A dynamo effect of resistive tearing modes on current profile flattening

Abstract

The dynamo effect of tearing modes is derived using the resistive magnetohydrodynamics equations. The dynamo effect is divided into two components, parallel and perpendicular to the magnetic field. First, the force-free plasma is considered. It is found that the parallel dynamo effect drives opposite current densities on either sides of the rational surface (k·B=0), completely flattening the λ=j·B/|B|2 profile near the rational surface. This may be a possible explanation for the Taylor relaxation mechanism. In contrast, farther from the rational surface, the parallel dynamo effect is much smaller, and the nonlinear dynamo form approximates the quasilinear form. Second, a pressure gradient is included. It is found that a finite λ gradient can exist after modification by the parallel dynamo effect. The perpendicular dynamo effect is found to eliminate the pressure gradient near the rational surface. Our results provide a further basis for the assumption that the current density is flat in the magnetic island for tearing mode theory.