Hybrid simulations of beta-induced Alfvén eigenmode with reversed safety factor profile

摘要

Abstract Based on the experimental parameters in the HL-2A tokamak, hybrid simulations have been carried out to investigate the linear stability and nonlinear dynamics of the beta-induced Alfvén eigenmode (BAE). It is found that the (m/n = 3/2) BAE is excited by co-passing energetic ions with q min = 1.5 in linear simulation, and the mode frequency is consistent with the experimental measurement. The simulation results show that the energetic ions β h, the injection velocity v 0, and orbit width parameter ρ h of energetic ions are important parameters determining the drive of BAE. Furthermore, the effect of q min (with the fixed shape of the q profile) is studied, and it is found that when q min ⩽ 1.5, the excited modes are BAEs, which are located near q = 1.5 rational surfaces; when q min > 1.5, the excited modes are similar to the reversed-shear Alfvén eigenmodes, which are mainly localized around q = q min surfaces. Nonlinear simulation results show that the nonlinear dynamics of BAE are sensitive to the EP drive. For the strongly driven case, firstly, redistribution and transport of energetic ions are trigged by 3/2 BAE, which raised the radial gradient of the distibution function of energetic ions near the q = 2 rational surface, and then an energetic particle mode (EPM) (m/n = 4/2) is driven in the nonlinear phase. Finally, these two instabilities triggered a significant redistribution of energetic ions, which results in the twice-repeated and mostlydownward frequency chirping of 3/2 BAE. For the weakly driven case, there are no 4/2 EPM being driven nor twice-repeated chirping in the nonlinear phase, since the radial gradient near q = 2 rational surface is small and almost unchanged.