Mode Conversion of the Fast Magnetosonic Wave in a Deuterium-Hydrogen Tokamak Plasma

Abstract

Mode conversion from the fast magnetosonic wave to a slow wave near the two-ion hybrid resonance is shown to explain recent experimental fast-wave damping results. A model for tunneling and mode conversion of the fast wave in the two-ion resonance zone incorporating k^ and plasma-density and magnetic-field profiles is used to explain the observations. The strong dependence of the absorption on & n and the species concentration which is obtained has important consequences for major plasma-heating programs which are planned for tokamaks.Recent experiments on the TFR, 1 ' 2 ATC, 3 TMOl, 4 and T-4 5 tokamaks have measured the damping of the fast wave as the resonance layer for the second ion-cyclotron harmonic ((o = 2co cd ) is scanned across the plasma cross section. When the second-harmonic resonance for deuterium is in the central plasma region, a strong absorption of the wave is noted. Wave absorption rapidly decreases outside two locations for the cyclotron harmonic resonance zone which are not symmetric with respect to the magnetic axis. A preliminary analysis 2 of the TFR experiment showed that the asymmetry could be explained by the presence of a two-ion hybrid resonance within the plasma due to a hydrogen-impurity component in the deuterium plasma. The experiments on the TMOl 4 and T-4 5 tokamaks found that the presence of even a small amount of hydrogen impurity can greatly increase the wave-absorption process and lower the eigenmode Q. We establish here that the damping rate of the fast wave can be attributed to a mode-conversion process in the two-ion hybridresonance layer which is very sensitive to the k u value of the eigenmode. The result of a detailed analysis of the mode-conversion problem is in semiquantitative agreement with the observations.Local dispersion relation, mode conversion, and its associated damping decrement.-We start with the wave equationwhere K is the hot-plasma dielectric tensor 6 derived from the coupled kinetic Vlasov-Maxwell equations. We further note that for the fast magnetosonic wave the wavelength transverse to the magnetic field is much larger than the ion gyroradius so that A / =fe JL 2 p i 2 /2«l. We then expand the Bessel functions which occur in each element of the 3x3 dielectric tensor to second order in their argument Xj. The resulting tensor is incor-porated in the dispersion relation obtained from the wave equation. The resulting matrix is expanded and terms are collected to second order in \j. We find from numerical computations that, at spatial locations outside the ion-cyclotron-harmonic resonances (lci>-tt<o cj (R)l»fe||#j), the dispersion relation is very well approximated by the following one where only the dominant terms are retained:where a = (cM z S/K e^Kxx \ &=», 2 -S, c = (o/cYfa?-LJ1fi X ?-R) 9 ^« = -KeAn^) a^' («AiiO, x [(to 2 -a> ci 2 )-* + (co 2 -4a> ci 2 )-*].S, R, and L are defined as in StiLx, 6 ti\\ is the parallel index of refraction and Z f is the derivative of the plasma dispersion function. We assume the \/R variation in toroidal field and a p...

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