New approach to magnetohydrodynamic stability: II. Sigma-stable diffuse pinch configurations

On the basis of the theory of σ stability, a classification of high-shear σ-stable diffuse pinch configurations is obtained by numerical solution of the Euler equation corresponding to the modified energy principle. Toroidal effects are introduced by putting a lower bound on the magnitude of the poloidal field in order to assure toroidal equilibrium and by deriving and employing the proper generalization of the Kruskal-Shafranov limit for m = 1 unstable configurations. The classification of high-shear σ-stable configurations consists of five different types, viz., tokamak, Bθ-reversed pinch, screw pinch, combined pinch, Bz-reversed pinch. Among the significant new results are: complete stability of some of the tokamak configurations for β up to 4%, a stable high-β (30%) Bθ-reversed pinch configuration that has not been investigated before, a stable diffuse screw pinch with β = 30% when currents are allowed to flow at the wall and with β = 8% with vanishing current at the wall, the possibility of containing diffuse high-β m = 1 stable plasmas without Bz-field reversal or pressure minimum on axis. Here, σ stability refers to times needed for fusion.