Hybrid simulation of q = 1 high-order harmonics driven by passing energetic particles in tokamak plasmas

High-order harmonics q(ψ_s) = 1 energetic particle modes (EPMs) have been observed in toroidal plasmas experiments with neutral beam injection. To investigate these phenomena, linear properties and nonlinear dynamics of these EPMs driven by passing energetic particles (EPs) are studied via the global hybrid kinetic-magnetohydrodynamic code M3D-K. Simulation results demonstrate that passing EPs' effects on high mode-number harmonics (q(ψ_s) = m/n = 2/2, 3/3, 4/4) instability are more obvious than the q(ψ_s) = 1/1 mode, especially when q-profile is sufficiently flat in the core region. Furthermore, the effects of the pitch angle Λ₀ and beam ion pressure P_hot/P_total on the features of high n components are also analyzed specifically. It is found that there exists only one resonant condition for these EPMs. In the nonlinear phase, these high mode-number harmonics can induce significant energetic ions redistribution and chirping up phenomena, which differs from the classical fishbone excited by passing EPs. These discoveries are conducive to better apprehend the underlying physical mechanisms of the high-order harmonics driven by passing EPs.