WAVE PROPAGATION IN A CYLINDRICAL GEOMETRY

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WAVE PROPAGATION IN A CYLINDRICAL GEOMETRY

H. Akiyama, T. Yamada, S. Takeda

To cite this version:

H. Akiyama, T. Yamada, S. Takeda. WAVE PROPAGATION IN A CYLINDRICAL GEOMETRY.

Journal de Physique Colloques, 1979, 40 (C7), pp.C7-543-C7-544. �10.1051/jphyscol:19797262�. �jpa-

00219248�

JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 40, JuiZZet 1979, page C7- 543

WAVE PROPAGATION IN A CYLINDFUCAL GEOMETRY

H. Akiyama, T. Yamada and S. Takeda.

Department of E Z e c t ~ i c a Z Engineering, Nagoya University, Nagoya, Japan.

A b s t r a c t : The p r o p a g a t i o n of t h e normal modes i n a n ion-beam-plasma system and t h e i o n - a c o u s t i c s o l i t a r y waves i s s t u d i e d i n a c y l i n d r i c a l d o u b l e plasma de- v i c e . A f t e r t h e f a s t ion-beam modes and ion-acous- t i c s o l i t a r y wave c o n c e n t r a t e a t t h e c e n t e r , den- s i t y d e p r e s s i o n s emerge. These phenomena a r e i n good agreement w i t h t h e r e s u l t s of t h e computer s i m u l a t i o n a b o u t t h e c y l i n d r i c a l i o n - a c o u s t i c waves.

INTRODUCTION :

Hershkowitz e t a l . o b s e r v e d t h e c y l i n d r i c a l s t a n d i n g waves produced by t h e ion-ion beam i n s t a - b i l i t y ( I ) , and t h e c y l i n d r i c a l i o n - a c o u s t i c s o l i t a - r y waves ( 2 ) . However, t h e r e p o r t a b o u t t h e propa- g a t i o n o f t h e c y l i n d r i c a l ion-beam modes i s n o t found. About t h e i o n - a c o u s t i c s o l i t a r y waves, t h e i r e x p e r i m e n t a l r e s u l t s o f t h e p r o p a g a t i o n v e l o c i t y and t h e h a l f - w i d t h a r e n o t i n agreement w i t h t h e t h e o r y . I n t h i s p a p e r , t h e p r o p a g a t i o n of t h e c y l i n d r i - c a l ion-beam modes and i o n - a c o u s t i c s o l i t a r y waves i s e x p e r i m e n t a l l y s t u d i e d , and t h e o b t a i n e d r e s u l t s a r e compared w i t h t h e t h e o r y and computer simula- t i o n .

EXPERIMENTAL DEVICE:

The c y l i n d r i c a l d o u b l e plasma d e v i c e used f o r t h e e x p e r i m e n t c o n s i s t s of t h e two c o n c e n t r i c a r g o n plasmas s e p a r a t e d by a n mesh g r i d . The i n n e r plasma of 67 cm i n l e n g t h and 32 cm ( o r 1 6 cm) i n d i a m e t e r i s produced by t h e d i s c h a r g e between t h e s e v e r a l f i l a m e n t s and b o t h end p l a t e s a s t h e anode. The o u t e r plasma i s produced by t h e d i s c h a r g e between t h e f i l a m e n t s and t h e c y l i n d r i c a l mesh anode of 40

cm i n d i a m e t e r . The t y p i c a l o p e r a t i n g p a r a m e t e r s a r e t h e e l e c t r o n t e m p e r a t u r e Te ^::1 t o 2 e V , i o n t e m p e r a t u r e T i : 0 . 1 t o 0.2 eV, plasma d e n s i t y Np ::

10' t o

lo9

lo-'

PROPAGATION OF ION-BEAM MODES:

A f t e r t h e s t e a d y ion-beam i s i n j e c t e d i n t o t h e i n n e r plasma by t h e p o t e n t i a l d i f f e r e n c e V between t h e mesh and p l a t e a n o d e s , t h e r e p e a t e d p u l s e s i g - n a l s w i t h t h e p u l s e w i d t h of 3 u s e c and a m p l i t u d e of 1 V a r e superimposed on v o l t a g e V t o e x c i t e t h e ion- beam modes. The s t e a d y beam v e l o c i t y Vb c a n b e v a r i e d by V .

The s p a t i a l e v o l u t i o n of t h e ion-beam modes i s shown i n F i g . 1 , where F , S and I - a r e t h e f a s t and slow ion-beam modes, and i o n - a c o u s t i c mode r e s p e c - t i v e l y . The fast-beam and i o n - a c o u s t i c modes a r e t h e p o s i t i v e d e n s i t y p u l s e s , and t h e slow-beam mode

( p s e c )

5 --" i s t h e n e g a t i v e den- s i t y p u l s e ( 3 ) . The d i s p e r s i o n r e l a t i o n s of t h e ion-beam modes a r e i n good agreement w i t h t h e t h e o r y i n t h e p l a n e geometry a t t h e r a d i a l p o s i t i o n r = 1 0

-

b I I I

-15 -10 -5 0 5 10 15 f e c t c a n b e n e g l i g i -

r

(cm)

F i g . 1 b l e .

36

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797262

We f i r s t c o n s i d e r t h e l i n e a r t h e o r y o f t h e ion- beam modes i n t h e c y l i n d r i c a l geometry t o e x p l a i n t h e e x p e r i m e n t a l r e s u l t s e x c e p t n e a r t h e c e n t e r . The f o l l o w i n g f o r m u l a s a r e r e a d i l y o b t a i n e d from t h e c o n t i n u i t y , motion and P o i s s o n e q u a t i o n s ,

where V p , Nb, n and C s a r e t h e phase v e l o c i t y o f t h e i n g o i n g fast-beam mode, t h e s t e a d y d e n s i t y o f beam i o n s , t h e p e r t u r b e d d e n s i t y o f t h e ion-beam mode and t h e i o n - a c o u s t i c v e l o c i t y r e s p e c t i v e l y . The t h e o - r e t i c a l c u r v e s o b t a i n e d from e q s . ( l ) and ( 2 ) a r e c l o s e t o t h e e x p e r i m e n t a l r e s u l t s f o r w a n d Vp a t t h e r a d i a l p o s i t i o n r 2 2.

The fast-beam mode grows w i t h t h e p r o p a g a t i o n , and ' t h e d e n s i t y d e p r e s s i o n a p p e a r s a t t h e c e n t e r . T h i s d e p r e s s i o n s p r e a d s w i t h t h e outward p r o p a g a t i o n o f t h e fast-beam mode. Then t h e d e n s i t y humps form- ed i n s i d e t h e d e p r e s s i o n a r e o b s e r v e d by t h e more d e t a i l e d measurement from 27 p s e c till 37 Usec.

These humps w i t h t h e ion-beam v e l o c i t y p r o p a g a t e i n - wards and outwards f i n a l l y t o a p p r o a c h t h e d e n s i t y of t h e s t e a d y s t a t e .

PROPAGATION OF ION-ACOUCTIC SOLITA3Y WAVE :

-

The i o n - a c o u s t i c s o l i t a r y wave i s e x c i t e d by t h e p o s i t i v e h a l f sine-wave p u l s e a p p l i e d t o t h e anode of t h e o u t e r plasma, where V 3.s n e a r l y e q u a l z e r o . The d i a m e t e r o f t h e i n n e r plasma i s changed t o 1 6 cm. I n F i g . 2 i s shown t h e dependence o f t h e a m p l i t u d e and w i d t h o f t h e i o n - a c o u s t i c s o l i t a r y wave o n t h e r a d i a l p o s i t i o n r , where n o , fin and D

a r e t h e s t e a d y plasma d e n s i t y , t h e p e r t i t r b e d d e n s i t y and t h e w i d t h o f t h e s o l i t a r y wave r e s p e c t i v e l y . The s o l i d l i n e of & / n o i s t h e t h e o r e t i c a l l i n e con- s i d e r i n g t h e Landau damping of t h e s o l i t a r y waves.

F i g . 2

The product 6 of t h e maximum s o l i t o n a m p l i t u d e and t h e s q u a r e of t h e w i d t h i s w i t h i n t h e t h e o r e t i c a l v a l u e s ( R = 4.3 f o r Ti/Te = 0.1, B = 6 f o r Ti/Te = 0) c o n s i d e r i n g t h e i o n t e m p e r a t u r e T i . The v e l o c i t y U o f t h e s o l i t a r y wave i s U = C s ( l

+

A f t e r t h e i o n - a c o u s t i c s o l i t a r y wave concen- t r a t e s a t t h e c e n t e r , t h e d e n s i t y d e p r e s s i o n a p p e a r s same a s t h e f a s t ion-beam mode. The d e n s i t y humps o b s e r v e d i n t h e e x p e r i m e n t o f t h e ion-beam modes a r e n o t o b s e r v e d . The s p a t i a l e v o l u t i o n of t h e s o l i t a r y wave i s i n good agreement w i t h t h e s i m u l a t e d r e s u l t s

REFERENCES:

(1) T. Romesser and N . Hershkowitz: Phys. of F l u i d s 18 (1075) 1354.

-

( 2 ) N. Hershkowitz and T. Romesser: Phys. Rev.

L e t t e r s

2

( 3 ) N. S a t o , H. S u g a i and R. Hatakeyama: Plasma Phys. 2 (1977) 187.

(4) T. Ogino and S. Takeda: J . P h y s . Soc. J a p a n

41

(1976) 257.