Internal kink stability of large aspect ratio high-β tokamaks

Theoretically, high-β (β∼ 1 ) tokamaks offer a large fusion power efficiency advantage over low-β devices. However, if high-β tokamaks are inherently unstable then such devices will never he realised. In particular, kink modes are thought to be the most serious obstacle to high-β operations. High-β tokamaks are characterized by a very large Shafranov shift with a thin "boundary layer" on the outboard side of the device and a large "core" region of vertical flux surfaces comprising most of the central volume. In this paper, the energy principle is used to compute the magnetohydrodynamic internal kink stability of such devices in the large aspect ratio limit with a low toroidal mode number. A class of internal kink mode similar to the usual low-β kink is present: the stability against these modes is computed. A set of parameters describing a kink stable high-β equilibrium is given. Stability is shown to be dependent on the shape of the plasma boundary.