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 β p and elliptical, triangular and rectangular plasma crosssections, 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.