We review the range of applications and use of the curlometer, initially developed to analyze Cluster multi‐spacecraft magnetic field data; but more recently adapted to other arrays of spacecraft flying in formation, such as MMS small‐scale, 4‐spacecraft configurations; THEMIS close constellations of 3–5 spacecraft, and Swarm 2–3 spacecraft configurations. Although magnetic gradients require knowledge of spacecraft separations and the magnetic field, the structure of the electric current density (for example, its relative spatial scale), and any temporal evolution, limits measurement accuracy. Nevertheless, in many magnetospheric regions the curlometer is reliable (within certain limits), particularly under conditions of time stationarity, or with supporting information on morphology (for example, when the geometry of the large scale structure is expected). A number of large‐scale regions have been covered, such as: the cross‐tail current sheet, ring current, the current layer at the magnetopause and field‐aligned currents. Transient and smaller scale current structures (e.g., reconnected flux tube or dipolarisation fronts) and energy transfer processes. The method is able to provide estimates of single components of the vector current density, even if there are only two or three satellites flying in formation, within the current region, as can be the case when there is a highly irregular spacecraft configuration. The computation of magnetic field gradients and topology in general includes magnetic rotation analysis and various least squares approaches, as well as the curlometer, and indeed the added inclusion of plasma measurements and the extension to larger arrays of spacecraft have recently been considered.

In this study, we use the magnetic field data measured by MErcury Surface, Space ENvironment, GEochemistry, and Ranging from 2011 to 2015 to investigate the average magnetic field morphology of Mercury's magnetotail in the down tail 0–3 R_M (R_M = 2,440 km, Mercury's radius). It is found that Mercury has a terrestrial‐like magnetotail; the magnetic field structure beyond 1.5 R_M down tail is stretched significantly with typical lobe field 50 nT. A cross‐tail current sheet separating the antiparallel field lines of lobes is present in the equatorial plane. The magnetotail width in north‐south direction is about 5 R_M, while the transverse width is about 4 R_M. Thus, the magnetotail shows elongation along the north‐south direction. At the cross‐tail current sheet center, the normal component of magnetic field (10–20 nT) is much larger than the cross‐tail component. The lobe‐field‐aligned component of magnetic field over current sheet can be well fitted by Harris sheet model. The curvature radius of field lines at sheet center usually reaches a minimum around midnight (100–200 km) with stronger current density (40–50 nA/m²), while the curvature radius increases toward both flanks (400–600 km) with the decreased current density (about 20 nA/m²). The half‐thickness of current sheet around midnight is about 0.25 R_M or 600 km, and the inner edge of current sheet is located at the down tail about 1.5 R_M. Our results about the field structure in the near Mercury's tail show an evident dawn‐dusk asymmetry as that found in the Earth's magnetotail, but reasons should be different. Possible reasons are discussed.

General relativity (GR) is a well-tested theory of gravity in strong and weak field regimes. Many modifications to this theory were obtained, including different scalar, vector, and tensor fields to the GR with non-minimal coupling to gravity. Kalb–Ramond (KR) gravity is also a modified theory formulated in the presence of a bosonic field. One astrophysical way to test gravity is by studying the motion of test particles in the spacetime of black holes (BH). In this work, we study the circular motion of charged particles and explore energetic processes around charged BHs in KR theory. First, we investigated the event horizon radius and analyzed horizon-no horizon regions in the BH charge and KR parameter space. Considering the Coulomb interaction, we derive and analyze the effective potential for charged particles around a charged KR BH. We investigate charged particles’ angular momentum and energy corresponding to circular orbits. We also investigate how the KR non-minimal coupling parameter affects the radius of the innermost stable circular orbits, the corresponding energy, and the angular momentum. We also investigated the electric Penrose process and charged-particle collisions near the KR BH. The presence of the nonzero KR parameter results in a decrease in the energy efficiency of the Penrose process. Also obtained is that the KR parameter’s positive (negative) values cause a decrease (increase) in the center of mass energy of colliding particles near the BH horizon.

Flapping motion of the current sheets of planetary magnetotails is a common dynamic phenomenon. Previous studies of the Earth's magnetotail suggest that its flapping motion has two forms, that is, kink‐like flapping that can propagate as waves toward both flanks and steady flapping that moves up and down but does not propagate. Although some models have been proposed to explain the kink‐like flapping, its mechanism remains unclear. This paper surveys 87 flapping events statistically with respect to their flapping types, using the multipoint measurements of Cluster. The statistical results show that the up‐down steady flapping events tend to occur around the midnight region, and the kink‐like flapping events tend to occur near both flanks of the magnetotail. Thus, we propose that kink‐like flapping motion is causally related to steady flapping motion; that is, the up and down motion of steady flapping around the midnight region induces kink‐like flapping waves, which propagate toward both flanks of the magnetotail.

In this study, the Empirical Mode Decomposition algorithm (EMD) and the Long Short Term Memory neural network (LSTM) are combined into an EMD‐LSTM model, to predict the variation of the >2 MeV electron fluxes 1 day ahead. Input parameters include the Pc5 power, AP, AE, Kp, >0.6 MeV, and historical electron flux values, are used for predictions. All the time resolution of parameters are daily integral values. As compared the prediction results of the EMD‐LSTM model with other classical prediction models, the results show that the 1 day ahead prediction efficiency of the >2 MeV electron fluxes possesses a prediction efficiency of 0.80, and the highest prediction efficiency can reach 0.93. These results are superior to the prediction accuracy of more previous models. Using two high‐energy electron flux storm events for validation, the results indicate that the performance of the EMD‐LSTM model in the period of the high‐energy electron flux storm is also relatively good, especially for the prediction of high‐energy electron fluxes at extreme points, and the predictions are closer to actual observations.