Low-frequency fishbone instability driven by passing fast ions via wave-particle resonance is studied within the framework of energetic particle mode (EPM), where and are toroidal transit frequency and poloidal transit frequency of passing fast ions respectively. The effects of finite orbit width of energetic particles are responsible for the low-frequency fishbone of EPM type. It is found that magnetic shear at the q = 1 radius plays an important role in the instability whereas the effect of background plasma beta is weak. In particular, for the case of co-injection of beam ions, there exists a critical magnetic shear below which the beam ion beta threshold for EPM excitation is very small. For moderate or higher magnetic shear, the beam ion beta threshold is much higher, on order of a few percent. These results are consistent with the observation of the low-frequency fishbone in the HL-2A tokamak.
Mitigation of MHD induced fast-ion redistribution in MAST and implications for MAST-Upgrade design