Hybrid magnetohydrodynamic-gyrokinetic simulation of toroidal Alfven modes

Resonant energetic particles play a major role in determining the stability of toroidal Alfven eigemnodes (TAE’s) by yielding the well-known driving mechanism for the instability and by producing an effective dissipation, which removes the singular character of local oscillations of the shear-Al&n continuum and gives discrete kinetic Alfven waves (KAW’s). Toroidal coupling of two counterpropagating KAW’s generates the kinetic analog of the TAE, the KTAE (kinetic TAE). The nonperturbative character of this phenomenon and of the coupling between TAE and KAW’s, and the relevance of finite drift-orbit effects limit the effectiveness of the analytical approach to asymptotic regimes, which are difficult to compare with realistic situations. A three-dimensional hybrid fluid-particle initial-value code for the numerical simulation of the linear and nonlinear evolution of toroidal modes of the Alfvdn branch has been developed. It is shown that for typical parameters the KTAE is, indeed, more unstable than the TAE.