Magnetic reconnection with null and X-points

Abstract

Null and X-points of magnetic fields are places at which magnetic field lines with fundamentally different topologies approach each other arbitrary closely before separating by a distance set by the overall size of the configurtion. Even in a collision-free plasma, magnetic field lines can change their topology on a scale $c/\\omega_{pe}$ due to electron inertia. On a time scale set by the shear Alfven wave these effects can spread all along the field lines that come within a $c/\\omega_{pe}$ distance near a null or an X-point. Traditional reconnection theories made the assumption that the reconnected magnetic flux had to be dissipated by an electric field. This assumption is false in three dimensional systems because an ideal evolution can spatially mix the reconnected flux. This reduces the required current density for reconnection to compete with evolution from being proportional to the magnetic Reynolds number $R_m$ to being proportional to $\\ln R_m$. In three dimensional space, null and X-points are shown to have analogous effects on magnetic reconnection.