Nonlinear destabilization of linearly stable tearing modes with multiple rational surfaces

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Abstract
The stability of finite size magnetic islands is analyzed in configurations with multiple resonant magnetic surfaces. It is demonstrated that there are configurations that are linearly stable which can be unstable to finite size perturbations. Two different examples of single helicity double tearing are given for configurations with two q=2 surfaces. In the first case the destabilization is due to the extension of magnetic separatrices out to regions of destabilizng current gradients. For the second case the modes are linearly stabilized by the suppression of the linear coupling of the rational surfaces by differential plasma rotation, which essentially decouples the perturbations around the different rational surfaces. A finite size magnetic island will interact quasilinearly with initial plasma rotation. The plasma rotation is then equilibrated and the mode destabilized.