Secondary instability in three-dimensional magnetic reconnection

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Abstract
The transition to turbulence in three‐dimensional reconnection of a magnetic neutral sheet is investigated. The transition can occur via a three‐step process. First, the sheet undergoes the usual tearing instability. Second, the tearing mode saturates to form a two‐dimensional quasisteady state. Third, this secondary equilibrium is itself ideally unstable when it is perturbed by three‐dimensional disturbances. Most of this paper is devoted to the analysis and simulation of the three‐dimensional linear stability properties of the two‐dimensional saturated tearing layer. The numerical simulations are performed with a semi‐implicit, pseudospectral‐Fourier collocation algorithm. A three‐dimensional secondary linear instability that grows on the ideal time scale is identified. An examination of the modal energetics reveals that the largest energy transfer is from the mean field to the three‐dimensional field, with the two‐dimensional field acting as a catalyst. Results of some high‐resolution, fully nonlinear calculations that provide insight into the complete evolution of the system are then presented. During the nonlinear phase, the modes with structure in the third dimension are, in general, more energetic than the purely two‐dimensional modes. The evolution is interpreted as being due to a kinking of flux tubes formed during the initial two‐dimensional tearing stage. The system reorganizes itself turbulently into a new three‐dimensional quasisteady state, which, however, dissipates much more energy than the two‐dimensional saturated state. The present work has important implications for a wide range of astrophysical processes that are believed to involve rapid magnetic energy release.

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