Magnetic reconnection in incompressible fluids

We investigate the dynamical relaxation of a disturbed X-type magnetic neutral point in a periodic geometry, with an ignorable coordinate, for an incompressible fluid. We find that the properties of the current sheet cannot be understood in terms of steady state reconnection theory or more recent linear dynamical solutions. Accordingly we present a new scaling law for magnetic reconnection consistent with fast energy dissipation, i.e., the dissipation rate at current maximum is approximately independent of magnetic diffusivity (η). The flux annihilation rate, however, scales as η1/4, faster than the Sweet-Parker rate of η1/2 but asymptotically much slower than the dissipation rate. These results suggest a flux pile-up regime in which the bulk of the free magnetic energy is released as heat rather than as kinetic energy of mass motion. The implications of our results for reconnection in the solar atmosphere and interior are discussed