High-beta tokamaks surrounded by force-free fields

The sharp-boundary model of ideal magnetohydrodynamics is presented in a form readily applicable to axisymmetric, high-β plasmas of arbitrary cross section. The usual vacuum region outside the plasma is replaced here by a layer of force-free currents, and the influence of force-free currents and cross-sectional shaping on the critical β is studied. Specific results are given for circular, elliptical, and racetrack-like cross sections. A new parameter q* is introduced in place of the Mercier q, and it is shown that q*≈1 is a reasonable estimate of the toroidal current limitation due to external kink modes in high-β plasmas with noncircular cross sections.