The Relation between Reconnected Flux, the Parallel Electric Field, and the Reconnection Rate in a Three-Dimensional Kinetic Simulation of Magnetic Reconnection

We investigate the distribution of parallel electric fields and their relationship to the location and rate of magnetic reconnection of a large particle-in-cell simulation of 3D turbulent magnetic reconnection with open boundary conditions. The simulation's guide field geometry inhibits the formation of topological features such as separators and null points. Therefore, we derive the location of potential changes in magnetic connectivity by finding the field lines that experience a large relative change between their endpoints, i.e., the quasi-separatrix layer. We find a correspondence between the locus of changes in magnetic connectivity, or the quasi-separatrix layer, and the map of large gradients in the integrated parallel electric field (or quasi-potential). Furthermore, we compare the distribution of parallel electric fields along field lines with the reconnection rate. We find the reconnection rate is controlled by only the low-amplitude, zeroth and first-order trends in the parallel electric field, while the contribution from high amplitude parallel fluctuations, such as electron holes, is negligible. The results impact the determination of reconnection sites within models of 3D turbulent reconnection as well as the inference of reconnection rates from in situ spacecraft measurements. It is difficult through direct observation to isolate the locus of the reconnection parallel electric field amidst the large amplitude fluctuations. However, we demonstrate that a positive slope of the partial sum of the parallel electric field along the field line as a function of field line length indicates where reconnection is occurring along the field line.