Dynamic Planar Magnetic Reconnection Solutions for Incompressible Plasmas

The planar magnetic reconnection problem for viscous, resistive plasmas is addressed. We show that solutions can be developed by superposing transient nonlinear disturbances onto quiescent “background” fields. The disturbance fields are unrestricted in form, but the spatial part of the background field must satisfy ∇2K= -λK. This decomposition allows previous analytic reconnection solutions, based on one-dimensional disturbance fields of “plane wave” form, to be recovered as special cases. However, we point out that planar disturbance fields must be fully two-dimensional to avoid the pressure problem associated with analytic merging models, that is, to avoid unbounded current sheet pressures in the limit of small plasma resistivities. The details of the reconnection problem are then illustrated using cellular background field simulations in doubly periodic geometries. The flux pile-up rate is shown to saturate when the pressure of the current sheet exceeds the hydromagnetic pressure of the background field. Although the presaturation regime is well described by one-dimensional current sheet theory, the nonlinear postsaturation regime remains poorly understood. Preliminary evidence suggests that, although after saturation the early evolution of the field can be described by slow Sweet-Parker scalings, the first implosion no longer provides the bulk of the energy release