Magnetic Reconnection in Three Dimensions – Spine, Fan and Separator Solutions

Magnetic reconnection in three spatial dimensions can occur in three distinct ways. In the case of reconnection at a neutral point, localized currents can accumulate either in the form of a quasi one-dimensional `fan' current, or as a cylindrical `spine' current aligned to the exhaust axis of the flow. A third possibility, which does not involve a null of the field, is separator reconnection, where reconnection occurs in two dimensions with a uniform guide field. In this paper we employ steady-state and time-dependent analytic models to predict resistive scaling laws associated with null point and separator reconnection. These predictions are then tested computationally by exploring dynamic simulations in 3D periodic geometries. We find that the simple, steady-state models provide an accurate description of a time-dependent, reconnecting current layer.