INTERACTION OF EM WAVES WITH A COMPRESSIBLE PLASMA COLUMN

HAL Id: jpa-00219277

https://hal.archives-ouvertes.fr/jpa-00219277

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTERACTION OF EM WAVES WITH A COMPRESSIBLE PLASMA COLUMN

Lj. Cander, B. Stanić

To cite this version:

Lj. Cander, B. Stanić. INTERACTION OF EM WAVES WITH A COMPRESSIBLE PLASMA COL- UMN. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-597-C7-598. �10.1051/jphyscol:19797289�.

�jpa-00219277�

JOURANL

DE PHYSIQUE CoZZoque

C7,

suppZ6ment au n07, Tome

40,

JuiZZet 1979, page

~ 7 - 597

INTERACTION ff EM WAVES WITH A COMPRESSIBLE PLASMA COLUMN

Lj.

R. Cander and B.V. ~ t a n i 6 * .

XGeomagnetic I n s t i t u t e , Grocka,

FacuZt~ o f EZectricaZ Engineering, University o f BeZgyad.

1. INTRODUCTION. The i n t e r a c t i o n o f an e l e - where H n ( l ) a r e t h e Hankel f u n c t i o n s o f the f i r s t ctromagneti c wave w i t h compressible plasma ha1 f- k i n d and o r d e r n . ~ ; and B; a r e s c a t t e r i n g coe- space o r plasma column has been e x t e n s i v e l y s t u - f f i c i e n t s t o be determined by t h e a p p r o p r i a t e d i e d i n r e s e n t years /I/-131. There have, howe- boundary c o n d i t i o n s

.

vet-, been v e r y few r e p o r t s w i t h numerical r e s u l t s 3. FORMAL SOLUTIONS. Supposing t h a t t h e com- about t h e i n t e r a c t i o n o f electromagnetic waves by p r e s s i b l e plasma can be described by t h e small- an i n f i n i t e l y l o n g compressible plasma column. s i g n a l t h e o r y and c o n s i d e r i n g o n l y t h e motion o f With t h e r e s e n t progress i n space e x p l o r a t i o n , a e l e c t r o n s , the plasma column i s governed by Max- problem o f t h i s k i n d has become an i m p o r t a n t one we1 1 's equations, t h e momentum equation and t h e which has some r e l a t i o n s w i t h space-communication combined equations o f c o n t i n u i t y and s t a t e 141.

technology and r a d i o astronomical problems. The A s t r a i g h t f o r w a r d m a n i p u l a t i o n o f t h i s equations present a n a l y s i s i n v e s t i g a t e s t h e s c a t t e r i n g o f g i v e s t h e f o l l o w i n g coupled second-order d i f f e - an o b l i q u e l y i n s i d e n t p l a n e electromagnetic wave r e n t i a l wave equations:

by an i n f i n i t e l y l o n g l o s s l e s s plasma column. Nu- m e r i c a l r e s u l t s f o r t h e d i f f e r e n t i a l s c a t t e r i n g cross s e c t i o n a r e obtained f o r a range o f acous- t i c v e l o c i t i e s i n elect,,ron gas.

2. FORMULATION OF THE PROBLEM. We consider t h e s c a t t e r i n g problem f o r the case where a plane electromagnetic wave i s i n c i d e n t on an i n f i n i t e l y

l o n g homogeneous l o s s l e s s compressible plasma co- w i t h 2

lumn o f r a d i u s a immersed i n f r e e space. The wave p = ~ - s i n + ~ , q;%-~in2@,,, g=se$)'"(ft-l).

v e c t o r

6

of an o b l i q u e l y i n c i d e n t wave i s assu-

R=.&

,f=ker, E = I - ~ ~ / ~ '

med t o be yz-plane and makes an angle +owith t h e

w

and w are, r e s p e c t i v e l y , t h e c i r c u l a r frequen- negative y-axis. For an i n c i d e n t wave whose e l e - c y o f t h e i n c i d e n t wave and e l e c t r o n plasma f r e q u P c t r i c f i e l d v e c t o r o f magnitude Eo makes t h e ency, P i s t h e pressure d e v i a t i o n from t h e mean angle

9

w i t h t h e x-axis, t h e a x i a l components and uo i s t h e a c o u s t i c v e l o c i t y i n e l e c t r o n gas.

t a k e t h e form The a x i a l components Ezn and Hz, o f t h e f i e l d

where

k.

=k c o s a

,

ki,=kosin&, ~ A = ~ ~ s i n ~ ,

i lY*O

Bn=-(koIy.) Eocos ']

,

^Fn=exp(in

Q +

i kizz-iwt)cosq and Jn a r e t h e Bessel functions o f t h e f i r s t k i n d and o r d e r n. The a x i a l components o f the s c a t t e r e d wave i n f r e e space a r e

and P deduced from eqn. ( 3 ) a r e

w i t h

Using t h e t r a n s v e r s e f i e l d components expressed i n terms o f t h e l r a x i a l components and r e l a t i o n f o r t h e r a d i a l component o f t h e average v e l o c i t y o f e l e c t r o n gas

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797289

y;-i. -i

w m Er wmno 7 ₍₅₎

one can now t o s a t i s f y t h e boundary c o n d i t i o n s a t t h e f r e e space-homogeneous compressible plasma i n t e r f a c e (Ja=koa). Matching t h e boundary c o n d i t i - ons gives

X . C = Y (6)

where X i s a 5x5 square m a t r i x , C and Y are 5x1 m a t r i c e s w i t h t h e elements

X1,= xl5=X3,= X33=x34=X44= XS1 =X5,=0

X ~ = . P ~ C O S + . ~

Q=

q,

II2

9,. Eol=Eosin?~ Hol=E,

C O S T .

The m a t r i x form ( 6 ) has been used f o r computation o f t h e s c a t t e r i n g c o e f f i c i e n t s A: and

. : B

4. NUMERICAL RESULTS. We consider o n l y t h e

case f o r an E i n c i d e n t plane electromagnetic wave

.

and t h e d i s t r i b u t i o n o f s c a t t e r e d energy -in cross- p o l a r i z e d f i e l d s i s expressed as f o l l o w s

The s c a t t e r e d f i e l d s i n above expressions a r e

s

S S

i

! IE~,E.,E:)=~:IOD,E:)+~:(E~E~,O)

WH: H,S,H;) = Fi;(~$i$)+ FlS,(qo,~;l

Angular v a r i a t i o n o f a normalized cross-polarized components o f s c a t t e r i n g cross s e c t i o n f o r v a r i -

i n Fig. I. The shapes of t h e curves a r e n o t i c e a b l y a f f e c t e d by t h e v a r i a t i o n o f a c o u s t i c v e l o c i t y mostly i n the angular i n t e r v a l ~ U 3 = + 5 0 ~ around t h e l a t e r a i d i r e c t i o n ( ~ = 1 8 0 ~ ) . I n t h e c a s e I b 0 . 0 8 t h e values o f E

/6d

increases and n o t i c e a b l e maximum appears at@=180°, whereas i t decreases f o r t h e case 0.001<0<0.08 and t h e prominent minimum

i s

seen a t 0=160°. These a r e j u s t a few o f t h e chara- c t e r i s t i c s t h a t can be deduced from t h e data g i v k n i n Fig.1 and one may conclude t h a t t h e angular d i - s t r i b u t i o n o f s c a t t e r e d energy i s v e r y s e n s i t i v e t o the values o f the a c o u s t i c v e l o c i t i e s . A l l com- p u t a t i o n s have been performed on a CDC 3600 compu- t e r .

F i g . ? . Normalized cross-polarized components o f s c a t t e r i n g cross s e c t i o n versus t h e azimuthal angle 9 f o r v a r i o u s values o f 0 / 4 ~ ~ = 3 0 ~ , k0a=0.5,

.

2 2 w, /w =0.5/.

REFERENCES

/ I /

Wait, J.,1964, Can. J.Phys.,

2,

1760.

/2/ Verma, Y., and Raemer, H., 1971, Radio Sci., 6, 113.

-

/3/

Kojima, T., I t a k u r a , K., and Higashi, T., 1972, J.App1. Phys.,

5,

^1309.

/4/ Chen, H.,1974, J . F r a n k l i n Ins., 297,

-

221.

ous a c o u s t i c v e l o c i t i e s i n e l e c t r o n gas i s p l o t t e d