Reconnection of quasi-singular current sheets: The "ideal" tearing mode

Abstract

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. © 2014. The American Astronomical Society. All rights reserved.