Kink instabilities in a high-β tokamak

A toroidal, circular cross section, sharp-boundary model of a high-pressure tokamak with currents confined to the surface, is tested for stability against kink modes. It is shown that for β > 0.21 ε, where ε is the inverse aspect ratio, the model is unstable to the n = 1 kink mode (n is the mode number the long way) for all values of the safety factor above and below the Kruskal-Shafranov limit. Along the n = 1 marginal stability line m = 2 (m is the mode number the short way) is found to be the dominant harmonic.