Axisymmetric MHD stability of sharp-boundary Tokamaks

For a sharp-boundary, constant-pressure plasma model of axisymmetric equilibria the MHD-stability problem of axisymmetric perturbations is solved by analytic reduction to a one-dimensional problem on the boundary and subsequent numerical treatment, using the energy principle. The stability boundaries are determined for arbitrary aspect ratio, arbitrary beta-p and elliptical, triangular and rectangular plasma cross-sections, wall stabilization not being taken into account. It is found that axisymmetric stability strongly depends on the plasma shape and is almost independent of the safety factor q.