Nonlinear dynamics of the tearing mode for any current gradient

Within the traditional frame of reduced MHD, a new systematic perturbation expansion provides the equation ruling the nonlinear growth and saturation of the tearing mode for any current gradient. The small parameter is the magnetic island width w. The evolution equation depends on w through a term wln(w/w0) where w0 is a nonlinear scale length which was absent in previous works. The technique is applicable to the case of an external forcing. The solution for a static forcing is computed explicitly and it exhibits three regimes in the dynamics.