Indeterminacy and instability in Petschek reconnection

Journal Article · Wed May 15 04:00:00 EDT 2013 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.4804337· OSTI ID:22218624

Forbes, Terry G. ^[1]; Priest, Eric R. ^[2]; Seaton, Daniel B. ^[3]; Litvinenko, Yuri E. ^[4]

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1. Institute for the Study of Earth, Oceans, and Space, University of New Hampshire, Durham, New Hampshire 03824 (United States)
2. Institute of Mathematics, University of St. Andrews, Fife KY16 9SS, Scotland (United Kingdom)
3. SIDC-Royal Observatory of Belgium, Ringlaan 3, 1180 Brussels (Belgium)
4. Department of Mathematics, University of Waikato, P.O. 3105, Hamilton (New Zealand)

We explain two puzzling aspects of Petschek's model for fast reconnection. One is its failure to occur in plasma simulations with uniform resistivity. The other is its inability to provide anything more than an upper limit for the reconnection rate. We have found that previously published analytical solutions based on Petschek's model are structurally unstable if the electrical resistivity is uniform. The structural instability is associated with the presence of an essential singularity at the X-line that is unphysical. By requiring that such a singularity does not exist, we obtain a formula that predicts a specific rate of reconnection. For uniform resistivity, reconnection can only occur at the slow, Sweet-Parker rate. For nonuniform resistivity, reconnection can occur at a much faster rate provided that the resistivity profile is not too flat near the X-line. If this condition is satisfied, then the scale length of the nonuniformity determines the reconnection rate.

• OSTI ID: 22218624
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 5 Vol. 20; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
ANALYTICAL SOLUTION
CHARGED-PARTICLE TRANSPORT
ELECTRIC CONDUCTIVITY
MAGNETIC RECONNECTION
MAGNETOHYDRODYNAMICS
PLASMA
PLASMA INSTABILITY
PLASMA SIMULATION
SINGULARITY