Three-dimensional spontaneous magnetic reconnection in neutral current sheets

The reconnection of magnetic field lines is one of the fundamental processes that lead to the eruptive release of stored magnetic energy in plasmas. A large number of observations and experiments, e.g., solar flares, geomagnetic substorms, the sawtooth instability in fusion experiments, and laboratory reconnection experiments, support this hypothesis. Magnetic reconnection is important for the evolution of magnetohydrodynamic (MHD) instabilities (e.g., the tearing mode and magnetic island coalescence8–10) in current sheets which are generally involved in the energy release process. It is also important at the dissipative scales in MHD turbulence. To explain the short time scales of the energy release processes in spite of large values of the Lundquist number S = μ0LVA/η0, fast reconnection models have been proposed but are generally restricted to two-dimensional geometry, including the stationary Petschek model and the spontaneous fast reconnection model. Both these models are one-fluid descriptions in which resistivity provides the nonideal effect required for reconnection and in both models the resistivity is localized at the central magnetic X-point. Models distinguishing between electron and ion effects, such as Hall MHD, two-fluid MHD, or kinetic treatments, permit still higher reconnection rates, even in the absence of resistivity. However, all these models require significant computational effort, which still prevents following the evolution of microscopic perturbations to large spatial and temporal scales in three dimensions. In the spontaneous fast reconnection model, a current sheet equilibrium is initially perturbed by a localized region of enhanced (anomalous) resistivity in the sheet center, which leads to the development of a simple X-point structure. Anomalous resistivity is permitted to occur in this model also at later times of the evolution if a threshold of the local current density j or of the local electron-ion drift velocity vD = (mi/e) j/ρ is exceeded (mi – ion mass, e – elementary charge, ρ – mass density). This couples the reconnection-driven flow to the evolution of the resistivity