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Preliminary experiment on the current sustaining in a magnetized toroidal plasma
Volume 36A, n u m b e r 3
PHYSICS
PRELIMINARY
EXPERIMENT IN
A
MAGNETIZED
LETTERS
ON
3 0 A u g u s t 1971
THE
CURRENT
TOROIDAL
SUSTAINING
PLASMA
K. HIRANO, K. M A T S U U R A and A. M O H R I Institute of Plasma Physics, Nagoya University, Nagoya, Japan
Received 20 June 1971
T r a v e l l i n g r . f . field is effective to induce d.c. p l a s m a c u r r e n t along toroidal m a g n e t i c field. W h i s t l e r wave is found to play an i m p o r t a n t role for the m e c h a n i s m . Bunched e l e c t r o n s moving with the wave a r e o b s e r v e d .
The s t a t i o n a r y s u s t a i n i n g of p l a s m a c u r r e n t i n a t o r o i d a l m a g n e t i c field is an i m p o r t a n t p r o b l e m for the continuous operation of Tokamak s y s t e m s . The u s e of t r a v e l l i n g e l e c t r o - m a g n e t i c waves of c o m p r e s s i o n a l Alfv~n wave was p r o posed by Wort [1]. The e x p e r i m e n t s of T h o n e m a n n et al. [2] and Delta P r o j e c t in USSR [3] showed that dc c u r r e n t s a r e excited by r.f. t r a v e l l i n g waves. In t h e s e p r e v i o u s e x p e r i m e n t , however, t o r o i d a l m a g n e t i c field was not applied. H e r e is d e s c r i b e d a n e x p e r i m e n t to study an i n f l u e n c e of the m a g n e t i c field on the c u r r e n t sustaining. The e x p e r i m e n t a l a p p a r a t u s is s i m i l a r to T h o n e m a n n ' s , except for the u s e of t o r o i d a l coils. The m a j o r and m i n o r d i a m e t e r s of a glass tube a r e 24 cm and 6 cm, r e s p e c t i v e l y . The t r a n s m i s s i o n l i n e a r r a n g e d a r o u n d the tube has its p h a s e velocity of 6.7 × 105 m / s . The r.f. power is fed to the line from a 2.68 MHz o s c i l l a t o r of 10 kW and the other end of the line is t e r m i n a t e d with a r e s i s t o r of 5 0 ~ . The wave length of the t r a v e l l i n g wave is o n e - t h i r d of the c i r c u m f e r e n c e of the t o r u s . C e n t r e conductors s e t a r o u n d the m a j o r axis g e n e r a t e the t o r o i d a l field, B t , of 1.5 × 10 -2 T at m a x i u m on the m i n o r axis of the t o r u s . A r g o n is fed into the tube for the working gas. The t r a v e l l i n g r.f. wave p r o d u c e s p l a s m a and s i m u l t a n e o u s l y d r i v e s the d.c. c u r r e n t , I t , c i r c u l a t i n g a r o u n d the torus. As shown in the fig., the current It observed by a Hall element has a peak at a certain value of Bt, which depends on the feeding gas pressure. It has been considered [3] that the driving force of toroidal current is J × B induced by the r.f.
field. According to this model, the c u r r e n t should a p p r e c i a b l y d e c r e a s e even at B t = 100 gauss, s i n c e the OJceT in the conductivity exp r e s s i o n is 10 or m o r e for the e x p e r i m e n t a l condition in which n ~ 5 × 1012 c m - 3 and
5x10-3 ~
~04xl0-3 ~3x10-3,
2.5x1(~3
0
I
50
1
Bt(gauss)
100
I
150
Fig. 1. Dependences of the toroidal dc current, It, on the toroidal magnetic field, Bt, and the gas pressure, p. R.f. power is 10 kW, and the gas is argon.
215
Volume 36A, n u m b e r 3
PHYSICS
T e ~ 7.5 eV. T h e o b s e r v e d d e p e n d e n c e in t h e figure, however, is quite different from the e x p e c t e d o n e f r o m t h i s m o d e l . T h e p e a k i n g of t h e c u r r e n t i s e x p l a i n e d b y t h e e x c i t a t i o n of of w h i s t l e r w a v e . T a k i n g t h e n u m e r i c a l v a l u e s of p a r a m e t e r s of t h e e x p e r i m e n t , t h e d i s p e r s i o n r e l a t i o n of t h e w h i s t l e r w a v e i s r e d u c e d to B t w ~ 2 × 10 - 1 2 n g a u s s
,
w h e r e , a s u s u a l , n i s t h e n u m b e r of e l e c t r o n s per cm 3 and Btw is the toroidal magnetic field at which the whistler wave is resonant. For example, in the case that gas pressure is 3 m t o r r , t h e l o w e s t c u r v e in t h e f i g u r e , n i s 5 × 1012 c m - 3 a n d B t w b e c o m e s 100 g a u s s , which agrees satisfactorily with the observed v a l u e of 80 g a u s s . T h e r e f o r e , it c a n b e s a i d t h a t t h e s i m i l a r p h y s i c a l s i t u a t i o n i s r e a l i z e d to t h a t of W o r t ' s , s i n c e b o t h w h i s t l e r w a v e a n d c o m p r e s s i o n a l A l f v ~ n w a v e b e l o n g to t h e s a m e branch. T h e o s c i l l a t o r y c o m p o n e n t of t h e t o r o i d a l c u r r e n t i s o b s e r v e d u s i n g a p i c k up loop. T h e f r e q u e n c y i s t h e s a m e a s t h e r.f. t r a v e l l i n g w a v e
216
LETTERS
30 August 1971
a t B t ¢ 0, w h i l e , a t Bt = 0, it b e c o m e s t w i c e . F r o m t h e p h a s e r e l a t i o n b e t w e e n t h e r.f. f i e l d a n d t h e s i g n a l of t h e c u r r e n t , t h e f o l l o w i n g f a c t s a r e f o u n d : in t h e c a s e B t = 0, e l e c t r o n s c a r r y i n g t h e o s c i l l a t o r y c u r r e n t l o c a t e in t w o c u s p r e g i o n s in a w a v e l e n g t h , a n d , w h e n B t i s s u f f i ciently strong, the electrons stay at the middle of t h e m i r r o r w h i c h i s f o r m e d w i t h t h e t o r o i d a l f i e l d a n d t h e c u s p f i e l d of t h e t r a v e l l i n g w a v e . T h e a u t h o r s w o u l d l i k e to e x p r e s s t h e i r h e a r t y t h a n k s to P r o f e s s o r K. H u s i m i f o r c o n t i n u o u s e n c o u r a g e m ent.
References [1] D . J . H . W o r t , Culham L a b o r a t o r y Report CLM-R255 (1970). [2] P . C . T h o n e r n a n n , W.T.Cowhig and P . A . D a v e n p o r t , Nature 169 (1952) 34. [3] N . A . B o r z u n o v , N.Ya. Kuz~mina, l. Kh. Nevyazhskii, S.M.Osovets, Yu.F.Petrov, B.I.Polyakov, I. A. Popov, K. V. Khodataev and V. P. Shimehuk, Soy. Phys. Doklady 8 (1964) 914.
PHYSICS
PRELIMINARY
EXPERIMENT IN
A
MAGNETIZED
LETTERS
ON
3 0 A u g u s t 1971
THE
CURRENT
TOROIDAL
SUSTAINING
PLASMA
K. HIRANO, K. M A T S U U R A and A. M O H R I Institute of Plasma Physics, Nagoya University, Nagoya, Japan
Received 20 June 1971
T r a v e l l i n g r . f . field is effective to induce d.c. p l a s m a c u r r e n t along toroidal m a g n e t i c field. W h i s t l e r wave is found to play an i m p o r t a n t role for the m e c h a n i s m . Bunched e l e c t r o n s moving with the wave a r e o b s e r v e d .
The s t a t i o n a r y s u s t a i n i n g of p l a s m a c u r r e n t i n a t o r o i d a l m a g n e t i c field is an i m p o r t a n t p r o b l e m for the continuous operation of Tokamak s y s t e m s . The u s e of t r a v e l l i n g e l e c t r o - m a g n e t i c waves of c o m p r e s s i o n a l Alfv~n wave was p r o posed by Wort [1]. The e x p e r i m e n t s of T h o n e m a n n et al. [2] and Delta P r o j e c t in USSR [3] showed that dc c u r r e n t s a r e excited by r.f. t r a v e l l i n g waves. In t h e s e p r e v i o u s e x p e r i m e n t , however, t o r o i d a l m a g n e t i c field was not applied. H e r e is d e s c r i b e d a n e x p e r i m e n t to study an i n f l u e n c e of the m a g n e t i c field on the c u r r e n t sustaining. The e x p e r i m e n t a l a p p a r a t u s is s i m i l a r to T h o n e m a n n ' s , except for the u s e of t o r o i d a l coils. The m a j o r and m i n o r d i a m e t e r s of a glass tube a r e 24 cm and 6 cm, r e s p e c t i v e l y . The t r a n s m i s s i o n l i n e a r r a n g e d a r o u n d the tube has its p h a s e velocity of 6.7 × 105 m / s . The r.f. power is fed to the line from a 2.68 MHz o s c i l l a t o r of 10 kW and the other end of the line is t e r m i n a t e d with a r e s i s t o r of 5 0 ~ . The wave length of the t r a v e l l i n g wave is o n e - t h i r d of the c i r c u m f e r e n c e of the t o r u s . C e n t r e conductors s e t a r o u n d the m a j o r axis g e n e r a t e the t o r o i d a l field, B t , of 1.5 × 10 -2 T at m a x i u m on the m i n o r axis of the t o r u s . A r g o n is fed into the tube for the working gas. The t r a v e l l i n g r.f. wave p r o d u c e s p l a s m a and s i m u l t a n e o u s l y d r i v e s the d.c. c u r r e n t , I t , c i r c u l a t i n g a r o u n d the torus. As shown in the fig., the current It observed by a Hall element has a peak at a certain value of Bt, which depends on the feeding gas pressure. It has been considered [3] that the driving force of toroidal current is J × B induced by the r.f.
field. According to this model, the c u r r e n t should a p p r e c i a b l y d e c r e a s e even at B t = 100 gauss, s i n c e the OJceT in the conductivity exp r e s s i o n is 10 or m o r e for the e x p e r i m e n t a l condition in which n ~ 5 × 1012 c m - 3 and
5x10-3 ~
~04xl0-3 ~3x10-3,
2.5x1(~3
0
I
50
1
Bt(gauss)
100
I
150
Fig. 1. Dependences of the toroidal dc current, It, on the toroidal magnetic field, Bt, and the gas pressure, p. R.f. power is 10 kW, and the gas is argon.
215
Volume 36A, n u m b e r 3
PHYSICS
T e ~ 7.5 eV. T h e o b s e r v e d d e p e n d e n c e in t h e figure, however, is quite different from the e x p e c t e d o n e f r o m t h i s m o d e l . T h e p e a k i n g of t h e c u r r e n t i s e x p l a i n e d b y t h e e x c i t a t i o n of of w h i s t l e r w a v e . T a k i n g t h e n u m e r i c a l v a l u e s of p a r a m e t e r s of t h e e x p e r i m e n t , t h e d i s p e r s i o n r e l a t i o n of t h e w h i s t l e r w a v e i s r e d u c e d to B t w ~ 2 × 10 - 1 2 n g a u s s
,
w h e r e , a s u s u a l , n i s t h e n u m b e r of e l e c t r o n s per cm 3 and Btw is the toroidal magnetic field at which the whistler wave is resonant. For example, in the case that gas pressure is 3 m t o r r , t h e l o w e s t c u r v e in t h e f i g u r e , n i s 5 × 1012 c m - 3 a n d B t w b e c o m e s 100 g a u s s , which agrees satisfactorily with the observed v a l u e of 80 g a u s s . T h e r e f o r e , it c a n b e s a i d t h a t t h e s i m i l a r p h y s i c a l s i t u a t i o n i s r e a l i z e d to t h a t of W o r t ' s , s i n c e b o t h w h i s t l e r w a v e a n d c o m p r e s s i o n a l A l f v ~ n w a v e b e l o n g to t h e s a m e branch. T h e o s c i l l a t o r y c o m p o n e n t of t h e t o r o i d a l c u r r e n t i s o b s e r v e d u s i n g a p i c k up loop. T h e f r e q u e n c y i s t h e s a m e a s t h e r.f. t r a v e l l i n g w a v e
216
LETTERS
30 August 1971
a t B t ¢ 0, w h i l e , a t Bt = 0, it b e c o m e s t w i c e . F r o m t h e p h a s e r e l a t i o n b e t w e e n t h e r.f. f i e l d a n d t h e s i g n a l of t h e c u r r e n t , t h e f o l l o w i n g f a c t s a r e f o u n d : in t h e c a s e B t = 0, e l e c t r o n s c a r r y i n g t h e o s c i l l a t o r y c u r r e n t l o c a t e in t w o c u s p r e g i o n s in a w a v e l e n g t h , a n d , w h e n B t i s s u f f i ciently strong, the electrons stay at the middle of t h e m i r r o r w h i c h i s f o r m e d w i t h t h e t o r o i d a l f i e l d a n d t h e c u s p f i e l d of t h e t r a v e l l i n g w a v e . T h e a u t h o r s w o u l d l i k e to e x p r e s s t h e i r h e a r t y t h a n k s to P r o f e s s o r K. H u s i m i f o r c o n t i n u o u s e n c o u r a g e m ent.
References [1] D . J . H . W o r t , Culham L a b o r a t o r y Report CLM-R255 (1970). [2] P . C . T h o n e r n a n n , W.T.Cowhig and P . A . D a v e n p o r t , Nature 169 (1952) 34. [3] N . A . B o r z u n o v , N.Ya. Kuz~mina, l. Kh. Nevyazhskii, S.M.Osovets, Yu.F.Petrov, B.I.Polyakov, I. A. Popov, K. V. Khodataev and V. P. Shimehuk, Soy. Phys. Doklady 8 (1964) 914.