Hybrid simulations of fishbones with high order harmonics in EAST Tokamak

This is the authors' abstract. We don't add key points for this paper.

The linear stability and nonlinear dynamics of fishbones with high order harmonics have been investigated by the global kinetic-magnetohydrodynamic (MHD) code M3D-K in the Experimental Advanced Superconducting Tokamak (EAST). Based on EAST discharge parameters with neutral beam injection (NBI) heating, linear simulations show that the modes with different toroidal mode numbers are primarily driven by trapped energetic particles (EPs) through toroidal precession resonance. The n = 1 mode is the typical fishbone, while there exists a transition for n = 2 mode from fishbone-like mode to energetic particle mode (EPM) when the EP pressure exceeds a critical value. For the n = 3 mode, the mode frequency remains almost unchanged with different EP pressure. Nonlinear simulations show that with weak EP drive, the m / n = 2 / 2 mode is driven by the MHD nonlinear coupling of the fundamental m / n = 1 / 1 mode. In this regime, the frequency of the m / n = 2 / 2 harmonic is twice that of the m / n = 1 / 1 mode, with both modes exhibiting downward frequency chirping. With strong EP drive, beta-induced Alfvén eigenmodes (BAEs) with higher mode frequencies emerge for both m / n = 1 / 1 and m / n = 2 / 2 components, and the m / n = 3 / 3 component is driven unstable with frequency chirping up. These simulation results highlight that nonlinear MHD coupling and fast ion redistribution are critical for understanding the dynamics of fishbones with high order harmonics.