Fundamental processes in plasmas act to convert energies into different forms, e.g., electromagnetic, kinetic and thermal. Direct derivation from the Valsov-Maxwell equation yields sets of equations that describe the temporal evolution of the magnetic, kinetic and internal energies in either the monofluid or multifluid frameworks. In this work we focus on the main terms that affect the changes in the kinetic energy. These are pressure gradient-related terms and electromagnetic terms. The former account for plasma acceleration or deceleration from a pressure gradient, while the latter from an electric field. The overall balance between these terms is fundamental to ensure the conservation of energy and momentum. We use in-situ observations from the Magnetospheric MultiScale (MMS) mission to study the relationship between these terms. We perform a statistical analysis of those parameters in the context of magnetic reconnection by focusing on small-scale Electron Diffusion Regions and large-scale Flux Transfer Events. The analysis reveals a correlation between the two terms in the monofluid force balance, and in the ion force and energy balance. However, the expected relationship cannot be verified from electron measurements. Generally, the pressure gradient related terms are smaller than their electromagnetic counterparts. We perform an error analysis to quantify the expected underestimation of gradient values as a function of the spacecraft separation compared to the gradient scale. Our findings highlight that MMS is capable of capturing energy and force balance for the ion fluid, but that care should be taken for energy conversion terms based on electron pressure gradients.

We carried out a statistical study of equatorial dipolarization fronts (DFs) detected by the Magnetospheric Multiscale mission (MMS) during the full 2017 Earth’s magnetotail season. We found that two DF classes are distinguished: class I (74.4%) corresponds to the standard DF properties and energy dissipation and a new class II (25.6%). This new class includes the six DF discussed in Alqeeq et al. (2022) and corresponds to a bump of the magnetic field associated with a minimum in the ion and electron pressures and a reversal of the energy conversion process. The possible origin of this second class is discussed. Both DF classes show that the energy conversion process in the spacecraft frame is driven by the diamagnetic current dominated by the ion pressure gradient. In the fluid frame, it is driven by the electron pressure gradient. In addition, we have shown that the energy conversion processes are not homogeneous at the electron scale mostly due to the variations of the electric fields for both DF classes.

Dipolarization events with inductive, radial electric fields are examined, using Van Allen Probes data between 2013 and 2018. Two cases are studied, followed by statistical analyses. These events were observed between evening and premidnight magnetic local times (MLTs) under moderate geomagnetic activities. Radial electric field variations, azimuthal magnetic field variations, and energetic protons were often observed when horizontal magnetic fields started to decrease in the dip region. Magnetic field lines were stretched with their motion similar to the gradient B/curvature drift velocities of energetic protons. Signs of electric fields changed when horizontal magnetic fields started to increase in the dipolarization front (DF). Electric field variations were correlated with magnetic field ones with ~ 90 deg. phase shift. These observations are mainly interpreted in terms of energetic proton structures drifting toward the probe locations, while being accompanied by standing waves.

We present observations in Earth’s magnetotail by the Magnetospheric Multiscale spacecraft that are consistent with magnetic field annihilation, rather than magnetic topology change, causing fast magnetic-to-electron energy conversion in an electron-scale current sheet. Multi-spacecraft analysis for the magnetic field reconstruction shows that an electron-scale magnetic island was embedded in the observed electron diffusion region (EDR), suggesting an elongated shape of the EDR. Evidence for the annihilation was revealed in the form of the island growing at a rate much lower than expected for the standard collisionless reconnection, which indicates that magnetic flux injected into the EDR was not ejected from the X-point or accumulated in the island, but was dissipated in the EDR. This energy conversion process is in contrast to that in the standard EDR of a reconnecting current sheet where the energy of antiparallel magnetic fields is mostly converted to electron bulk-flow energy. Fully kinetic simulation also demonstrates that an elongated EDR is subject to the formation of electron-scale magnetic islands in which fast but transient annihilation can occur. Consistent with the observations and simulation, theoretical analysis shows that fast magnetic diffusion can occur in an elongated EDR in the presence of nongyrotropic electron effects. We suggest that the annihilation in elongated EDRs may contribute to the dissipation of magnetic energy in a turbulent collisionless plasma.

We investigate electron whistler wave activity in the flux pile-up region of an asymmetric reconnection event at the magnetopause. The ~140Hz waves are right-hand polarized with a wave normal angle of ~20 degrees and track the magnetic field strength, consistent with electron whistler waves. Poynting flux direction indicates that the waves were generated at the reconnection site. The waves modulated the flux of 500eV electrons propagating parallel and anti-parallel to the magnetic field, as observed by EDI. Only two of four MMS spacecraft observe similar wave activity, suggesting that the waves are isolated within a narrow flux tube. While it is not possible to use the wave telescope technique, current density produced by 500eV electrons provides a means of estimating the parallel wave vector, k, from a single spacecraft. In addition, we fit the FPI electron parallel energy distribution with a kappa function then use Liouville mapping with 500eV EDI electrons to determine the parallel wave potential, 𝝓, and electric field, E. Combining this with the wave normal angle and Poynting flux direction provides an estimate for the perpendicular components of k and E.

Decomposing the electric field (E) into the contributions from generalized Ohm’s law provides key insight into both nonlinear and dissipative dynamics across the full range of scales within a plasma. Using high-resolution, multi-spacecraft measurements of three intervals in Earth’s magnetosheath from the Magnetospheric Multiscale mission, the influence of the magnetohydrodynamic, Hall, electron pressure, and electron inertia terms from Ohm’s law, as well as the impact of a finite electron mass, on the turbulent spectrum are examined observationally for the first time. The magnetohydrodynamic, Hall, and electron pressure terms are the dominant contributions to over the accessible length scales, which extend to scales smaller than the electron inertial length at the greatest extent, with the Hall and electron pressure terms dominating at sub-ion scales. The strength of the non-ideal electron pressure contribution is stronger than expected from linear kinetic Alfvén waves and a partial anti-alignment with the Hall electric field is present, linked to the relative importance of electron diamagnetic currents in the turbulence. The relative contribution of linear and nonlinear electric fields scale with the turbulent fluctuation amplitude, with nonlinear contributions playing the dominant role in shaping for the intervals examined in this study. Overall, the sum of the Ohm’s law terms and measured agree to within ~20% across the observable scales. These results both confirm general expectations about the behavior of in turbulent plasmas and highlight features that should be explored further theoretically.

Electrostatic solitary waves (ESWs) are a type of nonlinear time-domain plasma structure (TDS) generally defined by bipolar electric fields and propagation parallel to the local magnetic field. Formation mechanisms for TDSs in the magnetosphere have been studied extensively and are associated with plasma boundary layers and the braking of bursty bulk flows (BBFs). However, the rapid timescales over which these TDSs occur (< 2 ms) make them infeasible to count by eye over large time periods. Furthermore, high-cadence data are not always available. The Solitary Wave Detector (SWD) on NASA’s Magnetospheric Multiscale (MMS) mission quantifies the occurrence and amplitude of TDS throughout the constellation’s orbit; analysis of burst (65 kS/s) parallel electric field data indicates that the SWD captures appx. 60% of all bipolar TDS encountered in the tail region, enabling large-scale examination of their occurrence. Maps of TDS occurrence rates during several years of the MMS mission were generated from SWD data, showing enhanced TDS density in the tail region between 6-9 Re; enhance occurrence in or near shocks; and an unexpected enhancement in the dawn side of the tail and in the radiation belt.

Recently a polynomial reconstruction technique has been developed for reconstructing the magnetic field in the vicinity of multiple spacecraft, and has been applied to events observed by the Magnetospheric Multiscale (MMS) mission. Whereas previously the magnetic field was reconstructed using spacecraft data from a single time, here we extend the method to allow input over a span of time. This extension increases the amount of input data to the model, improving the reconstruction results, and allows the velocity of the magnetic structure to be calculated. The effect of this modification, as well as many other options, is explored by comparing reconstructed fields to those of a three-dimensional particle in cell simulation of magnetic reconnection, using virtual spacecraft data as input. We often find best results using multiple-time input, a moderate amount of smoothing of the input data, and a model with a reduced set of parameters based on the ordering that the maximum, intermediate, and minimum values of the gradient of the vector magnetic field are well separated. When spacecraft input data are temporally smoothed, reconstructions are representative of spatially smoothed fields. Two MMS events are reconstructed. The first of these was late in the mission when it was not possible to use the current density for MMS4 because of its instrument failure. The second shows a rotational discontinuity without an X or O line. In both cases, the reconstructions yield a visual representation of the magnetic structure that is consistent with earlier studies.

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.

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.

Magnetic reconnection X-lines have been observed to be more common duskward of midnight. Thin current sheets have also been postulated to be a necessary precondition for reconnection onset. We take advantage of the MMS tetrahedral formation during the 2017--2020 MMS tail seasons to calculate the thickness of the cross-tail neutral sheet relative to ion gyroradius. While a similar technique was applied to Cluster data, current sheet thickness over a broader range of radial distances has not been robustly explored before this study. We compare this to recent theories regarding mechanisms of tail current sheet thinning and to recent simulations. We find MMS spent more than twice as long in ion-scale thin current sheets in the pre-midnight sector than post-midnight, despite nearly even plasma sheet dwell time. The dawn-dusk asymmetry in the distribution of Ion Diffusion Regions, as previously reported in relation to regions of thin current sheets, is also analyzed.

Flux Transfer Events (FTEs) are transient phenomena produced by magnetic reconnection at the dayside magnetopause typically under southward interplanetary magnetic field (IMF) conditions. They are usually thought of as magnetic flux ropes with helical structures forming through patchy, unsteady, or multiple X-line reconnection. While the IMF often has a non-zero $B_Y$ component, its impacts on the FTE flux rope helicity remain unknown. We survey Magnetospheric Multiscale (MMS) observations of FTE flux ropes during the years 2015 – 2017 and investigate the solar wind conditions prior to the events. By fitting a force-free flux rope model, we select 84 events with good fits and obtain the helicity sign (i.e., handedness) of the flux ropes. We find that positive (negative) helicity flux ropes are mainly preceded by a positive (negative) $B_Y$ component. This finding is compatible with flux ropes formed through a multiple X-line mechanism.