Nonlinear evolution of neoclassical double tearing mode

A theory for the nonlinear neoclassical double tearing mode is presented. The equations governing the nonlinear evolution of the mode are obtained for both the locked islands and the islands with different rotation frequencies. The coupling of the two islands plays a destabilizing role in the island growth, especially when the phase between the two islands is locked. The perturbed bootstrap current has a strong stabilizing effect on the inner island but a weak destabilizing effect on the outer island. The inner island width is decreased when there is a relative rotation between the two islands, while the outer island is less affected by plasma rotation. The outer island width is found be an important parameter in determining the inner island width and the stability of the nonmonotonic $q$ -profile.