The influence of resistivity gradients on shock conditions for a Petschek reconnection geometry

Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petsc...

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Bibliographic Details
Published in:Annales geophysicae (1988) 2016-04, Vol.34 (4), p.421-425
Main Authors: Nabert, Christian, Glassmeier, Karl-Heinz
Format: Article
Language:English
Subjects:
Analysis
Cosmic rays
Diffusion rate
Electric properties
Electrical resistivity
Flow velocity
Fluid flow
Geometry
Magnetic field
Magnetic fields
Magnetic reconnection
Magnetohydrodynamic equations
Magnetohydrodynamics
Plasma
Propagation velocity
Shock waves
Singularities
Singularity (mathematics)
Spatial variations
Velocity
Wave propagation
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Summary:Shock waves can strongly influence magnetic reconnection as seen by the slow shocks attached to the diffusion region in Petschek reconnection. We derive necessary conditions for such shocks in a nonuniform resistive magnetohydrodynamic plasma and discuss them with respect to the slow shocks in Petschek reconnection. Expressions for the spatial variation of the velocity and the magnetic field are derived by rearranging terms of the resistive magnetohydrodynamic equations without solving them. These expressions contain removable singularities if the flow velocity of the plasma equals a certain characteristic velocity depending on the other flow quantities. Such a singularity can be related to the strong spatial variations across a shock. In contrast to the analysis of Rankine–Hugoniot relations, the investigation of these singularities allows us to take the finite resistivity into account. Starting from considering perpendicular shocks in a simplified one-dimensional geometry to introduce the approach, shock conditions for a more general two-dimensional situation are derived. Then the latter relations are limited to an incompressible plasma to consider the subcritical slow shocks of Petschek reconnection. A gradient of the resistivity significantly modifies the characteristic velocity of wave propagation. The corresponding relations show that a gradient of the resistivity can lower the characteristic Alfvén velocity to an effective Alfvén velocity. This can strongly impact the conditions for shocks in a Petschek reconnection geometry.
ISSN:1432-0576
0992-7689
1432-0576
DOI:10.5194/angeo-34-421-2016