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We review the range of applications and use of the curlometer, initially developed to analyze electric current density using 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. The method (and associated methods based on spatial gradients) has been shown to be easily adaptable to other multi-point and multi-scale arrays. 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 investigated directly, such as: the cross-tail current sheet, ring current, the current layer at the magnetopause and field-aligned currents. In addition, the analysis can support investigations of transient and smaller scale current structures (e.g. reconnected flux tubes, boundary layer sub-structure, 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 combination with plasma measurements and the extension to larger arrays of spacecraft have recently been considered. We touch on these extensions and on new methodology accessing the properties of the underlying formulism.

We review a number of studies, undertaken during the 10 years of Swarm, using distributed, multi-scale measurements arising from the combination with Cluster, MMS and ground based arrays. The scaling, coherence and correlation of field-aligned current sheets (FACs) connecting different regions of the magnetosphere have been explored with associated analysis techniques using these multi-point measurements at both low (LEO) and high altitudes, and in relation to (R1/R2) auroral boundaries. Individual events can map to conjugate current density distributions at the magnetopause and ring current and regions in between; as well as to associated ground signatures, driven by the external conditions. Large and small-scale (MLT) trends in FAC orientation can be inferred from dual-spacecraft (e.g. the Swarm A&C spacecraft). Conjugate effects seen in ground (dH/dt), ionospheric and magnetospheric magnetic signals show that intense, coherent FA currents can take place in the polar cusp during the main phase of a geomagnetic storm and at near tail local times during substorm activity, at different altitudes. In the former event the mesoscale FACs show vertical scaling and a corresponding geomagnetic disturbance, driven by unsteady magnetic reconnection at the magnetopause. In the latter event, the most intense dH/dt is shown to be associated with FACs driven into the ionosphere by the arrival of bursty bulk flows BBFs at geosynchronous orbit (linked via a modified sub-storm current wedge, SCW). In situ ring current morphology can also be investigated by MMS, THEMIS and Cluster during the Swarm era, and can be compared to distributions of R2-FACs.

The Earth’s ring current forms a complex current system at the boundary of the inner magnetosphere. It is highly dynamic because of the interaction between the solar wind with the Earth's magnetosphere (the influence of space weather), while its morphology depends on the nature of the magnetospheric-ionospheric (M-I) coupling, generating field-aligned currents (FACs). Its behaviour can therefore have a huge impact on the terrestrial environment. According to Ampere's law, these currents can be directly measured by perturbations in the magnetic field using multi-spacecraft observation techniques. We have analyzed the magnetic field data from the four MMS spacecraft in their small-sale configuration to obtain the in-situ current density and have carried out statistical analysis from several years of data. The form of the current density distribution and its changing nature has been investigated. Our results show that the current density exhibits a three-dimensional layered structure in the ring current region. The significant westward current on the day side flows to higher magnetic latitudes and complete closure there rather than to the magnetic equator. There are some differences between geomagnetic quiet period and storm period on current density, but the basic spatial structure remains similar and compares well with previous space mission data. Comparison with Swarm data at low Earth altitudes, we found that the stratification is consistent with the distribution of the R2 field-aligned currents seen both adjacent to the ring current and at ionospheric altitudes (at Swarm). In addition, significant continuous eastward currents exist in some latitudes and some regions, indicating the complexity of the ring current. Some of them can be explained by the formation of banana currents.

We directly estimate the in situ current density of the Earth’s ring current (RC) using the curlometer method and investigate its morphology using the small spatial separations and high accuracy of the Magnetospheric Multiscale mission (MMS). Through statistical analysis of data from September 2015 to the end of 2016, covering the region of 2-8 RE (Earth radius, 6371 km), we reveal an almost complete near-equatorial (within ) RC morphology in terms of radial distance and local time (MLT) which complements and extends that found from previous studies. We found no evidence of RC enhancement on the dusk-side during geomagnetic active periods, but details of local time (MLT) asymmetries in, and the boundary between, the inner (eastward) and outer (westward) currents are revealed. We propose that part of the asymmetry demonstrated here suggests that in addition to the overall persistence of the westward RC, two large banana-like currents are directly observed, one which could arise from a peak of plasma pressure near ~4.8 RE on the noon side and the other from a valley of plasma pressure which could arise near ~4.8 RE on the night side.

During geomagnetically disturbed times the surface geomagnetic field often changes abruptly, producing geomagnetically induced currents (GICs) in a number of ground based systems. There are, however, few studies reporting GIC effects which are driven directly by bursty bulk flows (BBFs) in the inner magnetosphere. In this study, we investigate the characteristics and responses of the magnetosphere-ionosphere-ground system during the 7 January 2015 storm by using a multi-point approach which combines space-borne measurements and ground magnetic observations. During the event, multiple BBFs are detected in the inner magnetosphere while the magnetic footprints of both magnetospheric and ionospheric satellites map to the same conjugate region surrounded by a group of magnetometer ground stations. It is suggested that the observed, localized substorm currents are caused by the observed magnetospheric BBFs, giving rise to intense geomagnetic perturbations. Our results provide direct evidence that the wide-range of intense dB/dt (and dH/dt) variations are associated with a large-scale, substorm current system, driven by multiple BBFs.

Magnetospheric Multiscale (MMS) data are used to investigate the energy dissipation in a reconnection diffusion region at the magnetopause. The four MMS spacecraft were separated by about 10 km such that comparative study between each spacecraft within the diffusion region can be implemented. Similar magnetic field and electric current behavior between each spacecraft indicates the formation of a quasi-homogeneous diffusion region structure. However, we find that the energy dissipation results between each spacecraft are different due to the temporal or spatial effect of the out-of-plane merging electric field (EM) during the dissipation region. Our study suggests that the intermittent energy dissipation in the reconnection dissipation region can be a common phenomenon, even under a stable diffusion region structure.

The ring current is an important part of the large-scale magnetosphere-ionosphere current system; mainly concentrated in the equatorial plane, between 2-7 RE, and strongly ordered between ± 30 ° latitude. The morphology of ring current directly affects the geomagnetic field at low to middle latitudes. Rapid changes in ring current densities can occur during magnetic storms/sub-storms. Traditionally, the Dst index is used to characterize the intensity of magnetic storms and to reflect the variation of ring current intensity, but this index does not reflect the MLT distribution of ring current. In fact, the ring current has significant variations with MLT, depending on geomagnetic activity, due to the influence of multiple factors; such as, the partial ring current, region 1/region 2 field-aligned currents, the magnetopause current and sub-storm cycle (magnetotail current). The form of the ring current has been inferred from the three-dimensional distribution of ion differential fluxes from neutral atom imaging; however, this technique can not directly obtain the current density distribution (as can be obtained using multi-spacecraft in situ data). Previous in situ estimates of current density have used: Cluster, THEMIS and other spacecraft groups to study the distribution of the ring current for limited ranges of either radial profile, or MLT and MLAT variations. Here, we report on an extension to these studies using FGM data from MMS obtained during the period September 1, 2015 to December 31, 2016, when the MMS orbit and configuration provided good coverage. We employ the curlometer method to calculate the current density, statistically, to analysis the MLT distribution according to different geomagnetic conditions. Our results show the clear asymmetry of the ring current and its different characteristics under different geomagnetic conditions.

The orientation of field-aligned current sheets (FACs) can be inferred from dual-spacecraft correlations of the FAC signatures between two Swarm spacecraft (A and C), using the maximum correlations obtained from sliding data segments. Statistical analysis of both the correlations and the inferred orientations shows clear trends in magnetic local time (MLT) which reveal behaviour of both large and small scale currents. The maximum correlation coefficients show distinct behaviour in terms of either the time shift, or the shift in longitude between Swarm A and C for various filtering levels. The lower-latitude FACs show the strongest correlations for a broad range of MLT centred on dawn and dusk, with a higher correlation coefficient on the dusk-side and lower correlations near noon and midnight, and broadly follow the mean shape of the auroral boundary for the lower latitudes corresponding to Region 2 FACs (and are most well-ordered on the dusk side). Individual events sampled by higher altitude spacecraft (e.g. the 4 Cluster spacecraft), in conjunction with Swarm (mapping both to region 1 and 2), also show two different domains of FACs: time variable, small-scale (10s km), and more stationary large-scale (>100 km) FACs. We investigate further how these FAC regimes are dependent on geomagnetic activity, focusing on high activity events. Both the statistical trends, and individual conjugate events, show comparable effects seen in the ground magnetometer signals (dH/dt) during storm/substorm activity and show distributions that are similar.

Magnetic reconnection is a universal physical process during which energy can be transferred from the electromagnetic field to the plasma. Energy dissipation in the diffusion region has always been a significant issue for understanding this energy transport. Using the four MMS spacecraft data, we investigate a magnetic reconnection diffusion region event at the magnetopause. Similar magnetic field and electric current behavior between each spacecraft indicates the formation of a quasi 2D structure. However, we find that the energy dissipation results of each spacecraft are different. Further analysis indicates that the reconnection electric field, EM, plays a key role in this process. Thus, we suggest that the energy dissipation of magnetic reconnection is unsteady on this spatial or temporal scale, even under stable diffusion conditions.

During geomagnetically disturbed times, geomagnetically induced currents (GICs) flow in power systems potentially causing damage to the system. The largest GICs are often produced when the surface geomagnetic field abruptly changes (for example, an induced rate of change of the horizontal magnetic field component, dH/dt). It is well established that intense dB/dt variations take place in the main phase of a geomagnetic storm, particularly while magnetic substorms occur during the active period. However, there are currently few studies that report intense dB/dt variations which are directly driven by bursty bulk flows (BBFs) at geosynchronous orbit. In this study, we investigate the characteristics and response in the magnetosphere-ionosphere system during the recovery phase of a geomagnetic storm that occurred on 7 January 2015 by using a multi-point approach combining space-borne Cluster and SWARM measurements, and a group of ground-based magnetometer observations. The locations of Cluster and SWARM map to the same conjugate region as the magnetometer ground stations at the time of the BBF. The measurements show that corresponding signals in all measurements occur simultaneously in this region. Our results suggest that the most intense dB/dt (dH/dt) variations are associated with R1-type FACs that are driven by BBFs at geosynchronous orbit around substorm onset.

Using the Parker Solar Probe measurements, this Letter reports two new types of multiband electrostatic waves in and near the heliospheric current sheet. They are classified into the f < f ce and f > f ce multiband electrostatic waves, in which most (or all) of the bands in the former type are lower than f ce, and all of the bands in the latter type are higher than f ce, where f and f ce denotes the wave frequency and the electron cyclotron frequency, respectively. This Letter also exhibits observational evidence of the existence of nonlinear wave–wave interactions of both types of electrostatic waves. In particular, the f > f ce multiband electrostatic waves are found to be modulated in the presence of low-frequency oblique ion-scale waves. According to the observed frequency distribution, this Letter proposes that the mode nature of the f < f ce multiband electrostatic waves could be the oblique ion acoustic wave or the lower-hybrid wave, and the f > f ce multiband electrostatic waves are the electron Bernstein mode wave. These findings provide a challenge to understand the complex electron and ion dynamical processes in and near the heliospheric current sheet.

We investigate a series of three small-scale flux transfer events (FTEs) associated with reconnected flux ropes, recently generated by a nearby, dayside magnetic reconnection line. The data are observed by the Magnetospheric Multiscale spacecraft near noon local time. We find that the associated FTEs are created by secondary magnetic reconnection and have different magnetic field topologies, which is a similar condition to that expected in the multiple X-line magnetic reconnection (MR) model. The calculated results show that the sizes of the FTEs become larger with the time elapsed and the MR reconnection jets at the FTEs are all located on the trailing and outer edges. The above features indicate that these FTEs are still in the evolutionary stage after they are ejected from the reconnection region. Our observations suggest that mesoscale or even typical size FTEs can be created from secondary MR, initially, and subsequently can evolve to a typical size in the process of spreading.

Alfv\'en vortex is a multi-scale nonlinear structure which contributes to intermittency of turbulence. Despite previous explorations mostly on the spatial properties of the Alfv\'en vortex (i.e., scale, orientation, and motion), the plasma characteristics within the Alfv\'en vortex are unknown. Moreover, the connection between the plasma energization and the Alfv\'en vortex still remains unclear. Based on high resolution in-situ measurement from the Magnetospheric Multiscale (MMS) mission, we report for the first time, distinctive plasma features within an Alfv\'en vortex. This Alfv\'en vortex is identified to be two-dimensional ($k_{\bot} \gg k_{\|}$) quasi-monopole with a radius of ~10 proton gyroscales. Its magnetic fluctuations $\delta B_{\bot}$ are anti correlated with velocity fluctuations $\delta V_{\bot}$, thus the parallel current density $j_{\|}$ and flow vorticity $\omega_{\|}$ are anti-aligned. In different part of the vortex (i.e., edge, middle, center), the ion and electron temperatures are found to be quite different and they behave in the reverse trend: the ion temperature variations are correlated with $j_{\|}$, while the electron temperature variations are correlated with $\omega_{\|}$. Furthermore, the temperature anisotropies, together with the non-Maxwellian kinetic effects, exhibit strong enhancement at peaks of $|\omega_{\|}| (|j_{\|}|)$ within the vortex. Comparison between observations and numerical/theoretical results are made. In addition, the energy-conversion channels and the compressibility associated with the Alfv\'en vortex are discussed. These results may help to understand the link between coherent vortex structures and the kinetic processes, which determines how turbulence energy dissipate in the weakly-collisional space plasmas.

We investigate the current carriers and current sources of an ion scale tangential magnetopause current layer using the Magnetospheric Multiscale four spacecraft data. Within this magnetopause current layer, ions and electrons equally contribute to the perpendicular current, while electrons carry nearly all the parallel current. The energy range of all these current carriers is predominantly from middle to high (>100 eV), where particles with higher energies are more efficient in producing the current. By comparing each term, two-fluid magnetohydrodynamic (MHD) theory is able to describe the current sources to a large degree because the sum of all the perpendicular currents from MHD theory could account for the currents observed. In addition, we find that the ion diamagnetic current is the main source of the total perpendicular current, while the curvature current can be neglected. Nevertheless, ions and electrons both carry comparable current due to the redistribution of the electric field and show features beyond the classic Chapman-Ferraro model, particularly on the front side of the boundary layer where the electric field reversal is most intense. We also show a second, comparative event in which ions do not satisfy MHD theory, while the electrons do. The small-scale, adiabatic parameter (square of curvature radius/gyroradius) supports our interpretation that this second event contains ion scale substructure. We suggest that comparing the predicted MHD current with plasma current can be a good method to judge whether the MHD theory is satisfied in each specific circumstance, especially for high-precision Magnetospheric Multiscale data.

Most studies on low-frequency electromagnetic cyclotron waves have assumed a small wave amplitude, which ensures the reasonable application of linear and quasi-linear theories. However, the topic of large-amplitude electromagnetic cyclotron waves has not received much attention. Using Magnetospheric Multiscale measurements, this study observes low-frequency, left-hand circularly polarized electromagnetic waves with magnetic fluctuation similar to 1-2 nT in the dusk flank side of the Earth's magnetosheath. Considering the ambient magnetic field similar to 15 nT therein, the relative wave amplitude is of the order of 0.1. These large magnetic field fluctuations result in a periodic variation of the ion pitch angle. The electron pitch angle exhibits a localized distribution feature with a timescale approximating the wave period. Moreover, some electrons are trapped at a pitch angle similar to 90 degrees, and the trapping is more remarkable as strong waves arise. These two features of the electron pitch angle distribution imply that the trapping of electrons (partly) results from large-amplitude electromagnetic cyclotron fluctuations. Our results illustrate the important role of large-amplitude electromagnetic cyclotron waves on the dynamics of charged particles.

Based on the theory of plasma continuous radiation, the relationship between the emission intensity of bremsstrahlung and recombination radiation and the plasma electron temperature is obtained. During the development process of a return stroke of ground flash, the intensity of continuous radiation spectrum is separated on the basis of the spectrums with obviously different luminous intensity at two moments. The electron temperature of the lightning discharge channel is obtained through the curve fitting of the continuous spectrum intensity. It is found that electron temperature increases with the increase of wavelength and begins to reduce after the peak. The peak temperature of the two spectra is close to 25 000 K. To be compared with the result of discrete spectrum, the electron temperature is fitted by the O I line and N II line of the spectrum respectively. The comparison shows that the high temperature value is in good agreement with the temperature of the lightning core current channel obtained from the ion line information, and the low temperature at the high band closes to the calculation result of the atomic line, at a low band is lower than the calculation of the atomic line, which reflects the temperature of the luminous channel of the outer corona.