GRID VERSUS PLATE EXCITATION OF THE ELECTRON CURRENT DRIVEN ION WAVE INSTABILITY

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GRID VERSUS PLATE EXCITATION OF THE ELECTRON CURRENT DRIVEN ION WAVE

INSTABILITY

R. Schrittwieser, E. Märk, S. Kuhn

To cite this version:

R. Schrittwieser, E. Märk, S. Kuhn. GRID VERSUS PLATE EXCITATION OF THE ELECTRON CURRENT DRIVEN ION WAVE INSTABILITY. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-581-C7-582. �10.1051/jphyscol:19797281�. �jpa-00219269�

JOURiVAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Yome 40, JuiZZet 1979, w g e C7- 581

GRID VERSUS PLATE EXCITATION OF THE ELECTRON CURRENT DRIVEN ION WAVE INSTABILITY

R. Schrittwieser, E. Mark and S. Kuhn.

I n s t i t u t e for TheoreticaZ Physics, U n f v e r s i t y o f Innsbruck, A-6020 Innsbruck, Austria.

I n t r o d u c t i o n :

The e l e c t r o n - c u r r e n t d r i v e n c o l l i s i o n l e s s i o n wave i n s t a b i l i t y has been e x t e n s i v e l y i n v e s t i g a t e d i n t h e single-ended Q-machines a t Innsbruck and Risd /1-4/. It i s e x c i t e d by applying a s u f f i c i e n t - l y l a r g e d.c. b i a s ( @ G ) t o an e l e c t r o d e ( g r i d o r p l a t e ) immersed i n t o t h e plasma column and appears t o be a s t r o n g l y n o n l i n e a r s t a n d i n g wave between t h e hot p l a t e (HP) and t h e e x c i t i n g e l e c t r o d e .

Recent experiments have shown t h a t t h e o n s e t of t h e i n s t a b i l i t y depends s e n s i t i v e l y on t h e t y p e of t h e e x c i t i n g e l e c t r o d e . I n t h e p r e s e n t c o n t r i b u t i o n we r e p o r t on comparative measurements i n vhich both a g r i d ( G ) and a c o l d p l a t e (CP) were used. A q u a l i t a t i v e e x p l a n a t i o n i s given.

Setup and R e s u l t s :

The experiments were c a r r i e d o u t i n t h e Inns- bruck Q-machine /I/. The plasma, produced by i o n i - z a t i o n of sodium on a h o t t u n g s t e n p l a t e (T = 2000 K ) , i s contained i n a n a x i a l magnetic f i e l d B of 2250 G. The e x c i t i n g e l e c t r o d e s , whose dimensions exceed t h e c r o s s s e c t i o n of t h e plasma column, a r e p e r p e n d i c u l a r t o 9 and l o c a t e d a t a d i s t a n c e L = 35 cm from HP. CP is a massive t u n g s t e n p l a t e , whereas G i s a t u n g s t e n mesh g r i d with wire diameter d =

= 0.02 cm, meshwidth a = 0.2 cm, and hence an o p t i - c a l t r a n s p a r e n c y ^T = 8 1 %.

The dependence of t h e i n s t a b i l i t y on t h e e x c i t - i n g d . c . b i a s is i n v e s t i g a t e d w i t h t h e "unpertur- bed" d e n s i t y ( i . e . with f l o a t i n g e l e c t r o d e s ) a s pa- rameter. The l a t t e r i s chosen f o r t h e following r e a s o n s : ( i ) I n t h e unperturbed s t a t e , t h e e l e c - t r o n s have a f u l l Maxwellian v e l o c i t y d i s t r i b u t i o n , so t h a t t h e c l a s s i c a l d e t e r m i n a t i o n of d e n s i t i e s from probe c h a r a c t e r i s t i c s y i e l d s r e l i a b l e r e s u l t s . This i s not t h e c a s e f o r OG > o s i n c e t h e n t h e e l e c t r o n s a r e d r i f t i n g with non-Maxwellian v e l o c i - t y d i s t r i b u t i o n s , and a d d i t i o n a l m o d i f i c a t i o n s a r e i n t r o d u c e d by t h e i n s t a b i l i t y . ( i i ) It w i l l be

shown below t h a t choosing t h e unperturbed d e n s i t y a s a paramenter i s convenient i n r e l a t i n g our theo- r e t i c a l c o n s i d e r a t i o n s t o t h e experimental evidence.

I n what f o l l o w s , t h e i n s t a b i l i t y ( f = 4-5 kHz) * i s c h a r a c t e r i z e d by t h e s a t u r a t i o n amplitude AG and t h e s p e c t r a l bandwith A f of t h e a . c . component of t h e c u r r e n t flowing through t h e e x c i t i n g e l e c t r o d e . F i g . 1 shows ^V.IV,

t h e depen- dence on OG o f AG and A f i n

t h e c a s e of 60r I ^a

1 I

g r i d e x c i - t a t i o n f o r t h r e e d i f - _{L 0} f e r e n t den- s i t i e s . Each ampli- t u d e curve has two r e - gimes: f o r s m a l l @

G A G

i s s m a l l and O ~ I V I

-

grows slowly. F i g . 1

Above a c e r -

t a i n p o i n t , t h e c u r v e bends upwards and t h e n i n - c r e a s e s l i n e a r l y with

%,

$

=

J2erPG/m,

E g e '

= KT ,'m, on t h e upper a b s c i s s a . ) We d e f i n e t h e t h r e s h o l d of t h e s t a n d i n g ion-wave i n s t a b i l i t y ,

@thr, a s t h a t v a l u e of QG a t which t h e s t r a i g h t r e - g r e s s i o n l i n e o f t h e second regime i n t e r s e c t s t h e O G - a x i s . This d e f i n i t i o n i s supported by p r e l i m i n a - r y experimental f i n d i n g s which seem t o i n d i c a t e t h a t below t h i s t h r e s h o l d t h e i n s t a b i l i t y has t h e c h a r a c t e r of a t r a v e l l i n g wave, whereas f o r l a r g e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797281

@ it h a s c l e a r l y been shown t o b e a s t a n d i n g wave G

/1-3/. C o n s i d e r i n g t h e Af-values d i s p l a y e d i n F i g . 1 we o b s e r v e t h a t above t h e t h r e s h o l d t h e i n s t a b i l i t y h a s a pronounced peak i n t h e f r e q u e n c y s p e c t r u m .

A s i s a l r e a d y e v i d e n t from t h e sample c u r v e s of F i g . 1 , Qthr i n c r e a s e s w i t h t h e u n p e r t u r b e d d e n s i t y n, s e e F i g . 2 . The s o l i d l i n e c o r r e s p o n d s t o t h e li- n e a r r e g r e s s i o n 0 = -0.4

+

t h r

The r e s u l t s o f c o m p a r a t i v e measurements where G i s r e p l a c e d by CP a r e shown i n F i g . 3 .

Note t h a t i n t h i s c a s e Qthr i s e s s e n t i a l l y i n - dependent o f n.

D i s c u s s i o n :

F o l l o w i n g Kuhn / 5 / , we e x p l a i n t h e i n c r e a s e i n Qthr w i t h n f o r g r i d e x c i t a t i o n by t h e s c r e e n i n g e f f e c t o f t h e s p a c e c h a r g e s h e a t h s around t h e g r i d w i r e s . For s m a l l v a l u e s o f @ e a c h w i r e i s s u r -

G

rounded by a s h e a t h whose t h i c k n e s s i s o f t h e o r - d e r o f t h e Debye l e n g t h , A D = ( ~ ~ ~ / 4 1 ~ n e ~ ) l / ~ . Thus we may speak o f a n e f f e c t i v e g r i d a r e a ,

which i s r o u g h l y g i v e n by t h e g e o m e t r i c g r i d a r e a p l u s t h e Debye s h e a t h s . F o l l o w i n g t h i s a r g u -

i n c r e a s e i n T~~~ w i t h n means t h a t f o r t h e same a s m a l l e r f r a c t i o n o f t h e incoming p a r t i c l e s i s G

a f f e c t e d by G i f t h e u n p e r t u r b e d d e n s i t y i s i n - c r e a s e d . I n o t h e r words, t o p e r t u r b t h e same f r a c - t i o n o f p a r t i c l e s a h i g h e r b i a s QG i s needed f o r h i g h e r n. T h i s a l s o i m p l i e s t h a t O t h r , t h e g r i d b i a s a t which t h e n e t e l e c t r o n d r i f t i s j u s t s u f - f i c i e n t f o r t h e o n s e t o f t h e i n s t a b i l i t y , s h o u l d i n c r e a s e w i t h n . T h i s e x p e c t e d b e h a v i o u r i s c l e a r - l y r e f l e c t e d by t h e measured @ - v a l u e s i n F i g . 2 .

t h r

The v e r t i c a l 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 a t d e n s i t y where t h e Debye s h e a t h s s t a r t c o a l e s c i n g . For l o w e r d e n s i t i e s , Debye s h i e l d i n g becomes e s s e n - t i a l l y u n i m p o r t a n t and G i s e q u i v a l e n t t o an i d e a l p l a t e . I n t h i s c a s e we e x p e c t v e r y low v a l u e s o f Othr / 6 / , which i s i n a c c o r d a n c e w i t h F i g . 2 .

From t h e above c o n s i d e r a t i o n s we s h o u l d e x p e c t t h a t i n t h e c a s e o f p l a t e e x c i t a t i o n Qthr s h o u l d a l s o be s m a l l and n e a r l y i n d e p e n d e n t o f n. The l a t - t e r f e a t u r e i s d e m o n s t r a t e d by F i g . 3 . However, we have n o t y e t found an e x p l a n a t i o n o f t h e r e l a t i v e - l y l a r g e v a l u e s of @ = 2-3 V. F u t u r e i n v e s t i g a -

t h r

t i o n s w i l l c o n c e n t r a t e on c l a r i f y i n g t h e r o l e o f s u r f a c e c o n t a m i n a t i o n which c o u l d b e one of t h e r e a s o n s f o r t h i s d i s c r e p a n c y .

Acknowledgements:

We t h a n k Prof.F.Cap f o r h i s i n t e r e s t and sup- p o r t , and Drs.J.J.Rasmussen and G.Auer f o r v a l u a - b l e d i s c u s s i o n s . T h i s work was s u p p o r t e d by Fonds z u r F61,derurlg d e r wissenschaECiichen Forschung . ( A u s t r i a ) u n d e r g r a n t Nos. 2781 and S-18/02.

R e f e r e n c e s :

/1/ N.Sato e t a l . , P h y s . F l u i d s

19

/ 2 / R. S c h r i t t w i e s e r , P h y s . L e t t .

65A

/ 3 / P.Michelsen e t al., Plasma P h y s . i n p r i n t . /4/ R.Hatakeyama e t a l . , P h y s . R e v . L e t t . s u b m i t t e d . / 5 / S.Kuhn, Plasma Phys. s u b m i t t e d .

/ 6 / M.T.C.Fang and S.Kuhn, s u b m i t t e d t o t h i s con- f e r e n c e .

ment we c a n d e f i n e an e f f e c t i v e t r a n s p a r e n c y

T~~~ = ( a - A D - d / 2 I 2 / a 2 , which i s p l o t t e d t o - g e t h e r w i t h AD i n F i g . 2 . P h y s i c a l l y s p e a k i n g , t h e