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We investigate the accuracy with which the reconnection electric field EMcan be determined from in situ plasma data. We study the magnetotail electron diffusion region observed by National Aeronautics and Space Administration's Magnetospheric Multiscale (MMS) on 11 July 2017 at 22:34 UT and focus on the very large errors in EMthat result from errors in an LMNboundary normal coordinate system. We determine several LMNcoordinates for this MMS event using several different methods. We use these Maxes to estimate EM. We find some consensus that the reconnection rate was roughly EM= 3.2 ± 0.6 mV/m, which corresponds to a normalized reconnection rate of 0.18 ± 0.035. Minimum variance analysis of the electron velocity (MVA‐ve), 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‐veand MDD‐B. The Land Mdirections are most reliably determined by MVA‐vewhen the spacecraft observes a clear electron jet reversal. When the magnetic field data have errors as small as 0.5% of the background field strength, the Mdirection obtained by MDD‐Btechnique may be off by as much as 35°. The normal direction is most accurately obtained by MDD‐B. Overall, we find that these techniques were able to identify EMfrom the virtual data within error bars ≥20%. The reconnection rate EMis estimated for one event using several techniques to find an MdirectionThe error bars in EMand the LMNcoordinate directions are estimated from virtual dataThe reconnection rate is likely EM= 3.2 mV/m ± 0.6 mV/m, which corresponds to a normalized rate of 0.18 ± 0.035

Using test‐particle simulations, we describe (in 2‐D) the interaction of an ensemble of electrons with a discrete whistler‐mode wave packet, which propagates with a moderate wave‐normal angle with respect to the background magnetic field. We evaluate both the average transport coefficients used in quasi‐linear diffusion transport and also the full nonlinear wave‐particle interactions. The magnitude of the calculated diffusion coefficients is found to increase proportionally to the wave amplitude squared, in agreement with quasi‐linear diffusion theory. Cyclotron resonance of counterstreaming electrons (n= 1 harmonic number) is more important for pitch angle scattering than Landau resonance. Landau resonance of costreaming electrons (n= 0) is comparable to cyclotron resonance for energy diffusion and advection. Strong acceleration of high pitch angle, costreaming electrons arises in nonlinear wave‐particle interactions with high‐amplitude waves. In our simulations with zero parallel electric field, the energy source for electron acceleration is the wave's perpendicular electric field, in both the cyclotron and Landau resonances. The Landau resonance can happen even with zero parallel electric field, if the wave packet propagates with a finite wave‐normal angle. This resonance between the particle's azimuthal velocity and the wave fields leads to trapping and substantial parallel acceleration. We present a detailed analysis on how an individual plasma wave packet interacts with electrons trapped in the Earth's Van Allen radiation belts. The waves are in the so‐called whistler mode, where both the wave fields and the electrons rotate around the background magnetic field lines at comparable frequencies, leading to substantial interaction between the two. In this investigation, we quantify both the average effect on a large group of particles and also the strong interactions that may happen with a selected few. Our results help quantifying how waves in the whistler mode contribute to the population balance of the radiation belts and especially how they can accelerate trapped electrons to high energies. Cyclotron resonance of counterstreaming electrons is dominant for pitch angle scattering, consistent with quasi‐linear theoryLandau and cyclotron resonances are comparable for acceleration; here the energy source is the wave perpendicular electric field in bothSubstantial Landau parallel acceleration occurs with a finite wave‐normal angle, even with negligible parallel electric field

We discuss methods to determine L‐M‐Ncoordinate systems for current sheet crossings observed by the Magnetospheric Multiscale (MMS) spacecraft mission during ongoing reconnection, where eLis the direction of the reconnecting component of the magnetic field, B, and eNis normal to the magnetopause. We present and test a new hybrid method, with eLestimated as the maximum variance direction of B(MVAB) and eNas the direction of maximum directional derivative of B, and then adjust these directions to be perpendicular. In the best case, only small adjustment is needed. Results from this method, applied to an MMS crossing of the dayside magnetopause at 1305:45 UT on 16 October 2015, are discussed and compared with those from other methods for which eNis obtained by other means. Each of the other evaluations can be combined with eLfrom MVAB in a generalized hybrid approach to provide an L‐M‐Nsystem. The quality of the results is judged by eigenvalue ratios, constancy of directions using different data segments and methods, and expected sign and magnitude of the normal component of B. For this event, the hybrid method appears to produce eNaccurate to within less than 10°. We discuss variance analysis using the electric current density, J, or the J× Bforce, which yield promising results, and minimum Faraday residue analysis and MVAB alone, which can be useful for other events. We also briefly discuss results from our hybrid method and MVAB alone for a few other MMS reconnection events. We discuss methods for determining coordinate systems in order to study magnetic reconnection events at the magnetopause, the boundary between the ionized gas in the region of space dominated by the Earth's magnetic field and the ionized gas coming from the solar wind. We introduce a new method that combines results from multiple methods in order to determine the three coordinate directions in space. We demonstrate this method by applying it to an event observed by the Magnetospheric Multiscale spacecraft on 16 October 2015 and at other times. Methods to determine L‐M‐Ncurrent sheet coordinates are described and testedQuality of results is judged by eigenvalue ratios and consistency using different data intervals and methods and with the geophysical contextFor the interval examined here, the uncertainty of the normal direction was at least several degrees but probably less than 10°

Temporal, spatial, and velocity‐space variations of electron phase space density are measured observationally and compared for the first time using the four magnetospheric multiscale (MMS) spacecraft at Earth's magnetopause. Equipped with these unprecedented spatiotemporal measurements offered by the MMS tetrahedron, we compute each term of the electron Vlasov equation that governs the evolution of collisionless plasmas found throughout the universe. We demonstrate how to use single spacecraft measurements to improve the resolution of the electron pressure gradient that supports nonideal parallel electric fields, and we develop a model to intuit the types of kinetic velocity‐space signatures that are observed in the Vlasov equation terms. Furthermore, we discuss how the gradient in velocity‐space sheds light on plasma energy conversion mechanisms and wave‐particle interactions that occur in fundamental physical processes such as magnetic reconnection and turbulence. Measuring spatial and temporal variations of space plasmas usually requires choosing between the following two approaches: (a) measure how the quantity of interest changes in time as the plasma flows past a single spacecraft, or (b) compare measurements of the quantity gathered from multiple, spatially separated spacecraft. The first approach requires measurements at two different times from the same spatial location, while the second requires simultaneous measurements taken from multiple spatial points. There are advantages and disadvantages to each of these existing approaches. While single‐spacecraft measurements may be gathered at high time resolution, a known limitation of single‐point data sets is the inability to distinguish between spatial and temporal variations: both a thin, slow‐moving structure and a thick, fast‐moving one could produce the same measured time series of a quantity when sampled at only a single spatial location. In many situations, multipoint measurements, such as those provided by NASA's Magnetospheric Multiscale (MMS) four‐spacecraft mission enable us to overcome that limitation; however, oftentimes electron‐scale structures of interest are even smaller than the close inter‐spacecraft separation of MMS, which means typical techniques for estimating spatial gradients from the four spacecraft also become inaccurate for those events. In this paper, we present a new approach for quantifying variations in a collisionless plasma that only requires information about the plasma particles and fields taken at a singlepoint in time and space. Temporal, spatial, and velocity‐space derivatives of electron phase space density are computed and compared for the first time using the Magnetospheric Multiscale spacecraftSingle‐spacecraft measurements show how parallel electric fields are balanced by electron pressure gradients at Earth's magnetopauseA simplified form of the electron distribution function provides intuition for interpreting nongyrotropic velocity‐space structures Temporal, spatial, and velocity‐space derivatives of electron phase space density are computed and compared for the first time using the Magnetospheric Multiscale spacecraft Single‐spacecraft measurements show how parallel electric fields are balanced by electron pressure gradients at Earth's magnetopause A simplified form of the electron distribution function provides intuition for interpreting nongyrotropic velocity‐space structures

We present in‐depth analysis of three southward‐moving meso‐scale (ion‐to magnetohydrodynamic‐scale) flux transfer events (FTEs) and subsequent crossing of a reconnecting magnetopause current sheet (MPCS), which were observed on 8 December 2015 by the Magnetospheric Multiscale spacecraft in the subsolar region under southward and duskward magnetosheath magnetic field conditions. We aim to understand the generation mechanism of ion‐scale magnetic flux ropes (ISFRs) and to reveal causal relationship among magnetic field structures, electromagnetic energy conversion, and kinetic processes in magnetic reconnection layers. Results from magnetic field reconstruction methods are consistent with a flux rope with a length of about one ion inertial length growing from an electron‐scale current sheet (ECS) in the MPCS, supporting the idea that ISFRs can be generated through secondary reconnection in an ECS. Grad‐Shafranov reconstruction applied to the three FTEs shows that the FTEs had axial orientations similar to that of the ISFR. This suggests that these FTEs also formed through the same secondary reconnection process, rather than multiple X‐line reconnection at spatially separated locations. Four‐spacecraft observations of electron pitch‐angle distributions and energy conversion rate j·E′=j·E+ve×B$\mathbf{j}\cdot {\mathbf{E}}^{\prime }=\mathbf{j}\cdot \left(\mathbf{E}+{\mathbf{v}}_{\mathrm{e}}\times \mathbf{B}\right)$suggest that the ISFR had three‐dimensional magnetic topology and secondary reconnection was patchy or bursty. Previously reported positive and negative values of j·E′$\mathbf{j}\cdot {\mathbf{E}}^{\prime }$, with magnitudes much larger than expected for typical MP reconnection, were seen in both magnetosheath and magnetospheric separatrix regions of the ISFR. Many of them coexisted with bi‐directional electron beams and intense electric field fluctuations around the electron gyrofrequency, consistent with their origin in separatrix activities. Magnetic reconnection is a physical process that converts magnetic energy into plasma energy by changing the connectivity of magnetic field lines from one region to another. Magnetic reconnection at the outer boundary of planetary magnetospheres, known as the magnetopause (MP), is key to the entry of solar wind plasma and energy into the magnetospheres that forms the basis for space weather phenomena in the magnetospheres. MP reconnection often occurs in a transient or patchy manner, forming magnetic flux ropes (FRs) with helical field lines of various sizes. They may become an important pathway for fast coupling between the solar wind and magnetosphere. However, the generation mechanism of a subclass of FRs, relatively small “ion‐scale” FRs, is poorly understood. Computer simulations show that they are formed in thin and elongated current sheets of single active reconnection site, but this scenario has not been confirmed by observations. Our observations based on NASA's Magnetospheric Multiscale mission show that ion‐scale FR can form in a thin current sheet of single ongoing reconnection site at Earth's MP. The observed FR showed signatures of complex field line connectivity and localized conversion from electromagnetic to electron energy and vice versa, indicating complex MP dynamics. Ion‐scale magnetic flux rope (ISFR) can be generated from reconnecting electron‐scale current sheet at the subsolar magnetopause (MP)Preceding mesoscale flux ropes had axial directions akin to that of the ISFR in the MP, suggesting the same generation mechanismThe ISFR had complex magnetic topology with three‐dimensional effects and involved patchy, intense energy conversion in separatrix regions Ion‐scale magnetic flux rope (ISFR) can be generated from reconnecting electron‐scale current sheet at the subsolar magnetopause (MP) Preceding mesoscale flux ropes had axial directions akin to that of the ISFR in the MP, suggesting the same generation mechanism The ISFR had complex magnetic topology with three‐dimensional effects and involved patchy, intense energy conversion in separatrix regions