PROPAGATION OF WHISTLER WAVES TRAPPED IN A NARROW DENSITY TROUGH

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Submitted on 1 Jan 1979

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PROPAGATION OF WHISTLER WAVES TRAPPED IN A NARROW DENSITY TROUGH

H. Sugai, K. Ido, H. Niki, S. Takeda

To cite this version:

H. Sugai, K. Ido, H. Niki, S. Takeda. PROPAGATION OF WHISTLER WAVES TRAPPED IN A NARROW DENSITY TROUGH. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-703-C7-704.

�10.1051/jphyscol:19797340�. �jpa-00219334�

JOURflAL. DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 40, J u i Z l e t 1979, page C7- 703

PROPAGATION OF WHISTLER WAVES TRAPPED IN A NARROW DENSITY TROUGH

H. Sugai, K. Ido, H. Niki and S. Takeda.

Department o f EZectrieaZ Engineering, Nagoya U n i v e r s i t y , Nagoya Japan.

A b s t r a c t : W h i s t l e r waves a r e o b s e r v e d t o , b e t r a p - ped i n t h e narrow d e n s i t y t r o u g h of w i d t h 2d < ^XI/

( p a r a l l e l wave l e n g t h ) . The p h a s e and a m p l i t u d e p r o f i l e of d u c t e d w h i s t l e r s i s measured a l o n g and a c r o s s t h e t r o u g h . The e x p e r i m e n t a l r e s u l t s a r e i n good agreement w i t h t h e r e c e n t t r a p p i n g t h e o r y .

Ducted p r o p a g a t i o n o f w h i s t l e r waves h a s been w i d e l y r e c o g n i z e d a s a mechanism g u i d i n g t h e wave energy a l o n g l i n e s of magnetic f i e l d i n geo-

magnetosphers ! I n t h e f i e l d - a l i g n e d d e n s i t y t r o u g h o r hump ( ' d u c t ' ) , w h i s t l e r s a r e t r a p p e d somewhat i n t h e manner of a m e t a l i c waveguide. The convention- a l r a y t h e o r y 1 c a n n o t b e a p p l i e d t o t h e narrow d u c t (2d ,< A,,). The r e c e n t t h e o r y 2 s o l v i n g t h e e i g e n - v a l u e problem h a s p r e d i c t e d t h a t w h i s t l e r waves a r e

I n t h i s paper we p r e s e n t l a b o r a t o r y e x p e r i - ments of w h i s t l e r wave t r a p p i n g i n t h e narrow den-

s i t y t r o u g h . The d e t a i l s of plasma d e v i c e h a s a l - r e a d y been r e p o r t e d e l s e w h e r e ? The experiment i s performed i n a n a f t e r g l o w plasma of d e n s i t y n ^z 7

10" cm-3 and e l e c t r o n t e m p e r a t u r e kT6 = 0 . 3 -

0.8 eV, under t h e m a g n e t i c f i e l d B o = 100 - 200 G . The f i e l d - a l i g n e d d e n s i t y t r o u g h i s a r t i f i c i a l l y produced i n t h e n o v e l f a s h i o n where t h e d e p t h and t h e w i d t h of t h e d u c t c a n b e c o n t r o l l e d a r b i t r a l l y . W h i s t l e r waves of f r e q u e n c y w / 2 ~ = 100 - 500 MHz a r e e x c i t e d w i t h a n e l e c t r i c d i p o l e a n t e n n a . The r f power a p p l i e d t o t h e e x c i t e r a n t e n n a i s s o s m a l l t h a t t h e wave n o n l i n e a r i t y and t h e e l e c t r o n h e a t i n g d u e t o a n t e n n a a c t i o n s 4 i s excluded.

While t h e wave e n e r g y f l o w d i v e r g e s i n t h e t r a p p e d even i n t h e narrow d e n s i t y t r o u g h . u n i f o r m d e n s i t y p r o f i l e , t h e narrow d e n s i t y t r o u g h

TROUGH

y,

.6 -4 -2 0 2 4 6

F i g . 1 . R e l a t i v e wave a m p l i t u d e s a c r o s s B o a t d i f f e r e n t a x i a l d i s t a n c e s from t h e e x c i t e r an- t e n n a , t o g e t h e r w i t h t h e d e n s i t y p r o f i l e s i n t h e a b s e n c e ( a ) and t h e p r e s e n c e (b) of t h e narrow d e n s i t y t r o u g h . w / O = 0.70,

52127~ = 508 MHz.

. RADIAL DISTANCE r(cm) RADIAL DISTANCE r ( c m )

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797340

c o n f i n e s t h e wave which d o e s n o t broaden w i t h i n - c r e a s i n g d i s t a n c e from t h e e x c i t e r . F i g u r e 1 d i s - p l a y s a comparison of t h e wave a m p l i t u d e p r o f i l e s a c r o s s B o , i n t h e a b s e n c e [ F i g . l ( a ) ] and i n t h e p r e s e n c e [ F i g . l ( b ) ] of t h e d e n s i t y t r o u g h . The p e r f e c t l y d u c t e d mode i s e s t a b l i s h e d a t z 2 25 cm, w h i l e t h e e f f e c t of r a d i a t i o n broadenning from t h e e x c i t e r a n t e n n a c a n n o t b e n e g l e c t e d f o r z ,< 1 5 cm.

The t r a n s v e r s e p r o f i l e s of wave a m p l i t u d e s show t h e e x p o n e n t i a l d e c a y o u t s i d e t h e t r o u g h . The t r a n s v e r s e decay l e n g t h A i s p l o t t e d i n F i g . 2 , a s a f u n c t i o n of t h e f r e q u e n c y n o r m a l i z e d by t h e e l e c - t r o n c y c l o t r o n f r e q u e n c y Q. The s o l i d l i n e i n F i g . 2 i n d i c a t e s t h e t h e o r e t i c a l c u r v e o b t a i n e d i n t h e s h a r p boundary model? The e x p e r i m e n t a l v a l u e s of A become minimum, around t h e c r i t i c a l f r e q u e n c y

The wave l e n g t h a s w e l l a s t h e wave a m p l i t u d e i s m o d i f i e d i n t h e p r e s e n c e o f t h e d e n s i t y t r o u g h . The measured d i s p e r s i o n r e l a t i o n s of t h e d u c t e d modes w e l l a g r e e w i t h t h e t h e o r e t i c a l o n e s , a s

shown i n F i g . 3.

R e f e r e n c e s

--

1. R.A. H e l l i w e l l , W h i s t l e r s and R e l a t e d Iono- spkzeric Phenomena ( S t a n f o r d Univ., S t a n f o r d , C a l i f . , 1 9 6 5 ) .

2. K. Mima, G. M o r a l e s , Y.C. Lee, and B.D. F r i e d , R e s e a r c h R e p o r t of I n s t i t u t e f o r F u s i o n Theory, Hiroshima U n i v e r s i t y (1978), Hiroshima, J a p a n . 3. H. S u g a i , M. S a t o , K. Ido, and S. Takeda, J.

phys. Soc. J a p a n 44, 1953 (1978).

4. H. S u g a i , M. Maruyama, M. S a t o , and S. Takeda, phys. F l u i d s 2, 690 (1978).

FREOUENCY w / n

F i g . 2 . E x p e r i m e n t a l p o i n t s and t h e o r e t i c a l l i n e of t h e t r a n s v e r s e decay l e n g t h A a s a f u n c t i o n of t h e normalized f r e q u e n c y w/Q. The d e n s i t y de- p r e s s i o n r a t e 6 = 33 %, and 2d = 1 . 4 cm.

O o c 1 2 3

WAVE NUMBER kgl(cm')

F i g . 3 . Cornparisor of t h e w h i s t l e r wave d i s p e r s i o n

r e l a t i o n s i n a u n i f o r m plasma and i n a narrow

d e n s i t y t r o u g h . S o l i d l i n e and c l o s e d c i r c l e s

c o r r e s p o n d t o t h e c a s e w i t h t h e t r o u g h , and dash-

ed l i n e and open c i r c l e s i n d i c a t e t h e c a s e with-

o u t t h e t r o u g h . n l = 6.9 x 10" ~ r n - ~ , Q/2n = 508

MHz, 8

3 0 X , and 2d = 1 . 4 cm.