The barely trapped suprathermal electrons can destabilize the internal kink mode when their density gradient is positive within the rational surface and the beta value of the suprathermal electrons exceeds a threshold value. With the assumption of two different models of energy distribution of the suprathermal electrons, the threshold beta value of the barely trapped suprathermal electrons, the real frequency, and the growth rate of the internal kink mode are found in this paper. The results are in reasonable agreement with the recent experimental observations on DIII-D tokamak [K. L. Wong, M. S. Chu, T. C. Luce et al., Phys. Rev. Lett. 85, 996 (2000)].

The barely trapped energetic electrons produced by the electron cyclotron resonance heating can interact efficiently with the internal kink mode and stabilize sawtooth oscillations. The effects of the spatial distribution and the pitch angle distribution of the energetic electrons are considered. The most effective stabilization is obtained when the peak of the spatial distribution locates on the q = 1 rational surface. This machanism gives a reasonable explanation of the difference between the high-field-side heating and the low-field-side heating on tokamaks.

The high frequency fishbone instability observed in experiments with near perpendicular neutral beam injection is interpreted as the ideal internal kink mode destabilized by circulating energetic ions. The mode frequency is close to the transit frequency of circulating ions. The beta value of the circulating ions is required to peak on the magnetic axis and the average value within the q=1 magnetic surface must exceed a critical value for the mode to grow up.