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.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- January 2014
- DOI:
- 10.1088/2041-8205/780/2/L19
- Bibcode:
- 2014ApJ...780L..19P
- Keywords:
-
- magnetic reconnection;
- magnetohydrodynamics: MHD;
- Sun: corona