Simple analysis of the nonlinear saturation of the tearing mode

A simple nonlinear treatment of the reduced magnetohydrodynamics equations, that describes the saturation of small width magnetic island, is presented. This procedure is an extension of Rutherford’s theory. It is found that the tearing mode saturates at a finite amplitude, ws, which is proportional to the linear stability parameter, Δ′. The correct value of the proportionality coefficient between ws and Δ′ is obtained in this paper, in agreement with numerical simulations.