1 - Nuclear Sciences and Applications - IAEA

768
electron velocity distribution is modelled by a two component distribution that comprises
a non-drifting or current carrying small superthermal population added to an
isotropic Maxwellian bulk. The superthermal deviation of the distribution from the
Maxwellian bulk is determined completely by the fraction of electrons in the tail (17)
and their thermal (vs) and drift (u) velocities. We assume that both the bulk (vt) and
tail thermal velocities are sufficiently low, i.e. fits = 2(c/vls) 2 > 1, to permit
analysis of the wave-plasma interaction around the SECH in the framework of the
weakly relativistic approximation. Starting from the general expression for the
dielectric tensor and carrying out the corresponding momentum space integration
within this approximation, we can express the tensor components in terms of the
dielectric function Fq(n) [4]. In a non-drifting isotropic Maxwellian plasma this
function reduces to the relativistic (Shkarofsky) plasma dispersion function [5]. The
dielectric tensor components e,j are then expanded in powers of the electron Larmor
radius retaining all terms up to the order /i,; 2 . Since we are considering the SECH
wave-plasma interaction at downshifted frequencies, the complete contribution of the
fundamental EC harmonic is included in e^.
The dispersion equation governing electromagnetic waves in a plasma confined
by a magnetic field whose direction is perpendicular to that of the density and temperature
gradients is given elsewhere [4]. Here this equation is treated as an expression
for the functional dependence of the complex perpendicular component of the wave
refractive index N± upon the following parameters: Y = coc/co, X/Y 2 =
(cdp/o)c) 2 , c/v,, c/vs, u/vs and Nj. The parallel component of the wave refractive
index is assumed to be real and determined by the direction of the wave vector of
the incident electromagnetic waves at the plasma-vacuum interface, Ny = cos 6,. In
order to examine the wave propagation in the equatorial plane of toroidal discharges,
the magnetic field variation is represented by B(x) = B(0)eV(l + (x/A)), where
x = rcos 0/a, = 0 or 0 = ir, a is the plasma radius and A is the aspect ratio. The
plasma equilibrium is represented by a parabolic electron density profile and a
(1 - x 2 ) 3 ' 2 profile for the bulk and tail electron temperatures, and the drift velocity.
3. EXTRAORDINARY MODE
Before discussing the absorption properties of the X-mode at downshifted frequencies,
we recall that the X-mode propagates in the plasma under the condition that
the electron density is smaller than the right hand cut-off density, i.e.
ajp(x)/co 2 < (1 - Nf)(l - «c(x)/w). So the largest allowable density decreases
with increasing ratio of the central EC frequency and the wave frequency, COC(0)/OJ.
From this, one can conclude that this scheme is ineffective in heating high density
plasmas. However, as we shall see later, in the presence of the superthermal tail the
wave-plasma interaction in the low frequency wing of the thermal profile is sufficiently
strong to damp the X-mode completely, even when the cut-off is present in
the low field side of the plasma column.