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Submitted on 1 Jan 1979
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RELATIVISTIC ELECTRON-POSITRON PLASMA QUASI-LINEAR RELAXATION AT THE PRESENCE
OF MAGNETIC BREMSSTRAHLUNG
J. Lominadze, G. Machabeli, A. Mikhailovsky
To cite this version:
J. Lominadze, G. Machabeli, A. Mikhailovsky. RELATIVISTIC ELECTRON-POSITRON PLASMA QUASI-LINEAR RELAXATION AT THE PRESENCE OF MAGNETIC BREMSSTRAHLUNG.
Journal de Physique Colloques, 1979, 40 (C7), pp.C7-713-C7-714. �10.1051/jphyscol:19797345�. �jpa- 00219339�
JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 40, JuilZet 1979, page C7- 713
RELATMSTIC ELECTRON-POSITRON PLASMA QUASI-LINEAR RELAXATION AT TI-E PRESENCE (r MAGNETIC BREMSSTRAHUNG
J.G. Lominadze, G.Z. Machabeli and A.B. Mikhailovsky.
Abastwnani Astrophysical Observatory, Academy of Sciences GSSR, T b i l i s i , U. S. S. R., I . V. K~urchaov I n s t i t u t e o f Atomic hkergy, Moscow, U. S. S. R.
Recently a s i g n i f i c a n t a t t e n t i o n i s w i t h beam p a r t i c l e s , a n d f o r t h e r e a l and payed t o i n s t a b i l i t i e s and non-linear phe- imaginary P a r t s of f3-wJuencY
4
nomena, connected w i t h them. I n adopted a2
O.KCU -23;t,t)
, r=qF W? ,p 3%
( 1 )models t h e y may t a k e p l a c e i n p u l s a r mag-
2
-
477 e2hn e t o s p h e r e s . Such plasma s p e c i f i c f ea- Here
up - 7 ,
h %-
d e n s i t y of t u r e s a r e determined by i t s u l t r a r e l a t i -v i t y and v e r y s t r o n g magnetic f i e l d ( B x10'~gauss).
An u l t r a r e l a t i v i s t i c p a r t i c l e i n a s t r o n g magnetic f i e l d l o s e s i t s t r a n s - v e r s e momentum due t o , magnetic bremsstra- hlung and a s a r e s u l t p a r t i c l e d i s t r i b u - t i o n r e l a x e s t o a one-dimensional. By t h e e x i s t i n g n o t i o n , p u l s a r magnetosphere is f i l l e d up w i t h e l e o t r o n - p o s i t r o n plasma, moving along magnetic f i e l d f o r c e l i n e
be am.
P e r t u r b a t i o n s , c h a r a c t e r i z e d by f r e - quency and growth r a t e ( 1 ,) a t t h e qua- s i - l i n e a r d i f f u s i o n of p a r t i c l e s .lead t o a t r a n s v e r s e momentum r i s e . Such r e l a x a - t i o n must complete w i t h a magnetic brems- s t r a h l u n g , l e a d i n g t o a t r a n s v e r s e momen- tum d e c r e a s e . A competition of t h e s e two p r o c e s s e s w i l l determine a f i n a l form of d i s t r i b u t i o n f u n c t i o n .
The i n i t i a l k i n e t i c e q u a t i o n ha8 w i t h a t y p i c a l Lorentz-f a c t o r
;1; lo2-lo3
a f o r m 'and w i t h e l e c t r o n - p o s i t r o n beam w i t h Lo-
% t ~ ~ P ~ ~ l ~ L o ) +4!hl)
=sQL
( 2 )r e n t z - f a c t o r
%t lo5-lo7.
A beam i n s t a b i - Here F,, F1-
a r e t r a n s v e r s e and l o n g i - l i t y /1/ e x c i t a t e d a t t h e Cherenkov r e s o - t u d i n a l components of bremsstrahlung nance of beam p a r t i c l e s w i t h Langmuire f o r c e ,o s c i l l a t i o n is g e n e r a t e d i n s u c h plasma.
n 3 7
P a r t i c l e d i s t r i b u t i o n due t o q u a s i - l i n e a r ~ Q
-
Li s o p e r a t o r of q u a s i l i n e a r d i f - p a r t i c l e i n t e r a c t i o n w i t h t h e e x c i t a t i o n s , f u s i o n . hr e l a x e s t o a one-dimensional w i t h an elon-
SQC PLap,
g a t e d t a i l . I n analogy w i t h n o n r e l a e i v i s - t i c c a s e /2/ one may e x p e c t t h a t such d i s -
t r i b u t i o n must be u n s t a b l e w i t h r e s p e c t Considering d e r i v a t i v e s t o be grea-
9,
t o p e r t u r b a t i o n s e x c i t e d a t t h e c y c l o t - t e r i n comparison w i t h
$+ ' ao- '2 '
We- @ r
Ir o n e resonance ( w - a + i j e ~ o wb= me
)
f i n d o u t from ( 2 ) i n a first approxima-e
t i o n by a s m a l l parameter.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797345
A I I ~ f o r !,,(Ft,t)in n e x t approximation by a s m a l l parameter we have equation
We suppose, t h a t b e f o r e t h e c y c l o t r o n i n s t a b i l i t y o u t s e t , wheq n o i s e s have been t h e r m a l , t h e f u n c t i o n
t
\, (pS, t
) have had p l a t o u form. If we suppose, t h a t qua- s i l i n e a r r e l a x a t i o n l a p s e (+
+ .css ) t h ebeam d e c e l e r a t e s completely
(
I,, (f2eo)qO)
Using t h i s parameter a s a c h a r a c t e r i s t i c of n o i s e s l e v e l a t r e l a x a t i o n s t a g e ( f o r f i n i t e
t
) we s h a l l g e t an e s t i m a t i o nr
4 5f o r beam d e c e l e r a t i o n time
= nc G- XI
It i s p o s s i b l e t o e s t i m a t e t h e t o t a l wave energy a s
t h e r e s t p a r t of beam energgr i s i r r a d i a - t e d , s o t h a t
We have considered c y c l o t r o n i n s t a - b i l i t y and connected w i t h it q u a s i l i n e a r r e l a x a t i o n of u l t r a r e l a t i v i s t i c p a r t i c l e beam i n r e l a t i v i s t i c plasma i n a s t r o n g magnetic f i e l d , t a k i n g i n t o account mag- n e t i c bremsstrahlung. Supposing t h a t such r a d i a t i o n is a s t r o n g one, we have g o t a system of one-dimensional q u a s i l i n e a r e q u a t i o n s and have found an asymptotic s o l u t i o n of t h e system f o r l a r g e time. It h a s been shown, t h a t a s a consequence of a q u a s i l i n e a r r e l a x a t i o n i n a c o n d i t i o n of s t r o n g magnetic bremsstrahlung a beam d e c e l e r a t i o n a p p e a r s and beam energy t r a n - sforms i n t o t h e energy of r a d i a t i o n .
The p r o c e s s c o n s i d e r e d i n t h i s paper i s important f o r p u l s a r magnetosphere phy- s i c s .
R E F E R E N C E S
1. J.G .Lominadze
,
A.B.Llikhai1ovsky,
mTP7 v.76, N . 3 , 1979.
2. A.B.8Aikhailovslry, "Teoria Plasmennikh N e u s t o i c h i v o s t e i " , v.1, "Atomizdat",
1975.
It's e a s y t o o b t a i n from (5) a n ' e f f e c t i v e t r a n s v e r s e momentum of beam p a r t i c l e s