Drift dissipative instability in an electromagnetic field

Volume

32A. number

DRIFT

PHYSICS

1

DISSIPATIVE

LETTERS

INSTABILITY

CEN de Saclay.

IN

AN

ELECTROMAGNETIC

J. TEICHMANN * 91 Gif-str,--Yl’rttC,/S.

Received

6 April

1 June 197U

FIELD

et. 0. /.Fvanr@

1970

The possibility of stabilizing the drift dissipative instability by applying an electromagnetic field with a dominant magnetic component (low impedance) is discussed.

hf

It has recently been shown, both theoretically [l] and experimentally [2] that the growth rate of dissipative instabilities can be reduced by applying an hf azimuthal magnetic field on the mean static field Ho. In this note we propose to generate the appropriate hf field by a system of external conductors. car. rying the hf current and situated parallel to Ho near the plasma boundary, fig. 1. The orientation of cur. rents may be either the same in each conductor or in the opposite sense in the neighbouring conductors, forming in this way the Picket-Fence arrangement. The electrical impedance of the system depends on geometrical factors, on the frequency 52 and on the arrangement of the backward conductor and can be kept sufficiently low. Thus the dominant components of the hf field are the azimuthal magnetic component Hq, which is sufficiently large in the skin depth. where the plasma is nonuniform and the radial electric component E,(r). Using a simple slab model let us demonstrate the effect of the hf field (E = ~,Eol(x) sinat, H= e,H, + eYH,lcosN) in laboratory, collision dominated. plasmas. Let US consider first the isothermal plasma. T, N 2’1 = T with ‘el <>LJ. W* ~~52 ~~wci’ W* = -cTk K/eHO, K = a In no ‘3 x. The gradient of Eel(x) leads to the drift velocity [3] Y = -ey[e2,/4m2,(S22 + u&)oce] 8E&,:CJx. “De Taking also into account the temperature gradient n = a 1nT ? In )zo, we obtain by using the similar procedure as in ref. [l] for the mean value of the perturbation of the electron density. taken over the time interval

7 -

ni e 1-7

52-’

for

Vei << S2 :

ea k,w

l-

[w -w*(l+rj)+g]A+bekZEolA’

where g = -kyVDe7 AR+iAI

+

+iA;

=

be

i-f;”

P,4=-‘0

(1)

w+g-qw*+iDeK2

n0

= e,/mevei,

De = T/m,

vei,

K2 = kz +k:H$l;Wi

i++q)Z2~(6)Z2q(6)Zfi(h)lq(h)J~(e),

= -2i(vei/bC2)

p;l_mP

6 = 2 kxkyDe Ho1 ‘Hos2.

i‘(P+q)Z2p(~)Z2q(6)‘(A)Zq(A)~$,(~), (Y = kZbeEol/S2

X =k;DeHf1/;1H2Q 0

’

<< 1.

The perturbation of the ion density may be established by neglecting the influence of the hf field [ 11. The condition of quasineutrality gives a dispersion relation from which it follows that for $p . cc 1, the drift modes oscillate with frequency w = w*( l+n 4 r-g and %;;;Eat;A t ‘> 1, t A’ 1 << IA t

Czechoslovak * On leave of absence from the Institute of Plasma Physics, Present address: CENG, Fusion, Bat. 10.05, CEDEX 85, 38 Grenoble,

Academy France.

of Sciences,

Prague.

47

Volume

32A.

number

PHYSICS

1

Fig.

For a plasma as follows:

with cold ions,

2

7 =

K De( 1+/3)+/3u. 1

+

Ti _ 0,

P[(g-rlW

AR

1 June

LETTERS

1

wci ,> v.

52 <
1970

k$>> lf?$~$,‘(w+iv~)~

1’

i the growth rate is

*)vi+K’DeWciK,‘~]

(3)

AR[w*(l+$-g]

where /3 = Te k$ mi w&. For sufficiently large amplitude Ho1 the parameter A is large, 1A / >> 1. Thus the growth rates are rather small comparison to the case without the hf field, where y in the isothermal plasma is of the order of Dek$%$p2. or pw*2,j’Dek$ for the case Ti - 0. For vei >>Q the collisional effects predominate over the acce 4’eration due to the gradient of the electric field and g N 0. The author wish to express

his gratitude

to Dr. T. Consoli

Re_ferences [l] A. A. Ivanov. J. Teichmann, Czech. J. Phys. B 19 (1969) 941. [Z] A. A. Ivanov. Yu. B. Kazakov. A. N. Lukianchuk, V. D. Rusanov, Teor. Fiz. 9 (1969) 356. [3) J. Teichmann. Nuclear Fusion 5 (1965) 107.

*****

48

for his support during this work.

S. S. Sobolev,

J. Teichmann,

Pisma

Zh. Exp.

i