Model of magnetic reconnection in space and astrophysical plasmas

Abstract

Maxwell's equations imply that exponentially smaller non-ideal effects than commonly assumed can give rapid magnetic reconnection in space and astrophysical plasmas. In an ideal evolution, magnetic field lines act as stretchable strings, which can become ever more entangled but cannot be cut. High entanglement makes the lines exponentially sensitive to small non-ideal changes in the magnetic field. The cause is well known in popular culture as the butterfly effect and in the theory of deterministic dynamical systems as a sensitive dependence on initial conditions, but the importance to magnetic reconnection is not generally recognized. Two-coordinate models are too constrained geometrically for the required entanglement, but otherwise the effect is general and can be studied in simple models. A simple model is introduced, which is periodic in the x and y Cartesian coordinates and bounded by perfectly conducting planes in z. Starting from a constant magnetic field in the z direction, reconnection is driven by a spatially smooth, bounded force. The model is complete and could be used to study the impulsive transfer of energy between the magnetic field and the ions and electrons using a kinetic plasma model.