Linear hybrid simulations of low-frequency fishbone instability driven by energetic passing particles in tokamak plasmas

A linear simulation study of energetic passing particle-driven low-frequency fishbone instability in tokamak plasmas has been carried out using the global kinetic-MHD (magnetohydrodynamics) hybrid code M3D-K. This work is focused on the interaction of energetic passing beam ions and n=1 mode with a monotonic safety factor q profile and $q_0<1.$ Specifically, the stability and mode frequency as well as mode structure of the n=1 mode are calculated for scans of parameter values of beam ion beta, beam ion injection energy, beam ion orbit width, beam ion beta profile, as well as background plasma beta. The excited modes are identified as a low-frequency fishbone with the corresponding resonance of ${\omega }_{\varphi }+{\omega }_{\theta }=\omega ,$ where ${\omega }_{\varphi }$ is the beam ion toroidal transit frequency and ${\omega }_{\theta }$ is the beam ion poloidal transit frequency. The simulated mode frequency is approximately proportional to the beam ion injection energy and beam ion orbit width. The mode structure is similar to that of internal kink mode. These simulation results are similar to the analytic theory of Yu et al.