Weak and reversed magnetic shear effects on internal kink and fishbone modes

Advanced tokamak scenarios often feature weak or reversed magnetic shear configurations. In this study, the hybrid kinetic-MHD model implemented in the NIMROD code is used to investigate the effects of reversed magnetic shear on internal kink and fishbone mode in a circular shaped limiter tokamak. In the absence of energetic particles (EPs), the mode growth rate initially increases and then decreases as the magnetic shear changes from positive to negative, indicating stabilizing effects of the reversed magnetic shear on the internal kink mode. In the presence of EPs, when the reversed magnetic shear region is sufficiently narrow, the transition from internal kink/fishbone modes to double kink/fishbone modes takes place, and the stabilizing effects of the reversed magnetic shear can significantly dominate the destabilization of EPs. For non-resonant modes, the EP beta fraction $\beta_f$ for excitation increases with $q_{min}$, concurrent with progressively lower growth rates in non-resonant fishbone modes. When the equilibrium profile has an internal transport barrier (ITB), broader ITB widths suppress internal kink modes more effectively, whereas steeper temperature gradients strengthen EP stabilization.