The effect of energetic-ions on magnetohydrodynamic instabilities is pivotal in the basic physics that will be vital in burning plasma experiments. Recently, it has been found in the HL-2A tokamak that an m/n = 2/1 unstable tearing mode (TM) interacts with energetic-ions, resulting in amplitude-bursting and frequency-chirping fishbone-like activities, and it is numerically identified that the co-passing energetic-ions play a dominant role in the wave-particle resonances (Chen et al 2019 Nucl. Fusion59 096037). Motivated by fully and deeply understanding such a resonant interaction between energetic-ions and TM, a more detailed study of global nonlinear hybrid kinetic-MHD simulations with M3D-K code is performed in the present work. The kinetic effect of co-passing energetic-ions from non-adiabatic response is interestingly found to be strongly destabilizing, while the net effect with both adiabatic and non-adiabatic contributions is weakly destabilizing. For passing energetic-ions, the m/n = 2/1 TM is found to be most unstable in the case of , where q0 is the central safety factor. Effects of energetic-ion beta and pinch angle determining different energetic-ion fractions on the resonance features, such as the growth rate, frequency chirping and mode structure, are discussed in detail. The relevant simulation results are consistent with the observations on HL-2A. Furthermore, the effects of both counter-passing and trapped energetic-ions on the TM have also been explored, but the corresponding resonance phase space is found to be very narrow in the plane. In addition, the redistribution and loss induced by the resonant interaction between TM and energetic-ions are analyzed in multiple-mode simulations. Significant redistribution and loss are clearly observed, and the scaling of energetic-ion loss fraction with the fluctuation amplitude is found to be , indicating that the loss is convective. These discoveries are conducive to understanding the mechanisms of TM-induced energetic-ion loss through the resonant interaction.
Manifestations of the geodesic acoustic mode driven by energetic ions in tokamaks