Nonlinear coupling of disparate helical tearing modes

Abstract

An analytical model has been developed for the nonlinear interaction of linear tearing modes with different helicities in cylindrical geometry. The linear tearing modes are nonlinearly coupled together by the v×B induced electrical field as soon as they exist. According to the standard scaling of linear tearing mode, the nonlinear coupling is mainly through the convective term in evolution equation of poloidal magnetic flux perturbation at resistive layer. The set of nonlinear equations, therefore, can be derived for the time evolution of the flux perturbations of nonlinear coupling modes by asymptotic matching to eliminate the space variable. The nonlinear coupling effect depends on the relative amplitudes of the tearing modes and the nonlinear coupling parameters {αmn}, which are determined by the relative slopes of equilibrium current density in singular layers. The marginally stable m/n mode could be destabilized by the nonlinear coupling with the other modes only if αmn<0. The flux perturbations include both the exponential growth and algebraical evolution. The latter is caused by the nonlinear coupling and becomes more important even dominant when the flux perturbations increase.