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.

Two-dimensional hybrid particle-in-cell (PIC) simulations are carried out on a constant L-shell (or drift shell) surface of the dipole magnetic field to investigate the generation process of near-equatorial fast magnetosonic waves (a.k.a equatorial noise; MSWs hereafter) in the inner magnetosphere. The simulation domain on a constant L-shell surface adopted here allows wave propagation and growth in the azimuthal direction (as well as along the field line) and is motivated by the observations that MSWs propagate preferentially in the azimuthal direction in the source region. Furthermore, the equatorial ring-like proton distribution used to drive MSWs in the present study is (realistically) weakly anisotropic. Consequently, the ring-like velocity distribution projected along the field line by Liouville’s theorem extends to rather high latitude, and linear instability analysis using the local plasma conditions predicts substantial MSW growth up to +- 27deg latitude. In the simulations, however, the MSW intensity maximizes near the equator and decreases quasi-exponentially with latitude. Further analysis reveals that the stronger equatorward refraction at higher latitude due to the larger gradient of the dipole magnetic field strength prevents off-equatorial MSWs from growing continuously, whereas MSWs of equatorial origin experience little refraction and can fully grow. Furthermore, the simulated MSWs exhibit a rather complex wave field structure varying with latitude, and the scattering of energetic ring-like protons in response to MSW excitation occurs faster than the bounce period of those protons so that they do not necessarily follow Liouville’s theorem during MSW excitation.

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.

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.

A method based on electron magnetohydrodynamics (EMHD) for the reconstruction of steady, two-dimensional plasma and magnetic field structures from data taken by a single spacecraft, first developed by Sonnerup et al. (2016), is extended to accommodate inhomogeneity of the electron density and temperature, electron inertia effects, and guide magnetic field in and around the electron diffusion region (EDR), the central part of the magnetic reconnection region. The new method assumes that the electron density and temperature are constant along, but may vary across, the magnetic field lines. We present two models for the reconstruction of electron streamlines, one of which is not constrained by any specific formula for the electron pressure tensor term in the generalized Ohm’s law that is responsible for electron unmagnetization in the EDR, and the other is a modification of the original model to include the inertia and compressibility effects. Benchmark tests using data from fully kinetic simulations show that our new method is applicable to both antiparallel and guide-field (component) reconnection, and the electron velocity field can be better reconstructed by including the inertia effects. The new EMHD reconstruction technique has been applied to an EDR of magnetotail reconnection encountered by the Magnetospheric Multiscale spacecraft on 11 July 2017, reported by Torbert et al. (2018) and reconstructed with the original inertia-less version by Hasegawa et al. (2019), which demonstrates that the new method better performs in recovering the electric field and electron streamlines than the original version.

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 elongated electron-scale current sheet. This energy conversion process is in contrast to that in the standard electron diffusion region (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 energy conversion is dominated by the annihilation. 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. The discovery of the annihilation-dominated EDR reveals a new form of energy conversion in the collisionless reconnection process.

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.