Ion Viscosity Stabilization of Tokamak Resistive Internal Kink Modes

For most of small and medium sized Tokamaks, the unstable mode responsible for the sawtooth crash is the resistive internal kink mode. However, the plasma parameters can be in the ion kinetic regime. In this paper, we consider the dependence of the mode growth rate on the magnetic shear which is changeable during a sawtooth cycle and find that the ion viscosity effect can completely stabilize the mode only for shear smaller than some critical value, corresponding to the stable phase of the sawtooth evolution. This is consistent with one of the salient phenomena of the sawtooth, the sudden onset.