The effects of alpha particles on the internal kink and fishbone modes
are studied analytically. The nonadiabatic contribution from untrappe
d alpha particles is negligible. Finite inverse aspect ratio, plasma b
eta, 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 m
agnitude and drift reversal effects on the ideal kink mode is small, b
ut the beta(alpha) threshold for the fishbone mode can be much lower t
han previously predicted [B. Coppi, S. Migliuolo, F. Pegoraro, and F.
Porcelli, Phys. Fluids B 2, 927 (1990)]. Moreover, the fishbone mode c
ould be excited by alpha particles, even when the plasma is stable in
the ideal magnetohydrodynamic (MHD) limit. In addition, the ion diamag
netic drift frequency (finite ion Larmor radius effect) has a strong d
estabilizing effect on the fishbone mode when it is comparable with th
e trapped alpha-averaged precessional drift frequency, even though it
stabilizes the plasma in the ideal MHD limit.