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 fi eld must satisfy del(2)K = -lambda K. This decomposition allows previous an alytic reconnection solutions, based on one-dimensional disturbance fields of "plane wave" form, to be recovered as special cases. However, we point o ut that planar disturbance fields must be fully two-dimensional to avoid th e pressure problem associated with analytic merging models, that is, to avo id unbounded current sheet pressures in the limit of small plasma resistivi ties. The details of the reconnection problem are then illustrated using ce llular background field simulations in doubly periodic geometries. The flux pile-up rate is shown to saturate when the pressure of the current sheet e xceeds the hydromagnetic pressure of the background field. Although the pre saturation regime is well described by one-dimensional current sheet theory , the nonlinear postsaturation regime remains poorly understood. Preliminar y evidence suggests that, although after saturation the early evolution of the field can be described by slow Sweet-Parker scalings, the first implosi on no longer provides the bulk of the energy release.