fisun. ON CHARGE-EXCHANGE OF IONS IN PLASMA. Journal de Physique

Colloques, 1979, 40 (C7), pp.C7-105-C7-106. �10.1051/jphyscol:1979752�. �jpa-00219458�

JOURNAL DE PHYSIQUE CoZZoque C7, suppzdment a u n07, Tome 40, ~ u i Z Z e t 1979, page C7- 105

ON CHARGE-EXCHANGE OF IONS IN PLASMA

A.K. Grigoriady, 0.1. Fisun.

I n s t i t u t e o f EZectrodynamics, K i e v 252057, U.S.S.R.

An i n f l u e n c e of plasma p a r t i c l e s on l e c u l a r terms f o r such slow c o l l i s i o n s a r e exchanging system i s d i s ~ l a i e d i n two wa- accompanied by t h e r e b u i l d i n g of t h e scre- 7s. On t h e on hand p a r t i c l e s a t d i s t a n c e s enlng cloud. One can show, t h a t under the- r,c ro" n a c t i n g a s s t a t i s t i c a l l y i n - se c o n d i t i o n s t h e i n t e r a c t i o n of t h e exch- dependent ones cause t h e appearance of a n anging couple w i t h the near-by p a r t i c l e s e f f e c t i v e detuning <HJ I and electron-ind- w i l l be dominant1 92.

uced charge-exchanged

.

On t h e o t h e r hand exchanging system i s under t h e a c t i o n of p a r t i c l e s being a t t h e d i s t a n c e s r > r o . Their i n f l u e n c e cannot be considered a s ' s t a t i s t i c a l l y independent because of t h e

s t r o n g s p a t i a l c o r r e l a t i o n s .

T h i s r e p o r t d e a l s with i n v e s t i g a t i o n of t h e e f f e c t of plasma p o l a r i z a t i o n on t h e r e s o n a n t charge-exchange. The i o n e n t - e r i n g t h e r e a c t i o n induces a s p a t i a l char- ge i n plasma; i t s p o t e n t i a l

b ) A,< I. I n t h i s case t r a n s i t i o n s of t h e l o c a l i z e d e l e c t r o n between t h e moving cen- t e r s i n t h e v i c i n i t y of two c r i t i c a l poi- t s RcI and Rc2 occur i n plasma m i c r o f i e l d with s t r e n g t h t o depend on t h e v e l o c i t y of i o n e n t e r i n g t h e r e a c t i o n . Since with t h e l o g a r i t h m i c zccuracy RCI = Rc2 = po,we can e x p r e s s t h e energy d i f f e r e n c e between t h e t h e s t a t e s

determines t h e ion-plasma i n t e r a c t i o n en- ergy. Here

s

i s d i e l e c t r i c response funct- i o n , v

-

₀ i s i o n v e l o c i t y .

The mechanism of t h e e f f e c t i v e d e f e c t formation connected w i t h c o l l e c t i v e i n t e r - a c t i o n s i s d e f i n e d by parameter A = wp.k

,

where w B i s t h e e l e c t r o n plasma frequency

,

5 i s t h e propagation time between t h e c r i - t i c a l p o i n t s .

a ) A > > I . T r a n s i t i o n s between t h e quasimo

-

f o r t h e c r i t i c a l p o i n t s a s

-

.[

^udu

\

^Im t ( k , k v o u ) I

where u=cos(E,vo) A-

, p

i s t h e impact parame- t e r .

2 2 The crude e s t i m a t e g i v e s us H b qopokd.

* L , t h e r e f o r e t h e r a t i o H/<H? - I O - * ~ ~ / ~ L (L i s Coulomb logarithm, g = kzn-I). It f o l l o w s t h a t such plasma parameters e x i s t where t h e energy d i f f e r e n c e of t h e q u a s i

-

molecular terms i s due t o t h e c o l l e c t i v e phenomena. Let u s study t h i s e f f e c t f o r se-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979752

v e r a l concrete conditions.

Equilibrium plasma.Yhe response f u n c t i o n

i s - 2

where

~ ( z ) = I

-

z exp(-z 2 )

+

i ( ' ~ r / 2 > ~ ' ~ . z . e x ~ ( - z 2 / 2 ) .

Then ₌ qokd P o

d T

^LG(X)

.

( 3 )

Here G(x) = (P(x)

-

xP'(x))/2x2, P(x) i s t h e i n t e g r a l of p r o b a b i l i t y , x = v /v e Te.

Nonequillbrium s t a b l e plasma. Tidman-Dup

-

r e e mode13for two-temperature e l e c t r o n g a s I n t h i s case .-,

where a = (T/T')'/~. The e f f e c t i v e d e f e c t i n t h i s system can be w r i t t e n i n t h e form

J I

where B(a,x) =

~w ^.

A s we can s e e , t h e magnitude of t h e d e f e c t i s p r o p o r t i o n a l t o t h e numbers of f a s t pa- r t l c l e s .

Turbulent plasma. A s an example of t u r b u l - e n t system l e t us consider a c o l l i s i o n

-

l e s s unmagnetized plasma with developed e l e c t r o s t a t i c turbulence. When t h e a u t o

-

c o r r e l a t i o n time o r t h e f i e l d f l u c t u a t i o n s i s l e s s t h a n time f o r r e s o n a n t p a r t i c l e s t o d i f f u s e i n t h e wave number space, t h e e x p r e s s i o n f o r a d i e l e c t r i c f u n c t i o n t a k e s a form ⁴

t h e random f l u c t u a t i n g e l e c t r i c f i e l d t o t h e thermal energy d e n s i t y , F ( z ) = W(z)

2 2

( z 4 - ~ ~ z +15)

+

( Z

-7).

S u b s t i t u t i o n ( 5 ) i n t o ( 2 ) g i v e s

where Bt i s t h e p o s i t i v e f u n c t i o n a l of x.

ehe formula ( 6 ) f o l l o w s t h a t t h e ran- dom f i e l d fluctuations i n t u r b u l e n t plas- ma l e a d t o decrease of detuning. ~ h r s r e - s u l t s from s c a t t e r i n g of plasma e l e c t r o n s on t h e t u r b u l e n t p u l s e s reducing t h e t e s t p a r t i c l e s correlations with surroundings.

I n t h i s sense an inr'luence of f l u c t u a t i - ons on plasma p o l a r i z a t i o n properties i s analogous t o b l n a r y collision e f f e c t s .

Let us f i n d t h e plasma parameter ran- ge, where t h e charge-exchange p r o c e s s w i l l be determined by t h e e f f e c t of t h e dyna

-

mica1 p o l a r i z a t i o n . The a d i a b a t i c condlt- i o n H.T&-' > I r e q u i r e s the following i n e q u a l i t y f o r a case of thermodynamical e q u i l i b r i u m

n > 2, ~ . I o - ' ~ T ~ / ~ Q ( x ) , n(cmW3), T(K)

,

where _-1

0 ( x ) = x G ( x )

.

This m e q u a l i t y t o g e t h e r with c o n d i t i o n s I , g < I r e s t r i c t t h e plasma para- P

meters, where t h i s e f f e c t i s possible.

References

whereDis the r a t i o of energy d e n s i t y of