On the nature of 3D reconnection

Abstract

In two dimensions the theory of magnetic reconnection is now highly developed and fairly well understood. A general configuration will contain X-type neutral points and separatrix field lines which link to it. Reconnection occurs by the breaking and rejoining of field lines at the X-point and the transfer of flux across the separatrices from one topological region to another.

In three dimensions the process is completely different! Several types of null point now exist but they have a common skeleton of field lines that link to it, consisting of an isolated spine curve and a fan surface. When a null point is present in a three-dimensional configuration, separatrix surfaces may be defined separating topologically distinct regions. However, two quite distinct types of reconnection are possible depending on the boundary conditions. “Spine reconnection” has a singular jetting flow along the spine curve and “fan reconnection” has a singular swirling flow at the fan surface.

When there are no null points in the configuration, a difficulty arises since there are no separatrices and all field lines are topologically equivalent. It has been discovered,

However, that reconnection can still take place, since the mapping of field lines from one part of the surface enclosing a finite volume to another reveals the presence of “quasi-separatrix layers”. Here the mapping function has extremely steep gradients and the field lines can slip rapidly through the plasma by a process of “magnetic flipping”.