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THRESHOLD ELECTRON DRIFT FOR THE SPONTANEOUS EXCITATION OF
NON-ELECTROSTATIC ION-CYCLOTRON OSCILLATIONS IN WEAKLY IONIZED PLASMAS
N. Pavlović-Brajušković, B. Milić
To cite this version:
N. Pavlović-Brajušković, B. Milić. THRESHOLD ELECTRON DRIFT FOR THE SPONTA- NEOUS EXCITATION OF NON-ELECTROSTATIC ION-CYCLOTRON OSCILLATIONS IN WEAKLY IONIZED PLASMAS. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-655-C7-655.
�10.1051/jphyscol:19797318�. �jpa-00219309�
JOURNAL DE PHYSIQUE Colloque C7, suppliment au n07, Tome 40, J u i l l e t 1979, page C7- 655
THRESHOLD ELECTRON DRFT FOR THE S P O M A N E W S EXCITATION OF NON-ELECTROSTATIC
ION-CYCLOTRON OSCILLATIONS IN WEAKLY IONIZED PLASMAS
N. ~ a v l o v i & ~ r a j u ~ k o v i 6 and B. ~ i l i 6 ' .
Department of Physics, Faculty o f Sciences, Kragujevac, Yugoslavia,
' ~ e ~ a r t m e n t o f Physics and Meteorology, Faculty o f Sciences, Belgrade, YugosZavia.
Ion-cyclotron o s c i l l a t i o n s i n plasmas a r e g e n e r a l l y t r e a t e d a s e l e c t r o s t a t i c i n most the- o r i e s , a l t h o u g h it i s obvious t h a t t h e y a r e of n o n - p o t e n t i a l c h a r a c t e r . ' I n t h i s p a p e r an a t t - empt i s made, t h e r e f o r e , t o i n v e s t i g a t e some o u t s t a n d i n g c h a r a c t e r i s t i c s of t h e s e o s c i l l a - t i o n s , assuming t h a t t h e y a r e n o t e l e c t r o s t a - t i c . A uniform and i n f i n i t e weakly i o n i z e d pla- sma i s c o n s i d e r e d , and i t i s assumed t o be pla- ced i n a homogeneous and ' s t a t i c B p a r a l l e l t o a c o n s t a n t d.c. Eo. The e n s u i n g agomalous Dopp- l e r e f f e c t e v e n t u a l l y g i v e s r i s e t o ion- (and, of c o u r s e , a l s o e l e c t r o n - ) c y c l o t r o n waves of growing amplitude. T h i s f a c t o f spontaneous ex- c i t a t i o n h a s been l o n g ago observed experiment- a l l y [lJ, and t h e v a l u e of t h e t h r e s h o l d d r i f t h a s been found [zJ t o i n c r e a s e w i t h e l e c t r o n t e m p e r a t u r e ( o r r a t h e r w i t h T / T ~ ) , b u t t h e t h e o r e t i c a l e x p l a n a t i o n s ~ , g based on t h e a s s - umption t h a t t h e e x c i t e d a v e s a r e l o n g i t u d i n a l were n o t q u i t e s a t i s f a c t o r y .
I n t h i s paper t h e problem of t h e determin- a t i o n of t h e t h r e s h o l d d r i f t h a s been r e c o n s i d - e r e d f o r t h e plasma d e s c r i b e d above, and f o r i o n - c y c l o t r o n waves of n o n - e l e c t r o s t a t i c charac- t e r . The t h r e s h o l d d r i f t h a s been determined from t h e c o n d i t i o n of marginal i n s t a b i l i t y ,
I m ~ u O , and t h e n e c e s s a r y d i s p e r s i o n eqtiation i s t a k e n i n t h e s t a n d a r d F r e s n e l ( r a t h e r t h a n Poisson) form
where€#$ a r e t h e components o f t h e plasma d i - electric t e n s o r . The l a t t e r q u a n t i t i e s have been determined f r o m t h k i n e t i c e q u a t i o n s f o r e l e c t r o n and i o n o n e - p a r t i c l e d i s t r i b u t i o n fun- c t i o n s , u s i n g a modified BGK c o l l i s i o n i n t e g r a l f o r e-n and i - n e l a s t i c c o l l i s i o n s [5], w i t h a Maxwellian f $ and a s h i f t e d Maxwellian f:. Af- t e r t h e s t a n d a r d procedure of l i n e a r i z i n g , app- l y i n g t h e Fourier-Laplace t r a n s f o r m a t i o n s , ev- a l u a t i n g t h e components o f t h e complex am l i t - u d e s of t h e c u r r e n t d e n s i t y p e r t u r b a t i o n f6],
t h e o b t a i n e d d i s p e r s i o n e q u a t i o n y i e l d s t h e f o l - lowing e x p r e s s i o n f o r t h e t h r e s h o l d e l e c t r o n
t h d r i f t f o r t h e spontaneous e x c i t a t i o n of t h e g harmonic of t h e i o n - c y c l o t r o n o s c i l l a t i o n s :
where X ( a i ) i s a r a t h g qomplicated f u n c t i o n of t h e argument z i = ! ti b e i n g t h e i o n Larmor r a d i u s ) , which describes t h e e f f e c t s of f i n i t e Larmor r a d i u s i n t h e p r o c e s s of spontan- eous e x c i t a t i o n considered h e r e . The approxim- a t i v e e x p r e s s i o n s f o r t h i s f u n c t i o n a r e d i f f e r - e n t a t z i 4 I and a t zi3$ 1 ( r e s p e c t i v e l y , long- wave and short-wave l i m i t s , w i t h r e s p e c t t o i o n Larmor r a d i u s ) . It h a s been found t h a t i n t h e long-wave l i m i t , t h e temperature dependance ( a p p e a r i n g through t h e c o l l i s i o n f r e q u e n c i e s , thsmal v e l o c i t i e s and t h e v a r i a b l e zi) of t h e t h r e s h o l d e l e c t r o n d r i f t f o r t h e spontaneous e x c i t a t i o n of fbe rnth harmonic of t h e non-elec- t r o s t a t i c i o n - c y c l o t r o n o s c i l l a t i o n s is:
I n t h e short-wave l i m i t , on t h e c o n t r a r y , t h e t h r e s h o l d d r i f t i n q u e s t i o n i s p r a c t i c a l l y i n - dependent of t h e o r d e r of t h e harmonic rn, and i t i s much l a r g e r t h a n i n t h e former c a s e . It i s g i v e n by:
Hence, i n b o t h s h o r t - and long-wave l ' m i t s , a t e m p e r a t u r e 'dependance of t h e form T$2 i s found. T h i s i s i n accordance w i t h t h e behaviour found i n [z), which sugge,sts t h q t the waves e x c i t e d i n t h a t experiment were n o t e l e c t r , o s t a - t i c . It would be of i n t e r e s t t o observe exper- i m e n t a l l y the Ti-dependance of t h e t h r e s h o l d d r i f t ; i n t h e longwave l i m i t i t should be a f u n c t i o n of m, a c c o r d i n g t o t h e t h e o r y develop- ped h e r e .
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Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797318
