Locating magnetic reconnection x-lines in 3D PIC simulations

In a three-dimensional PIC simulation of turbulent magnetic reconnection, a reconnection 'X-line' can be identified as a separator in the magnetic topology. From this x-line, it is possible to compute the reconnection rate by evaluating the line integral of the electric field along the separator. This technique is used in a reconnection simulation of a symmetric Harris sheet driven by inflow at the upstream boundaries with a strong guide field (such that the magnetic field is non-vanishing everywhere and there are no magnetic nulls). The results of this analysis are compared to the General Magnetic Reconnection theory (GMR) [Hesse and Schindler, 1998], showing that in this symmetric case GMR agrees with our topological approach to finding the location of the x-line. The parallel electric field is non-trivial along the entire length of the x-line, however, suggesting that the reconnection diffusion region cannot be identified by local measures of the breakdown of ideal MHD alone. We discuss the implications of these results for NASA's upcoming Magnetospheric Multiscale mission.