A TIME DOMAIN METHOD FOR TRANSIENT SCATTERING OF ELECTROMAGNETIC WAVES IN PLASMAS

(1)

HAL Id: jpa-00219276

https://hal.archives-ouvertes.fr/jpa-00219276

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.

A TIME DOMAIN METHOD FOR TRANSIENT SCATTERING OF ELECTROMAGNETIC WAVES IN

PLASMAS

Miloš Skorić, Božidar, V. Stanić

To cite this version:

Miloš Skorić, Božidar, V. Stanić. A TIME DOMAIN METHOD FOR TRANSIENT SCATTERING

OF ELECTROMAGNETIC WAVES IN PLASMAS. Journal de Physique Colloques, 1979, 40 (C7),

pp.C7-595-C7-596. �10.1051/jphyscol:19797288�. �jpa-00219276�

(2)

JOURNAL DE PHYSIQUE CoZZoque C7, suppt6rnent au n07, Tome 40, JuiZZet 1979, page C7- 595

A T~ME DOMAIN METHOD FOR TRANSIENT SCATTERING OF ELECTROMAGNETIC WAVES M PLASMAS

~ i l o z M. Skori6 and 6o:idar V. stanid'.

Boris K i d r i c I n s t i t u t e o f Nuclear S c i e n c e s

-

Vinca, POB 522, 11000 BeZgrade,

Faculty o f EZectricaZ Engineering, U n i v e r s i t y o f Belgrade, 11000 Belgrade, Yugoslavia.

T h e o r e t i c a l i n v e s t i g a t i o n s of t h e t r a - n s i e n t r e s p o n s e of a c o l d plasma media t o an e l e c t r o m a g n e t i c p u l s e (EMP) e x c i t a t i o n i s of c u r r e n t i n t e r e s t . T h i s c l a s s of p r o b - lem h a s been p r e v i o u s l y c o n s i d e r e d by s e - v e r a l m e t h o d s : F o u r i e r - L a p l a c e t r a n s f o r m a p p r o a c h , based on a f r . e q u e n c y domain a n a - l y s i s / I - 2 / , s o l u t i o n o f t h e t i m e d e p e n d e n t Maxwell's e q u a t i o n s 1 3 - 4 1 , and t h e u s e of t h e t i m e domain m u l t i p l e - s c a t t e r i n g t e c h - n i q u e 151.

~. In t h i s c o n t r i b u t i o n a new and d i r e c t

c l a s s i c a l p a p e r s by A . Sommerfeld and L . B r i l l o u i n / 9 / .

A n i n c i d e n t wave f i e l d of an a r b i t r a r - r y EMP a t t h e o b s e r v a t i o n p o n t ~ ( 7 ) i s

3

where T:T(?) i s r e t a r d e d t i m e v a r i a b l e . I n t r o d u c i n g

T ~ T ( ? ) = ~ . Y (?) (1 )

where t i s t h e t i m e v a r i a b l e and Y(?) d e p - e n d s on a t y p e of t h e i n c i d e n t E Y P ( e n . p l a n e , s p h e r i c a l , e t c ) , d e t e r m i n i n g t h e i n - i t + a l c o n d i t i o n a s :

T ( 0 ) =

-

' P ( o ) = 0 _{( 2 )} t i m e domain a p p r o a c h t o t h e problem of t h e The w a v e f r o n t of t h e i n c i d e n t EMP p r o - t r a n s i e n t r e s p o n s e of c o l d m a g n e t o p l a s m a s p a g a t e s t h r o u g h t h e plasma a t t h e s p e e d i s d e v e l o p e d . Based on a c o n c e p t of a S e l f of l i g h t i n vacuum and w i t h o u t d i s t o r t i o n c o n s i s t e n t f i e l d and D a r w i n - H e r t r e e s c a t t e r - / 9 / -

i n g f o r m a l i s m , s p a c e - t i m e d e p e n d e n t i n t e g r a l E l e c t i o n d i p o l e moment

7

a t t h e p o i n t e q u i t i o n (STIE) i s f o r m e d i n a s i m p l e and MI

(TI)

i n plasma c a u s e d by t h e t r a n s i e n t d i r e c t way. The p r o p o s e d s p a c e - t i m e i n t e g -

r a l e q u a t i o n method (STIEM), / 6 / h c o u l d be a p p l i e d i n t h e a n a l y s i s of t h e t r a n s i e n t r e s p o n s e of an a r b i t r a r y EMP i n t i m e - v a r y - i n g inhomoge-neous l o s s y magnetopl asmas of a r b i t r a r y g e o m e t r i c a l s t r u c t u r e .

1 . SPACE-TIME INTEGRAL EQUATION M E T H O D STIEM d e v e l o p e d h e r e i s d e r i v e d by t h e e x t e n s i o n of t h e harmonic s t e a d y s t a t e Dar- w i n - H e r t r e e s c a t t e r i n g method 1 7 - 8 1 t o t h e domain o f t r a n s i e n t EMP. P h y s i c a l a n a l y s i s and e x p l a n a t i o n of p r o p a g a t i o n and d i s t o r - t i o n of EMP i n d i s p e r s t v e media i s g i v e n i n

EMP i s :

where ^{T ,}=T(p1 )

.

I n t r o d u c i n g an e l e m e n t a r y H e r t z i a n v e c t o r / I / , dFe a t ~ ( f ) s c a t t e r e d by t h e e l e m e n t a r y plasma volume dV, s u r r o u n d i n g M I ( F l ) and summing up a l l t h e c o n t r i b u t i o n s i n t h e volume of p l a s m a , t h e t o t a l t i m e d e p e n d e n t s c a t t e r e d f i e l d s ( s e l f - c o n s i s t e n t f i e l d s ) a r e :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797288

(3)

- - b

jJtk1= J j / { ~ ~ ~ } - n

4%

R

- R )

c(y

^{( 5 )}

vn r,

w h e r e ,n= n ( r l ) i s t h e e l e c t r o n d e n s i t y , R = I ~ ~

-ti,

and s p a c e d e r i v a t i v e s a r e a p p l i e d t o t h e c o o r d i a n t e s of t h e o b s e r v a t i o n p o i n t

~ ( 7 ) , V l ) r i s a symbol f o r t h e i n t e r s e c t i o n of t h e plasma volume V a n d r w i t h r d e f i e d a s : r : c r l - R 2 0 , where E f l ? ) i s d i f f e r e n t f o r v a r i o u s t y p e s of i n c i d e n t E Y P , d e p e n d i n g on

7

and t a s a p a r a m e t e r . Due t o t h e s p a c e - t i m e d e p e n d e n c e of t h e volume of i n t e g r a - t i o n

Vnr,

r e l a t i o n s ( 4 ) and ( 5 ) d e f i n e STIE f o r t h e s c a t t e r e d f i e l d s o f EMP w i t h an ex- p l i c i t form o b t a i n e d by t h e s u b s t i t u t i o n of t h e e x p r e s s i o n f o r which i s d e r i v e d from t h e e l e c t r o n e q u a t i o n of m o t i o n . In t h e d e - r i v a t i o n of t h e STIE ( 4 ) , ( 5 ) we have n o t made a n y p r e s u m p t i o n s a b o u t t h e c h a r a c t e r i s - t i c s of t h e plasma m e d i a . In t h a t way STIEM c o u l d be a p p l i e d i n t h e t r a n r i e n t a n a l y s i s of g e n e r a l i z e d c o l d plasma c o n f i g u r a t i o n s .

I 1 STIE FOR P L A N E EMP SCATTERED B Y A N ANISO- TROPIC LOSSY PLASMA HALF SPACE

F o r an a r b i t r a r y p l a n e EMP e x c i t a t i o n one o b t a i n s : f : c t - ( F 1 . 3 + ~ ) 3 O w i t h

f

a s a wave normal u n i t v e c t o r . I t i s n o t d i f f i c u l t t o c o n c l u d e t h a t

r

d e f i n e s t h e i n t e r i o r of a p a r a b o l o i d w i t h t h e a x i s i n

f

d i r e c t i o n and f o c u s a t t h e o b s e r v a t i o n p o i n t

~ ( 7 ) .

F o r a n i s o t r o p i c s t r a t i f i e d l o s s y p l a s - m a ( + ~ d i r e c t i o n ) h a l f s p a c e and n o r m a l l y i n - c i d e n t l i n e a r l y p o l a r i z e d p l a n e E Y P , from t h e e l e c t r o n e q u a t i o n o f m o t i o n o n e o b t a i n s :

"A A

where p = p x + i p y ; v=v-iwc , u c and v a r e e l e c t r -

v - c t - ( 3 . 3 + R ) and u = z + v / 2 one o b t a i n s t h e ct+z @

STIE g i v e n a s : ct-2

-S(t-t,)

**

, +

, - - -L-jvJn[9Je

i d i + i j d .

E ( C 4 - z . 7 ) - Zrn&C2 d

0 - % - 0

A E*=ET; +iE; where

E t

^and ^E,* a r e p a r a l l e l and c r o s s p o l a r i z e d components of s c a t t e r e d f i e l d , r e s p e c t i v e l y . The a b o v e e x p r e s s i o n f o r t h e STIE i s i n a g r e e m e n t w i t h t h e e q u a t i o n of Gray and % o w h i l l / l o / o b t a i n e d by t h e u s e of m u l t i p l e - s c a t t e r i n g t e c h n i q u e . For V=O t h e r e s u l t a q r e e s w i t h / 5 / .

I I I CONCLUSION

A method o f s e l f c o n s i s t e n t f i e l d and D a r w i n - H a r t r e e m i c r o s c o p i c s c a t t e r i n g f o r - malism i s a p p l i e d i n t h e t i m e domain and t h e

s p a c e t i m e i n t e g r a l e q u a t i o n f o r t h e s c a t t e - r e d f i e l d i s 0 b t a i n e d : D u e t o t h e g e n e r a l i t y of t h e p r o p o s e d method i t c o u l d be a p p l i e d i n t h e t r a n s i e n t a n a l y s i s of a t i m e - v a r y i n g inhomoqeneous l o s s y m a g n e t o p l a s m a s f o r an a r b i t r a r y EYP e x c i t a t i o n . T r a n s i e n t s c a t t e r - i n q of an p l a n e EMP i n a s t r a t i f i e d l o n g i t u - d i n a l l y a n i s o t r o p i c l o s s y plasma h a l f s p a c e i s c o n s i d e r e d a s a s p e c i a l c a s e .

REFERENCES

/ 1 / C . M . Knop, P r o c . IEEE, 56,1341 , 1 9 6 8 . / 2 / J . R . W a i t , P h y s . ~ f F l u w s , 1 2 , 1 5 2 1 , 1 9 6 9 . / 3 / E . O t t e t . a l . C a n . J . P h y s . 4 6 , 1 5 9 , 1 9 6 8 .

/ 4 / J . C . F i e l d , Radio S c i . ,6;-503,1971

.

/ 5 / G.K.Gray, e t a l , R a d i o S c i . , ~ , 5 7 , 1 9 7 4 . / 6 / M.M.SkoriC,M.Sc.Thesis,Belgrade,l976.

/ 7 / C . G . D a r w i n , T r a n s . C a m b . P h i l . S o c . 2 3 , 1 3 7 , 1 9 2 4 .

/ 8 / D.R.Hartree,Proc.Camb.Phil . S o c . g , 9 7 , 1 9 2 9 .

/ 9 / L . B r i l l o u i n , " W a v e p r o p . a n d Group V e l o c i - t y " ,Acad. P r e s s , N . Y . 1 9 6 0 .

/lO/K.G.Gray, e t a l . , Radio S c i . 9 ,

-

559,1974.

on c y c l o t r o n and c o l l i s i o n f r e q u e n c y , and E * = E+E i

.

I n t r o d u c i n g a new s e t of v a r i a b l e s