Theory of pressure-induced islands and self-healing in three-dimensional toroidal magnetohydrodynamic equilibria

The role of singular currents in three-dimensional toroidal equilibria and their resolution by magnetic island formation is discussed from both analytical and computational points of view. Earlier analytical results are extended to include, small vacuum islands, which may, in general, have different phases with respect to pressure-induced islands. In currentless stellarators, the formation of islands is shown to depend on the resistive parameter D_R, as well as the integrated effect of global Pfirsch-Schlüter currents. It is demonstrated that the pressure-induced "self-healing" effect, recently discovered, computationally, is also, predicted by analytical theory.