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.

An $LMN$ coordinate system for magnetic reconnection events is sometimes determined by defining $N$ as the direction of the gradient across the current sheet and $L$ as the direction of maximum variance of the magnetic field. The third direction, $M$, is often assumed to be the direction of zero gradient, and thus the orientation of the X line. But when there is a guide field, the X line direction may have a significant component in the L direction defined in this way. For a 2D description, a coordinate system describing such an event would preferably be defined using a different coordinate direction $M’$ oriented along the X line. Here we use a 3D particle-in-cell simulation to show that the X line is oriented approximately along the direction bisecting the asymptotic magnetic field directions on the two sides of the current sheet. We describe two possible ways to determine the orientation of the X line from spacecraft data, one using the minimum gradient direction from Minimum Directional Derivative analysis at distances of the order of the current sheet thickness from the X line, and another using the bisection direction based on the asymptotic magnetic fields outside the current sheet. We discuss conditions for validity of these estimates, and we illustrate these conditions using several Magnetospheric Multiscale (MMS) events. We also show that intersection of a flux rope due to secondary reconnection with the primary X line can destroy invariance along the X line and negate the validity of a two-dimensional description.

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.

Magnetic reconnection converts magnetic energy into particle energy, with ion outflows being a prominent manifestation, particularly in geospace. Hall fields are indicators of rapid energy conversion in collisionless magnetic reconnection, yet the associated ion processes and signatures are not fully understood. Here, we analyze in-situ data and simulations to identify a distinct signature in the off-diagonal component of the ion pressure tensor. This signature displays a bipolar reversal that correlates with ion outflows across the reconnection X-line. The bipolar signal arises from a distorted velocity distribution during ion acceleration. Initially, Hall electric fields induce dawnward ion motion, which is followed by enhanced ion acceleration due to reconnection electric fields during cyclotron motion around the reconnected magnetic field. This interaction distorts the velocity distribution, producing the observed bipolar signals. The off-diagonal component of the ion pressure tensor reflects increased ion acceleration and energy conversion due to Hall electric fields.

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 electron-scale current sheet (ECS), which were observed on 8 December 2015 by the Magnetospheric Multiscale spacecraft near the subsolar magnetopause under southward and duskward magnetosheath magnetic field conditions. Our aims are to understand the generation mechanism of ion-scale magnetic flux ropes (ISFRs) and to reveal causal relationship among magnetic structures of the ECS, electromagnetic energy conversion, and kinetic processes in magnetic reconnection layers. Magnetic field reconstruction methods show that a flux rope with a length of about one ion inertial length existed and was growing in the ECS, supporting the idea that ISFRs can be generated from secondary magnetic reconnection in ECS. Grad-Shafranov reconstruction applied to the three FTEs shows that the FTE flux ropes had axial orientations similar to that of the ISFR in the ECS. 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 suggest that the ISFR had three-dimensional magnetic topology and secondary reconnection was patchy or bursty. Previously reported positive and negative values of , with magnitudes much larger than expected for typical magnetopause 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.

Space plasmas are composed of charged particles that play a key role in electromagnetic dynamics. However, to date, there has been no direct measurement of the distribution of such charges in space. In this study, three schemes for measuring charge densities in space are proposed. The first scheme is based on electric field measurements by multiple spacecraft. This method is applied to deduce the charge density distribution within Earth’s magnetopause boundary layer using Magnetospheric MultiScale constellation (MMS) 4-point measurements, and indicates the existence of a charge separation there. The second and third schemes proposed are both based on electric potential measurements from multiple electric probes. The second scheme, which requires 10 or more electric potential probes, can yield the net charge density to first-order accuracy, while the third scheme, which makes use of seven to eight specifically distributed probes, can give the net charge density with second-order accuracy. The feasibility, reliability, and accuracy of these three schemes are successfully verified for a charged-ball model. These charge density measurement schemes could potentially be applied in both space exploration and ground-based laboratory experiments.

Lower hybrid waves are investigated at the magnetosheath separatrix region in asymmetric guide-field reconnection by using the Magnetospheric Multiscale (MMS) mission. Three of the four MMS spacecraft observe clear wave activities around the lower hybrid frequency across the magnetosheath separatrix, where a density gradient is present. The observed waves are consistent with generation by the lower hybrid drift instability. The characteristic properties of these waves include: (1) the waves propagate toward the x-line in the spacecraft frame due to the large out-of-plane magnetic field, which is in the same direction of the diamagnetic drift of the x-line; (2) the wave potential is about 20\% of the electron temperature. These drift waves effectively produce cross-field particle diffusion, enabling the transport of magnetosheath electrons into the exhaust region. The observations presented in this study indicate unique features of asymmetric guide-field reconnection.

In this paper, we analyzed the fine structure of the rotational discontinuity (RD) in the magnetopause of the open magnetosphere by using the MMS four-point magnetic field measurements. It is found that RD is very common within the magnetopause when reconnection occurs at the magnetopause. Furthermore, RD usually occurs closer to the magnetosheath side of the magnetopause. RD is very thin and its thickness is usually much smaller than 0.1 Re. The magnetic field rotation maximums and magnetic strength minimums within the RD. The radius of curvature of the magnetic field lines reaches its minimum value in the RD (~0.03-0.62 Re). In addition, the radius of curvature of magnetic field line of RD is usually larger than the thickness of RD structure, indicating that the magnetic field lines are partly lying in the RD. Generally，the field-aligned current dominates in the RD.

Whistler waves are often observed in magnetopause reconnection associated with electron beams. We analyze seven MMS crossings surrounding the electron diffusion region (EDR) to study the role of electron beams in whistler excitation. Waves have two major types: (1) Narrow-band waves with high ellipticities and (2) broad-band waves that are more electrostatic with significant variations in ellipticities and wave normal angles. While both types of waves are associated with electron beams, the key difference is the anisotropy of the background population, with perpendicular and parallel anisotropies, respectively. The linear instability analysis suggests that the first type of wave is mainly due to the background anisotropy, with the beam contributing additional cyclotron resonance to enhance the wave growth. The second type of distribution excites broadband waves via Landau resonance, and as seen in one event, the beam anisotropy induces an additional cyclotron mode. The results are supported by particle-in-cell simulations. We infer that the first type occurs downstream of the central EDR, where background electrons experience Betatron acceleration to form the perpendicular anisotropy; the second type occurs in the central EDR of guide field reconnection. A parametric study is conducted with linear instability analysis. A beam anisotropy alone of above ~3 likely excites the cyclotron mode waves. Large beam drifts cause Doppler shifts and may lead to left-hand polarizations in the ion frame. Future studies are needed to determine whether the observation covers a broader parameter regime and to understand the competition between whistler and other instabilities.

We report observations of the ion dynamics inside an Alfven branch wave that propagates near the reconnecting dayside magnetopause. The measured frequency, wave normal angle and polarization are within 1% with the predictions of a dispersion solver, and indicate that the wave is an electromagnetic ion cyclotron wave with very oblique wave vector. The magnetospheric plasma contains hot protons (keV), cold protons (eV), plus some heavy ions. The cold protons follow the magnetic field fluctuations and remain frozen-in, while the hot protons are at the limit of magnetization. The cold proton velocity fluctuations contribute to balance the Hall term in Ohm’s law, allowing the wave polarization to be highly-elliptical and right-handed, a necessary condition for propagation at oblique wave normal angles. The dispersion solver indicates that increasing the cold proton density facilitates generation and propagation of these waves at oblique angles, as it occurs for the observed wave.

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.

Based on direct measurement by the MMS spacecraft in the years of 2017 and 2018, we perform studies on the vorticity field () within the reconnection jet in the plasma sheet. A typical event on 26 July 2017 shows clearly the evolution of the field with the jet velocity: is weak in the decelerated BBF and strong in the fast BBF. The strongest -field is in the decaying BBF, around the dipolarization fronts. Despite the evolution of the BBF, the -field is characterized by the perpendicular vorticity (ω). Statistical results confirm the close correlation between BBF and . Higher means stronger . This accounts for the dawn-dusk asymmetry of the -field. The anisotropic is more significant in the V-dominating BBF than in the V-dominating BBF. The -field within the reconnection jet is β-dependence. The β-dependence -field tends to be stronger in super-M jet than in sub-M jet.