Kink instabilities in a high-β tokamak with elliptic cross section

A toroidal, elliptic 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 the optimum configuration corresponds to a vertical ellipse in which the ratio of the major to minor axes is 2.2. For this case, the maximum critical $\beta$ for stability against kink modes is $\text{β\hspace{0.17em}=\hspace{0.17em}0.37a/R.}$ For $\text{β\hspace{0.17em}>\hspace{0.17em}0.37a/R}$ the model is unstable for all values of the safety factor above and below the Kruskal‐Shafranov limit.