Determining the Orientation of a Magnetic Reconnection X Line and Implications for a 2D Coordinate System

Abstract

An LMN coordinate system for magnetic reconnection events is sometimes determined by defining N as the direction of the gradient across the current sheet and L as the direction of maximum variance of the magnetic field. The third direction, M, is often assumed to be the direction of zero gradient, and thus the orientation of the X line. But when there is a guide field, the X line direction may have a significant component in the L direction defined in this way. For a 2D description, a coordinate system describing such an event would preferably be defined using a different coordinate direction M′ oriented along the X line. Here we use a 3D particle‐in‐cell simulation to show that the X line is oriented approximately along the direction bisecting the asymptotic magnetic field directions on the two sides of the current sheet. We describe two possible ways to determine the orientation of the X line from spacecraft data, one using the minimum gradient direction from Minimum Directional Derivative analysis at distances of the order of the current sheet thickness from the X line, and another using the bisection direction based on the asymptotic magnetic fields outside the current sheet. We discuss conditions for validity of these estimates, and we illustrate these conditions using several Magnetospheric Multiscale (MMS) events. We also show that intersection of a flux rope due to secondary reconnection with the primary X line can destroy invariance along the X line and negate the validity of a two‐dimensional description.