1 - Nuclear Sciences and Applications - IAEA

616 BATCHELOR et al.
to match asymptotically the geometrical optics modes. Using ( + ,— ,||)
representation, and eliminating E- within Maxwell equations, we obtain
(D 2 + 1) E+ + (z? 2 + 1 + i^) ] e»+E+ = 0
where £> = d/d£, e±± = e^ — njj , and e c is the cold plasma dielectric
tensor at resonance. The operator e++ is obtained from the Vlasov
equation for each specific problem. We study two distinct problems of
practical interest: (i) minority fundamental resonance, and (ii) second
harmonic resonance. In the first case, we obtain
where
\ /^^lexp (A) , , _ ft , Xi = (SB
2 J \u\ \l u l ° an \
and Go is the normalized equilibrium distribution function. There is no
slow mode within the resonance layer in this case. The transmission
coefficient is the same as for geometrical optics and there is no reflection
for waves incident from the high-field side. In the case of low-field incidence
the absorption is drastically increased by up to 50%.
For the second problem we obtain a fourth-order integro-differential
equation associated with the existence of both fast and slow modes within
the boundary layer. We have
e++E+ = -i -D I d(,'F ^-^ ^ exp [in(£ - £')] &&+(?)
We prove that reciprocity relations hold for a pair of related systems,
one with +BP, the other with — Bp. By solving the fourth-order integrodifferential
equation numerically we find that conversion to the slow mode
is greatly reduced, and correspondingly energy absorption increases. Figure
2 compares the local and nonlocal absorption for a = 1, for the cases
of high and low-field side incidence. For high-field incidence, absorption is
substantially increased. Due to a higher rate of wave reflection for small
values of parallel refractive index, the increase in the low-field side absorption
is smaller. In conclusion, when the poloidal field is not tangent
to B = constant surfaces, there is increased absorption of wave energy by
plasma near the resonance layers, an effect also seen in related works by
Smithe et aL [3].