RECONNECTION OF QUASI-SINGULAR CURRENT SHEETS: THE “IDEAL” TEARING MODE

A strong indication that fast reconnection regimes exist within resistive magnetohydrodynamics was given by the proof that the Sweet–Parker current sheet, maintained by a flow field with an appropriate inflow–outflow structure, could be unstable to a reconnecting instability which grows without bound as the Lundquist number, S, tends to infinity. The requirement of a minimum value for S in order for the plasmoid instability to kick in does little to resolve the paradoxical nature of the result. Here we argue against the realizability of Sweet–Parker current sheets in astrophysical plasmas with very large S by showing that an “ideal” tearing mode takes over before current sheets reach such a thickness. While the Sweet–Parker current sheet thickness scales as ∼S−1/2, the tearing mode becomes effectively ideal when a current sheet collapses to a thickness of the order of ∼S−1/3, up to 100 times thicker than S−1/2, when (as happens in many astrophysical environments) S is as large as 1012. Such a sheet, while still diffusing over a very long time, is unstable to a tearing mode with multiple x-points: here we detail the characteristics of the instability and discuss how it may help solve the flare trigger problem and effectively initiate the turbulent disruption of the sheet.