Hybrid simulations of reversed shear Alfvén eigenmodes and related nonlinear resonance with fast ions in a tokamak plasma. (3rd September 2020) - Yang, Y.R.; Chen, W.; Ye, M.Y.; Yuan, J.B.; Xu, M.
Abstract: Reversed shear Alfvén eigenmodes (RSAEs) are often observed in HL-2A reversed shear discharges with q m i n   ∼   1 . The modes are highly localized near q m i n, and their frequencies sweep downward or upward as q m i n 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 ( q m i n / n ) first and then upward ( q m i n < m / n ) as q m i n 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 q m i n − m / n, 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 q m i n = 1 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 ( n ω ϕ − ω ) / ω θ   =   2.5 instead of the linear resonance condition ( n ω ϕ − ω ) / ω θ   =   2, 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).