Hybrid magnetohydrodynamic-particle simulation of linear and nonlinear evolution of Alfvén modes in tokamaks

Abstract

Linear and nonlinear properties of moderate-toroidal-number (n) shear-Alfvén modes in tokamaks are investigated by using a hybrid MHD-particle simulation code, which solves the coupled set of MHD (magnetohydrodynamic) equations for the electromagnetic fields and gyrocenter Vlasov equation for a population of energetic ions. The existence of unstable toroidal Alfvén eigenmodes (TAE’s) and their kinetic counterpart is shown for low values of the energetic-ion pressure gradient. Above a certain threshold value, the energetic particle continuum mode (EPM) is destabilized, with growth rate fast increasing with increasing energetic-particle pressure gradient. The threshold shows an inverse dependence on n. High-n EPM’s could then be unstable in realistic plasma conditions. Neglecting MHD nonlinearities, for the sake of simplicity, it is shown that nonlinear TAE saturation appears to be due to the trapping of resonant energetic ions in the potential well of the wave. Saturation of the EPM occurs instead because of a macroscopic outward displacement of the energetic-ion population, with potentially dramatic consequences on α-particle confinement; such conclusions are not modified by the inclusion of MHD nonlinearities.