INTERACTION OF THE INTENSE MICROWAVE BEAM WITH A FLOW OF LOW TEMPERATURE PLASMA (Pt.2. The theory)

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Submitted on 1 Jan 1979

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INTERACTION OF THE INTENSE MICROWAVE BEAM WITH A FLOW OF LOW TEMPERATURE

PLASMA (Pt.2. The theory)

Ai. Rogashkova

To cite this version:

Ai. Rogashkova. INTERACTION OF THE INTENSE MICROWAVE BEAM WITH A FLOW OF LOW TEMPERATURE PLASMA (Pt.2. The theory). Journal de Physique Colloques, 1979, 40 (C7), pp.C7-641-C7-642. �10.1051/jphyscol:19797311�. �jpa-00219302�

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JOURNAL DE PHYSIQUE ColLoque C7, supple'ment au n07, Tome 40, J u i l Z e t 1979, page C7- 6 4 1

INTERACTION OF THE INTENSE MICROWAVE BEAM WITH A FLOW OF LOW TEMPERATURE PLASMA (Pt.2. The theory)

AI. Rogashkova.

I n s t i t u t e o f Radioengineering and Electronics, Academy of Sciences, Moscou, U.S.S.R.

To e x p l a i n the experimentally observed space d i s t r i b u t i o n of t h e plasma stream d e n s i t y d i s t u r b e d by t h e i n t e n s e beam of radiowaves (1) t h e o r e t i c a l a n a l y s e s h a s been performed.

Let u s assume t h a t the plasma stream moves a l o n g t h e a x i s w i t h t h e c o n s t a n t v e l o c i t y Vo. The electromagnetic wave pro p a g a t e s along t h e a x i s Y. I t s i n t e n s i t y i s described by t h e expression:

E2 =jlZgi4)(-Zyk),

(1 1

where

A

i s a c h a r a c t e r i s t i c dimension of the f i e l d nonunif ormity.

The l i n e a r i z e d macrascopic t r a n s f e r e q u a t i o n s f o r t h e d e n s i t y and temperature o f e l e c t r o n s in t h e e l e c t r i c f i e l d a r e used t o d e s c r i b e t h e d i s t u r b a n c e of a stream

azY

au

² K ~ E ~

a e . - d - - ~ ~ = - - aa

₂ _E;' ₍₂₎

a2v

J V W

Z L - ? k a r - ~ l ( = - ~ - + - - L as2 ud a@ ^u,

^ud

'

⁽³⁾

v h e r e

W= - AT , {=

^J& i s t h e r e l a t i v e

T,"

&'

v a r i a t i o n s of e l e c t r o n d e n s i t y and tempe- r a t p r e , 8. %/A r ~ f 3 & $ , ~ = & ~ 3 ⁹

d r

^-the

recombination c o e f f i c ~ e n t , 1;

,

T,"

-

^{t h e}

undisturbed v a l u e s of d e n s i t y and tempe- r a t u r e of plasma stream; 11, =0,5 f o r the weakly i o n i z e d plasma. The system (1),(2) i s t r u e under f o l l o w i n g c o n d i t i o n s : K l z K and

xaym . ^{4,4, -}

t h e i o n and n e u t r a l d e n s i t y the temperature of i o n s and n e u t r a l s i s supposed t o be unchanged.

The plasma stream i s uniform i n absen- ce of t h e e l e c t r i c a l f i e l d s o y , °

, ⁷ ^' ^:

^do

n o t depend on t h e coordinates. The coef- f i c i e n t A i s determined by t h e r e l a - t i o n :

A =

^d(d

,&a

a(vr,o, ^,

^i.e. ^{i t}c h a r a c t e r i z e s t h e r a t e of dependence of t h e r e - combination c o e f f i c i e n t and i o n i z a t i o n frequency on t h e temperature;

d =

l t , / ~ ) , ;

i s t h e v e l o c i t y of termodiffusion:

ST( V i

-

t h e i o n - n e u t r a l

; 2 ) d = 2 ~ m '

c o l l i s i o n frequency; 8,

-

t h e e l e c t r o n f r e e p a t h l e n g t h ;

8 -

t h e f r a c t i o n a l l o s t by a n e l e c t r o n i n a c o l l i s i o n w i t h a n e u t r a l p a r t i c l e :

6' -

t h e plasma con- d u c t i v i t y ;

Ep -

t h e plasma f i e l d [21

.

In t h e assumption ( 1 ) a s o l l u t i o n of Eq ( 2 ) is:

,+,,

-p

F z n Y ~ $

[ , j ~ l , d l ~ l + $ ~ f + , d [ ~ - p(,o,

⁺ ₊

11- 2

I * \

( 4 ) +

e

The s o l u t i o n i s t r u e in the r e g i o n

Q <

0; (@ is t r u e i n t h e r e g i o n 6 , 0

qz--

t h e i n t e g r a l of e r r o r s ;

t h e c o n s t a n t s

&2=f-1/p

^determine

a dimension of t h e plasma stream tempera- t u r e d i s t u r b a n c e .

An a n a l y t i c a l s o l u t i o n of t h e equation (3) on t h e b a s i s of a n expression ( 4 ) i s impossible t o o b t a i n .

However a c a l c u l a t i o n of a space pat- t e r n shows t h a t f u n c t i o n

q(@)

i s c l o s e l y aproximated by e i t h e r

e-rlel

^{o r}^e-'2

f u n c t i o n s v e r s u s a parameters of t h e prob- lem.

Suppose v ~ ~ & f l ~ ~

.

Then the solu- t i o n of eq ( 3 ) t a k e s t h e form:

The experiment was performed u s i n g t h e argon plasma f o r which ~3.1

o - ~ .

I n t h e undisturbed plasma stream

/leD

^{( 1}r 4 ) .

lo1]/

/cm3,

T,"=

^(1+2).I O ~ O K ,

Tz

=600°K. T h i s

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797311

(3)

corresponds t o the values of t h e parame- t e r s : [0,05+0,21, &--lo-*;

(a/%)€

DEO~+IO]

^;(~~/zg)-io-'.

In Fig.1 a r e represented the numerical c a l c u l a t i o n s of the s t a t i o n a r y disturban- c e s of temperature and d e n s i t y f o r K = a , 0 5 ; d = 0 , 0 2 ; @hd)=50; (~p:/~)=0,15.

It i s assumed t h a t J s =lo-lo l/cm sec, 2 The function

e4*

determining a f i e l d l o c a l i z a t i o n in space i s denoted by a broken l i n e . It follows from the calcula- t i o n s r e p r e s e n t e d on Fig.1 t h a t the si- zes of disturbances introduced by a r a d i o beam i n t o plasma g r e a t l y exceed a radiobeam width. Under the above parameters a stream convection d o n ' t a f f e c t on the space temperature d i s t r i b u t i o n curve. It i s almost symmetrical i n r e l a t i o n t o the plane 8 =O. The

4

curve i s however markedly displaced in the 8

-

d i r e c t i o n . It i s known the parameters

& , ^vL , 5

a r e functions of the e l e c t r o n temperature and consequently they change i n a process of an e l e c t r o n heating.

In Fig.2 the curves a r e calculated f o r )"

In t h i s case a l s o the stream convection s l i g h t l y influences upon the space d i s t - r i b u t i o n '4 and g r e a t l y a f f e c t s on the function

f

: the region with an increa- sed d e n s i t y is formed being displaced i n space up t o the i n j e c t o r . It i s due t o the convection and ambipolar d i f f u s i o n v e l o c i t i e s a r e approximately equal and opposite. This r e s u l t s i n the e l e c t r o n ac- cumulation.

Thus the a n a l y s i s shows t h a t the plas- m a density decreases i f the plasma stream convection v e l o c i t y i s much more than the d i f f u s i o n v e l o c i t y , the disturbance s i z e s exceeding f i e l d s i z e and d i s p l a c i n g in the d i r e c t i o n of the stream v e l o c i t y . I T the convection and d i f f u s i o n v e l o c i t i e s a r e close both decrease and increase of the e l e c t r o n d e n s i t y take place in compa- r i s i o n t o the undisturbed s t a t e .

The performed t h e o r e t i c a l a n a l y s i s accounts f o r the experimental r e s u l t s : the e l e c t r o n d e n s i t y disturbed d i s t r i b u t i r on i s assymetric; the disturbed region

s i z e g r e a t l y exceeds the radiobeam width.

This a n a l y s i s e x p l a i n s the n a t u r e of the e l e c t r o n disturbed d e n s i t y space d i s t r i - bution.

REE'EREMCES :

1 .N .A.Amnd, S.A.Rogashkov, E. G. Shustin.

I n t e r a c t i o n of the microwave beam with a flow of low temperature ( P a r t 1.

Exper.) Proceedings of the X I V Conf.

on PIG, 1979: Grenoble, France.

il.A.V.Gurevich, A.B.Shvartsburg. The non- l i n e a r theory of the radiowave propaga- t i o n in ionosphere. "Nauka", 1973, tiioscow.

INTERACTION OF THE INTENSE MICROWAVE BEAM WITH A FLOW OF LOW TEMPERATURE PLASMA (Pt.2. The theory)

HAL Id: jpa-00219302

https://hal.archives-ouvertes.fr/jpa-00219302