Critical β of a D-shaped toroidal plasma with sharp boundary

Under the cap-cyclide coordinate system, the marginal stability of a sharp boundary toroidal plasma whose cross section is D shaped is examined using the energy principle. The analytical results are valid for arbitrary β, arbitrary aspect ratio, and arbitrary elongation of the plasma. There exists a maximum elongation for a given aspect ratio. The critical beta βc is computed for several aspect ratios and elongations. For given aspect ratio, βc increases as long as the elongation increases.