Reversed shear Alfvén eigenmodes (RSAEs) are often observed in HL-2A reversed shear discharges with . The modes are highly localized near , and their frequencies sweep downward or upward as decreases. In this work, kinetic-magnetohydrodynamics (MHD) hybrid simulations based on experimental parameters in the HL-2A tokamak are carried out to investigate the linear stability and nonlinear dynamics of RSAEs. Linear simulations show that the frequencies of RSAEs sweep downward () first and then upward () as decreases, which is rarely seen in previous simulation work. The frequency and mode structure of the instabilities are consistent with experimental observations. For the same , the critical value of the fast ion beta required to destabilize down-sweeping RSAEs is higher than that of up-sweeping RSAEs. Both the up-sweeping and down-sweeping RSAEs are mainly driven by co-passing fast ions. The nonlinear simulation results of n = 3 and show that the frequency of the mode chirps up and down with corresponding hole-clump structures of energy perturbation appearing in the phase space. In the nonlinear phase, the dominant resonance condition becomes instead of the linear resonance condition , which can be the result of a nonlinear interaction between wave and particles. This work provides a new proof for the theory of nonlinear wave-particle resonance proposed recently (Chen and Zonca 2019 Plasma Sci. Technol.21 125101).
Hybrid simulation of fishbone instabilities in the EAST tokamak