Nonlinear magnetohydrodynamic (MHD) effects on Alfvén eigenmode evolution were investigated via hybrid simulations of an MHD fluid interacting with energetic particles. The investigation focused on the evolution of an n = 4 toroidal Alfvén eigenmode (TAE) which is destabilized by energetic particles in a tokamak. In addition to fully nonlinear code, a linear-MHD code was used for comparison. The only nonlinearity in that linear code is from the energetic-particle dynamics. No significant difference was found in the results of the two codes for low saturation levels, δB/B ∼ 10−3. In contrast, when the TAE saturation level predicted by the linear code is δB/B ∼ 10−2, the saturation amplitude in the fully nonlinear simulation was reduced by a factor of 2 due to the generation of zonal (n = 0) and higher-n (n ⩾ 8) modes. This reduction is attributed to the increased dissipation arising from the nonlinearly generated modes. The fully nonlinear simulations also show that geodesic acoustic mode is excited by the MHD nonlinearity after the TAE mode saturation.
Nonlinear saturation of reverse shear Alfvén eigenmodes induced by kinetic electrons