Nonlinear interaction of tearing modes: A comparison between the tokamak and the reversed field pinch configurations

The multiple helicity nonlinear interaction of resistive tearing modes is compared for the tokamak and reversed field pinch configurations using the magnetohydrodynamic equations. Unlike the case of the tokamak disruption, for which this interaction is destabilizing when islands overlap, the nonlinear coupling of the dominant helicities is shown to be a stabilizing influence in the reversed field pinch. The behavior of the coupled instabilities in the two configurations can be understood as a consequence of the stability properties of the nonlinearly driven modes. In the case of the tokamak disruption, quasilinear effects linearly destabilize the dominant driven mode, which then feeds energy to the driving mode. For the reversed field pinch the driven modes remain stable, acting as a brake on the growth of the dominant instabilities. Furthermore, for the reversed field pinch configuration, numerical results indicate that nonlinear coupling of different helicities results in noticeably more rapid saturation of the dominant instabilities than was observed in single helicity studies.