Nonlinear growth of the double tearing mode

Abstract

A theory for the growth of the double tearing mode in the early nonlinear stage is presented. The equations governing the nonlinear evolution of double tearing modes are formulated and are solved in different parameter regimes. When the phase difference between the two islands is π, the coupling of the two islands plays a destabilizing role. The island growth is of the form w∼t in the early nonlinear stage. The instability condition for the nonlinear double tearing mode is found, and is the same as that for the linear double tearing mode. When current profile is flattened near the two rational surfaces, the coupling plays the dominant role in determining the nonlinear growth.