NONLINEAR COUPLING OF DISPARATE HELICAL TEARING MODES

An analytical model has been developed for the nonlinear interaction o f linear tearing modes with different helicities in cylindrical geomet ry. The linear tearing modes are nonlinearly coupled together by the v XB induced electrical field as soon as they exist. According to the st andard scaling of linear tearing mode, the nonlinear coupling is mainl y through the convective term in evolution equation of poloidal magnet ic flux perturbation at resistive layer. The set of nonlinear equation s, therefore, can be derived for the time evolution of the flux pertur bations of nonlinear coupling modes by asymptotic matching to eliminat e the space variable. The nonlinear coupling effect depends on the rel ative amplitudes of the tearing modes and the nonlinear coupling param eters {alpha(mn)}, which are determined by the relative slopes of equi librium current density in singular layers. The marginally stable m/n mode could be destabilized by the nonlinear coupling with the other mo des only if alpha(mn) < 0. The flux perturbations include both the exp onential growth and algebraical evolution. The latter is caused by the nonlinear coupling and becomes more important even dominant when the flux perturbations increase.