Steady state magnetic reconnection in planar geometries

Abstract

The problem of nonlinear, steady state magnetic reconnection in incompressible plasmas is considered. A self-consistent treatment is developed which allows a formal analytic solution of the resistive induction equation, valid for all sub-Alfvénic velocity fields. This solution relates the velocity stream function to the global magnetic field structure and highlights several key properties of the resistive system. In particular, the field lines are isobars of uniform current density and characteristics of the velocity stream function. The impact of this analysis on "fast" magnetic reconnection is then considered. Despite strong constraints on the flow topology - no separatrix flows are allowed - fast, nonlinear models can be developed self-consistently. It is shown that the reconnection rate is maintained against reductions in the plasma restrictivity by the increasing amplitude but decreasing width of the current layer aligned to the separatrix. It is concluded that "open" flow topologies allow fast reconnection to continue under conditions which lead to stalling in "closed" or periodic geometries.