Nonlinear interaction of fast particles with Alfvén waves in toroidal plasmas

Abstract

A numerical algorithm to study the nonlinear, resonant interaction of fast particles with Alfvén waves in tokamak geometry has been developed. When the instability is sufficiently weak, it is known that the wave-particle trapping nonlinearity will lead to mode saturation before wave–wave nonlinearities are appreciable. The spectrum of linear modes can thus be calculated using a magnetohydrodynamic normal-mode code, then nonlinearly evolved in time in an efficient way according to a two-timescale Lagrangian dynamical wave model. The fast particle kinetic equation, including the effect of orbit nonlinearity arising from the mode perturbation, is simultaneously solved for the deviation, δf=f−f0, from an initial analytic distribution f0. High statistical resolution allows linear growth rates, frequency shifts, resonance broadening effects, and nonlinear saturation to be calculated quickly and precisely. The results have been applied to an International Thermonuclear Experimental Reactor [ITER EDA Doc. Series No. 7 (International Atomic Energy Agency, Vienna, 1996), p. V-32] instability scenario. Results show that weakly damped core-localized modes alone cause negligible alpha transport in these reactor-like plasmas—even with growth rates one order of magnitude higher than expected values. However, the possibility of significant transport in reactor-type plasmas due to weakly unstable global modes remains an open question.