STABILITY OF STRAIGHT TOKAMAK EQUILIBRIA WITHOUT WALL STABILIZATION

A specific straight tokamak equilibrium surrounded by vacuum and witho ut a conducting wall is proved to be stable to all ideal magnetohydrod ynamic (MHD) modes by analytically evaluating linear stability. The an alysis starts with a circular-cylindrically symmetric equilibrium whic h has a piecewise constant current profile. The effect of corruption, which is of great importance to the stability of axisymmetric modes, i s taken into account by using perturbation methods. Stability of axisy mmetric modes is proved by solving the eigenvalue problem up to second order in the corrugation amplitude. Whereas elliptical corruption (N= 2) leads to instability for arbitrary current density, an equilibrium with N greater-than-or-equal-to 3 May be stabilized to axisymmetric mo des by current reversal. To treat nonaxisymmetric global modes, the po tential energy is evaluated using tokamak scaling. A sufficient stabil ity criterion is derived according to which the equilibrium is stable to nonaxisymmetric modes if the current density in the outer plasma ar ea is reversed and in the center sufficiently peaked, and if the safet y factor q at the magnetic axis is greater than unity, increasing mono tonically toward the plasma edge.