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 $\text{β\hspace{0.17em}>\hspace{0.17em}0.21\hspace{0.17em}ε}$ , where $\epsilon$ is the inverse aspect ratio, the model is unstable to the $\text{n\hspace{0.17em}=\hspace{0.17em}1}$ 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 $\text{n\hspace{0.17em}=\hspace{0.17em}1}$ marginal stability line $\text{m\hspace{0.17em}=\hspace{0.17em}2}$ ($m$ is the mode number the short way) is found to be the dominant harmonic.