A Four-Fluid Model and Analysis of m = 1 Internal Kink Instability

Starting from the four-fluid equation which can simply and effectively describe the motion of trapped particles, we derive the eigenmode equations and the dispersion relation for m=1 internal kink mode with the effects of trapped particles, diamagnetic drifts, finite resistivity and anomalous electron viscosity included. Then, using those results, we find the trapped particles effects have substantial influence on m=1 internal kink mode in the cases with and without high-energy alpha particles in the core plasma.