Simple and rigorous solution for the nonlinear tearing mode

Abstract The nonlinear evolution and saturation of tearing modes is described in the small magnetic island width limit by a new approach which is rigorous, simple, and accurate. Within the usual asymptotic matching technique, a new scaling ansatz avoids the use of the traditional j=j(ψ) approach, and reduces the nonlinear problem to an elementary linear one. The newly calculated island width is in excellent agreement with available numerical simulations. Tearing mode saturation is interpreted as produced by a local dynamo providing the current sheet required by global magnetic features.