Perturbative analysis of the tearing mode saturation

Abstract

The saturation of the tearing mode in a plasma column is investigated in the framework of the resistive magnetohydrodynamics approximation. In particular, a perturbative procedure is adopted to evaluate the structure of the magnetic island in three relevant physical conditions, depending on the model for the evolution of the resistivity, which may be affected by the growth of the mode. In cylindrical geometry, which is well suited to describe a large-aspect-ratio, low-beta tokamak plasma, the magnetic island is asymmetric with respect to the magnetic surface where reconnection occurs. New relations for the saturated island width ws as a function of the relevant features of the equilibrium current density profile, i.e., its gradient and curvature at the reconnecting surface, are obtained. Finally, equivalent relations are also derived in the slab limit.