How accurately can we measure the reconnection rate $E_M$ for the MMS diffusion region event of 2017-07-11?

TL;DR

This study assesses the accuracy of measuring the magnetic reconnection rate $E_M$ in the Earth's magnetotail using in-situ data from MMS, highlighting the errors introduced by coordinate system uncertainties and comparing multiple analysis methods.

Contribution

It systematically evaluates different coordinate determination techniques and quantifies their errors in estimating the reconnection electric field during a specific MMS event.

Findings

Reconnection rate estimated at 3.2 mV/m with ±0.06 mV/m uncertainty.

Coordinate axes determined by multiple methods show reasonable agreement.

Errors in coordinate axes can lead to up to 35° deviation, affecting $E_M$ accuracy.

Abstract

We investigate the accuracy with which the reconnection electric field $E_M$ can be determined from in-situ plasma data. We study the magnetotail electron diffusion region observed by NASA's Magnetospheric Multiscale (MMS) on 2017-07-11 at 22:34 UT and focus on the very large errors in $E_M$ that result from errors in an $LMN$ boundary-normal coordinate system. We determine several $LMN$ coordinates for this MMS event using several different methods. We use these $M$ axes to estimate $E_M$. We find some consensus that the reconnection rate was roughly $E_M$=3.2 mV/m $\pm$ 0.06 mV/m, which corresponds to a normalized reconnection rate of $0.18\pm0.035$. Minimum variance analysis of the electron velocity (MVA-$v_e$), MVA of $E$, minimization of Faraday residue, and an adjusted version of the maximum directional derivative of the magnetic field (MDD-$B$) technique all produce {reasonably} similar coordinate axes. We use virtual MMS data from a particle-in-cell simulation of this event to estimate the errors in the coordinate axes and reconnection rate associated with MVA-$v_e$ and MDD-$B$. The $L$ and $M$ directions are most reliably determined by MVA-$v_e$ when the spacecraft observes a clear electron jet reversal. When the magnetic field data has errors as small as 0.5\% of the background field strength, the $M$ direction obtained by MDD-$B$ technique may be off by as much as 35$^\circ$. The normal direction is most accurately obtained by MDD-$B$. Overall, we find that these techniques were able to identify $E_M$ from the virtual data within error bars $\geq$20\%.