Stability of exact toroidal MHD-equilibrium with non-circular cross-section

Abstract

In recent experiments on toroidal plasma confinement, the aspect ratio is relatively small so that the usual expansions of equilibrium solutions in powers of the inverse aspect ratio are not applicable. A class of exact solutions has recently been found by the authors. A very simple particular solution has a bell-shaped current distribution and seems useful for the descriptton of equilibria of the tokamak or pinch type. The stability of this particular solution is investigated against localized modes by applying Mercier's criterion in the neighborhood of the magnetic axis. It is shown that this solution is unstable for a plasma with vertically elongated cross-section, as, e.g., the belt pinch. It is then shown that it is possible to construct a stable solution by an appropriate superposition of two exact solutions. (MOW)