Numerical investigation into the peripheral energetic-particle-driven MHD modes in Heliotron J with free boundary hybrid simulation

The interaction between energetic particles (EPs) and EP-driven magnetohydrodynamic (MHD) instabilities in Heliotron J, a low-shear helical axis stellarator/heliotron, is investigated with MEGA, a hybrid MHD-EP simulation code with the free boundary condition, on the last closed flux surface. The n/m = 1/2 energetic particle mode (EPM) and the n/m = 2/4 global Alfvén eigenmode (GAE) in the peripheral plasma region of Heliotron J are successfully modeled with the free boundary condition. The free boundary condition affects the EP driving rate of the n/m = 1/2 EPM and the n/m = 2/4 GAE through the changes in the mode spatial profile. Under the fixed boundary condition, the linear growth rate of the EP-driven MHD mode with low mode numbers is underestimated. The interaction between EP and these experimentally-observed modes is kinetically analyzed. It is found that the strongest EP–shear Alfvén wave interactions arise from the toroidicity-induced resonances in the high-velocity region. These high-velocity EPs can efficiently interact with the peripheral EP-driven mode. The additional toroidally-asymmetric resonances are localized in the low-velocity region; therefore, their effects are weak for the bump-on-tail EP velocity distribution function