Calculating the Electron Diffusion Region Aspect Ratio with Magnetic Field Gradients

Abstract

We calculate the aspect ratio of the electron diffusion region (EDR) during symmetric magnetic reconnection using magnetic field gradients measured by the Magnetospheric Multiscale mission (MMS). The technique introduced in this paper is validated using a particle-in-cell (PIC) simulation, compared with the reconnection rate for three MMS-observed magnetotail EDRs, then compared with the EDR aspect ratio predicted by scaling dependencies on asymptotic upstream electron $\beta$. For the MMS events, we find that the EDR aspect ratio determined using the magnetic field gradients are within uncertainty of the normalized reconnection rate found by previous studies for three MMS-observed EDRs. Because the magnetic field gradients are velocity-frame independent and typically very well measured by MMS, the technique can be used to obtain the normalized reconnection rate with higher fidelity than established methods.