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.