Magnetic reconnection is responsible for the major reconfigurations of the magnetosphere that lead to energy transport and deposition into the ionosphere. The fast rate at which magnetic energy is converted to plasma kinetic energy is likely enabled by the polarization Hall electric field that results from the separation of ions and electrons at small scales. Signatures of Hall fields have played a key role in identifying and studying reconnection, but the density of accumulated charge has not been quantified. We use the 4-point measurements of the Magnetospheric Multiscale mission to compute the divergence of the electric field and present the first observations of charge density in the diffusion region of magnetic reconnection. We show how it ties into the Hall system, discuss measurement uncertainties, analyze quality estimates, and make comparisons to 2D simulations. Charge density is briefly presented for other phenomena, and ranges from 2% or less of the background plasma density for magnetic reconnection and electron-scale magnetic holes and peaks to upwards of 4% for electron phase space holes.

In order to determine particle velocities and electric field in the frame of the magnetic structure, one first needs to determine the velocity of the magnetic structure in the frame of the spacecraft observations. Here, we show how to determine a two dimensional magnetic structure velocity for the magnetic reconnection event observed in the magnetotail by the Magnetospheric Multiscale (MMS) spacecraft on 11 July 2017. We use two different multi-spacecraft methods, Spatio-Temporal Difference (STD) and the recently developed polynomial reconstruction method. Both of these methods use the magnetic field measurements, and the reconstruction technique also uses the current density measured by the particle instrument. We find rough agreement between the results of our methods and with other velocity determinations previously published. We also explain a number of features of STD and show that the polynomial reconstruction technique is only likely to be valid within a distance of two spacecraft spacings from the centroid of the MMS spacecraft. Both of these methods are susceptible to contamination by magnetometer calibration errors.

We examine the July 11th, 2017 electron diffusion region (EDR) observed by the Magnetospheric Multiscale (MMS) mission using Poynting’s theorem. The terms in Poynting’s theorem are determined using a linear gradient approximation to obtain barycentric averages within the MMS tetrahedron. We find that Poynting’s theorem is approximately balanced in the EDR, and the balance is improved if the calculation of ∇∙S is restricted to the LN plane. The work rate per unit volume J∙E is mostly balanced by the divergence of the electromagnetic energy flux ∇∙S, indicating that the electromagnetic energy density remains relatively constant within the EDR during the encounter. We also use particle-in-cell (PIC) simulations to examine Poynting’s theorem near an x-line evolving in time. The central EDR in the simulation is characterized by approximate time independent balance in Poynting’s theorem during reconnection growth, while the outer EDR exhibits time-dependent fluctuations indicative of more chaotic behavior.