Nonlinear Evolution of Tearing Modes with Resistivity and Hyper-Resistivity

The nonlinear resistive tearing modes with hyper-resistivity has been analytically investigated. In contrast to the flux average method used by previous works, in the present work the quasilinear method has been extended to obtain the time evolution equation for nonlinear tearing modes. This equation can describe the general evolution of nonlinear tearing modes with both plasma resistivity and hyper-resistivity effects, especially the transition between these two situations. It is difficult to obtain its analytical solution directly. One special solution has been obtained. It is found that the magnetic flux grows with time to the one third power. Some discussions about two limiting cases for resistivity or hyper-resistivity dominant will be presented.