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We calculate the aspect ratio of the electron diffusion region (EDR) during symmetric magnetic reconnection using magnetic field gradients measured by the Magnetospheric Multiscale (MMS) Mission. The technique introduced in this paper is validated using a particle-in-cell simulation and used to calculate the EDR aspect ratios for three MMS-observed magnetotail EDRs which are compared with the EDR aspect ratio predicted by scaling dependencies on asymptotic upstream electron β. We then use the aspect ratio to calculate the normalized reconnection rate and show that it is 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. Plain Language SummaryMagnetic reconnection is a plasma process which occurs throughout the universe. It accelerates and heats nearby particles, and can redistribute energy over vast scales. The rate at which it occurs, the reconnection rate, is one of the most important quantities describing reconnection. Reconnection occurs within an electron-scale region where ions and electrons are decoupled from the magnetic field, known as the electron diffusion region (EDR). Theory and simulations have shown the dimensions of the EDR scale with the reconnection rate. In this paper, we introduce a new method to determine the aspect ratio of the EDR and use it to find the reconnection rate for three EDRs observed by the Magnetospheric Multiscale Mission. This new method has fewer sources of error than established methods for determining reconnection rate using spacecraft data, and could provide a simpler way of studying the mechanisms which control the reconnection rate. HEUER ET AL.

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.