Alpha particle effects on the internal kink and fishbone modes

The effects of alpha particles on the internal kink and fishbone modes are studied analytically. The nonadiabatic contribution from untrapped alpha particles is negligible. Finite inverse aspect ratio, plasma β, and plasma shaping effects can significantly enhance the trapped particle drift reversal domain in the pitch angle space and reduce the bounce-averaged magnetic drift frequency. The decrease of the drift magnitude and drift reversal effects on the ideal kink mode is small, but the β_α threshold for the fishbone mode can be much lower than previously predicted [B. Coppi, S. Migliuolo, F. Pegoraro, and F. Porcelli, Phys. Fluids B 2, 927 (1990)]. Moreover, the fishbone mode could be excited by alpha particles, even when the plasma is stable in the ideal magnetohydrodynamic (MHD) limit. In addition, the ion diamagnetic drift frequency (finite ion Larmor radius effect) has a strong destabilizing effect on the fishbone mode when it is comparable with the trapped alpha-averaged processional drift frequency, even though it stabilizes the plasma in the ideal MHD limit.