The work analyzes dependences of eddy diffusion coefficients in the X, Y, and Z directions of the GSM coordinate system on the plasma parameter β, taking into account the distance from Earth, the direction of the interplanetary magnetic field, and conditions of geomagnetic activity in the magnetotail according to MMS mission data. These parameters are determined by root-mean-square velocities of ions and their autocorrelation time. Eddy diffusion coefficients characterize the magnitude of turbulent transport in the magnetotail and are the parameters of the model of turbulent plasma sheet. We have analyzed more than 20000 12-min intervals during which the MMS satellites were located within a region with plasma density more than 0.1 cm–3 and average ion energy more than 0.5 keV. It is shown that as the plasma parameter increases, the eddy diffusion coefficients increase as well. This increase stops at β~1. Analysis of the relative contribution of changes in root-mean-square velocity and autocorrelation time to the eddy diffusion coefficient has revealed that there is no significant dependence on autocorrelation time.

The spectra of fluctuations of electric and magnetic fields in the plasma sheet of the Earth’s magnetotail according to Magnetospheric Multiscale Mission data were statistically analyzed for the years 2017–2022 during periods with small plasma velocity. The results of measurements of the FIELDS instrument suite were considered. Three-hour intervals were identified, during which the satellites were inside the plasma sheet and the plasma parameter β > 1. Over 100 thousand spectra of fluctuations of the electric field by the EDP/DCE instrument and the magnetic field by the FGM instrument were analyzed. Intervals with plasma velocities exceeding 100 km/s were excluded. For each interval, the spectral indices were calculated in the frequency range 0.014–16 Hz. It is shown that the values of the spectral indices differ significantly for the electric and magnetic fields. The dependences of the spectral indices on the fluctuations of the electric and magnetic fields averaged over the interval are obtained.

The geophysical processes in the dayside polar cusp on December 22, 2003 under the northern orientation of the interplanetary magnetic field (IMF), relatively high speed and low density of the solar wind by using the ground-based optical observations on Spitsbergen and DMSP F16 spacecraft observations were examined. A comparison of spacecraft and ground-based observations shows that soft electron precipitation in the cusp region determine the region of the auroral luminosity in the (OI) 630.0 nm emission. The peculiarity of the event under consideration is the observation of a bright rayed auroral arc bordering the dayside cusp from its polar edge. The results of observations of the low-altitude DMSP F16 spacecraft during its pass over the rayed arc were analyzed. Explanations of the observed phenomena are proposed based on the analysis of changes in the spectra of precipitating electrons and the formation of an electron beam by a field-aligned electric field.

In the present study, the influence of the solar wind dynamic pressure on the plasma and magnetic pressures of the magnetosphere is studied. We use 11-year Time History of Events and Macroscale Interactions during Substorms (THEMIS) instruments for plasma and magnetic field measurements in the magnetosphere and the OMNI database for solar wind dynamic pressure and IMF data. We focus on the effects of the solar wind dynamic pressure (PSW) and consider only times in which the interplanetary magnetic field (IMF) components are within +/- 5 nT. We find that the plasma pressure inside the magnetosphere follows the solar wind dynamic pressure and that an increase in PSW also influence the day-night pressure asymmetry. Our analysis also reveals the existence of ion and electron drifts from midnight toward the dusk and dawn sectors, respectively. We observe a local magnetic pressure minimum located near a plasma pressure maximum at around 11 RE on the nightside. Comparing the effect of PSW on both plasma and magnetic pressures, we observe trends which are consistent with the diamagnetic properties of plasmas. In general, the distribution of plasma pressure within the Earth's magnetosphere is an important criterion for evaluating the magnetostatic equilibrium and electric current system. The outcome of this study should provide additional methodologies for the characterization of key plasma characteristics within the magnetosphere. Magnetospheric activity and space weather are driven by the interaction of the solar wind and the Earth's magnetic field. The solar wind dynamic pressure and interplanetary magnetic field (IMF) are two important factors that affect the behavior of the Earth's magnetosphere. The interaction between these two factors are complex and can have significant effects on our planet. Based on 11-year plasma and magnetic field measurements, obtained from THEMIS satellites, we investigated the effect of solar wind dynamic pressure on the plasma and magnetic pressures within the Earth magnetosphere. In this study, we show that changes in the plasma pressure within the magnetosphere are linked to variations in the solar wind dynamic pressure. Our findings confirm that the plasma pressure inside the magnetosphere is mainly controlled by the solar wind dynamic pressure, which can be attributed to pressure balance. Overall, the distribution of plasma pressure within the Earth's magnetosphere is a key parameter for evaluating the magnetostatic equilibrium and electric current system. Our results are expected to offer scientists additional methodologies for characterizing main plasma parameters in the magnetosphere. Increase in solar wind dynamic pressure leads to increase in plasma and magnetic pressures in the magnetosphere Larger solar wind dynamic pressure make the plasma pressure more symmetric around the Earth Observations reveal a local magnetic pressure minimum located near a plasma pressure maximum around 11RE on the nightside

Geophysical processes in the region of the dayside polar cusp on December 22, 2003, were studied for a northern orientation of the interplanetary magnetic field (IMF) and a relatively high-velocity, low-density solar wind, using ground-based optical observations in Svalbard and DMSP F16 satellite data. Comparison of satellite and ground-based observations shows that soft electron precipitation in the cusp region determines the auroral glow in the 630.0 nm (OI) emission. The peculiarity of the considered event is observation of a bright rayed arc of the aurora rimming the dayside cusp from its polar edge. The results of observations by the low-flying DMSP F16 satellite as it intersected the rayed arc were analyzed. Explanations for the observed phenomena are proposed, based on analysis of changes in the spectra of precipitating electrons and formation of a field-aligned electron beam by the field-aligned electric field.

The start of the space era marked the discovery of the Earth’s radiation belts. Sixty-five years after that discovery, there are still many unknowns in its dynamics, but there is also a lot of understanding about many processes. This review summarizes a broad overview of a particular topic: the effect of geomagnetic storms on the radiation belts from a historical perspective. In writing this review, we aim to preserve, rescue, and put together the initial attempts at understanding the radiation belts since most of the literature is somewhat hidden or forgotten. This is particularly relevant for students and young researchers, who did not live the initial stages of the space age. To help in this endeavor, we included the description of the main satellite missions and their instruments starting from the first satellites like Sputnik and Explorer and finishing with contemporary missions like Van Allen Probes and Arase, and different techniques. In this review, we also tried to include the majority of points of view about the dynamics of radiation belts, giving everybody a chance to analyze them and make their conclusions. We selected a limited number of papers from one side that are representative with respect to a specific topic and from the other side help to see the evolution of our knowledge about radiation belts. We made a special tribute to pioneering works of the 50s and 60s and also included some interesting results, which are almost impossible to read in English. So this review is a good starting point for navigating the ocean of modern space physics related to the outer radiation belt.

The Earth's magnetosphere is filled with a collisionless plasma that exhibits non-Maxwellian particle distributions which are well described by Kappa functions. In contrast to the Maxwellian, the Kappa contains not only density and temperature but also the kappa index that allows us to characterize the energetic tails. In this study, we analyze the response of the ion and electron Kappa distributions, obtained by fitting ion and electron fluxes measured by the five THEMIS satellites, to changes of the solar wind dynamic pressure. It was found that the solar wind dynamic pressure strongly affects the values of the kappa index, and that its impact depends on the magnetic local time (MLT). In particular, there is a significant dawn-dusk asymmetry for low PSW values which is enhanced in the night side. Further, we observe a narrow partial ring-shaped structure at different azimuthal extension that divides the plasma into two clearly defined domains. The results obtained reflect the global reconfiguration of the magnetosphere caused by variations of the solar wind dynamic pressure. Kappa distribution parameters and their average values for different ranges of PSW and MLT are provided, which we believe will contribute as realistic inputs to the modeling of the magnetosphere. The Kappa distribution function, which combines the Maxwellian-type and the power-law distributions, has been widely used in literature to describe particle populations in space and astrophysical plasmas. In such environments, ions and electrons rarely experience collisions and they are out of thermal equilibrium, which allows us to get insights into the mechanism of energy transfer in these plasmas. The goal is to investigate the roles of non-thermal particle distributions, and their response to solar wind dynamic pressure in poorly collisional plasma environments such as the Earth magnetosphere. The availability of high cadence Time History of Events and Macroscale Interactions during Substorms (THEMIS) satellite data have enabled us to conduct this statistical analysis using THEMIS and OMNI database. Our findings confirm that the ion and electron kappa parameters exhibit distinct behaviors when subjected to the dynamic pressure exerted by the solar wind. Moreover, we find an interesting narrow partial ring shaped structure at different azimuthal extension exhibiting a local minimum for ion kappa parameters, and a local maximum for electron kappa parameters. The behavior of Kappa distribution parameters in the Earth magnetosphere in response to the variation of the solar wind dynamic pressure is studied The solar wind dynamic pressure strongly influence ion and electron kappa indices The core energy (Ec) exhibits a significant dawn-dusk asymmetry for ions and much weaker for electrons in various range of PSW

The article presents the results of a statistical analysis of the distribution of the eddy diffusion coefficient depending on the coordinates in the plasma sheet of Earth’s magnetosphere based on data from the Magnetospheric Multiscale Mission satellite system (MMS) for the period from 2017 to 2022. The localization of satellites inside the plasma sheet was recorded from the concentration and temperature of plasma ions according to the data of the same instruments and the value of plasma parameter β. Significant anisotropy of the eddy diffusion coefficient was revealed. The dependence of the eddy diffusion coefficient on the interplanetary magnetic field is analyzed, showing that with the southern orientation of the interplanetary magnetic field, the eddy diffusion coefficients are 1.5–2 times greater than with the northern orientation. It is also shown that under disturbed geomagnetic conditions (SML < –200 nT), the eddy diffusion coefficients are several times greater than under quiet geomagnetic conditions (SML > –50 nT).

In this work, we discuss the problems associated with the formation of the outer radiation belt (ORB) taking into account previous results, including the recent ones. In our opinion, the traditional approaches to the dynamics of the ORB have the following problems: • inconsistency between the times provided by the popular “quasilinear” approach to the ORB description and the observed electron acceleration times; • impossibility to describe ORB dynamics during magnetospheric storms using the “quasilinear” approach when the particle fluxes after storm restore to their pre-storm values, i.e., belong to the storms of the third type according to Reeves et al. (2003, https://doi.org/10.1029/2002GL016513 ) classification; • impossibility of explaining the Tverskaya’s relation, which connects the position of the maximum of the relativistic flux formed after storm with the minimum value of the Dst/SYM-H variation, as well as the acceleration of relativistic electrons during magnetospheric substorms even in the absence of storms. We show that such difficulties do not appear if we take into account the large- scale magnetospheric dynamics, including auroral oval shift toward low latitudes during storms, substorm injections into the region of depressed magnetic field during storm recovery phase and the action of the adiabatic mechanism of electron deceleration and acceleration. The action of stochastic mechanisms of ORB acceleration is also discussed.

The results of observations of low-altitude spacecraft crossing the daytime sector of the auroral zone and of high-apogee spacecraft in the equatorial plane of the magnetosphere were analyzed in order to identify the main processes leading to the formation of dayside polar cusps. Observations from the DMSP F7 spacecraft were used to analyze the latitudinal characteristics of ion precipitation in the cusp region and to study the latitudinal profile of ion pressure in the cusp depending on the IMF parameters. A significant difference was found in identifying the cusp boundaries using an automated data processing system and direct analysis of spacecraft observations. It is shown that for small negative values of the Bz-component of the IMF (〈Bz〉 = –3.0 nT), an ordinary feature of the cusp is the latitudinal profile of the ion pressure (Pi) with a width of 1° of latitude with two maxima, one of which is located in the equatorward and the other in the poleward of the cusp. For large negative Bz values (–6, –8 nT), the polar maximum in the latitudinal profile Pi disappears; only the equatorial maximum remains, the Pi level at the maximum increases, and the width of the cusp decreases to 0.7°. For Bz IMF > 0, the most characteristic is the Pi profile with a maximum ion pressure in the polar part of the cusp. The cusp for Bz > 0 is located at higher latitudes than for Bz < 0, and its average latitudinal width increase to 1.4° of latitude. In the prenoon sector MLT, the most typical for periods with a large negative By-component of the IMF (〈By〉 = –6.3 nT, 〈Bz〉 = –1.7 nT) is a cusp with a width of 1.4° of latitude with a flat top in the latitudinal Pi profile. Comparison of the pressure distributions observed at low heights with data from high-apogee satellites confirmed the possibility of describing the formation of the cusp as a diamagnetic cavity and using observations in the cusp to determine the ion pressure in the magnetosheath.

Abstract Since the discovery of the large‐scale field‐aligned currents it is widely acknowledged that gaps exist between the Region 1 (R1) and Region 2 (R2) currents in which the current values are relatively small as compared to neighboring regions. Assuming that the field‐aligned currents are generated by plasma pressure gradients, we analyzed data collected by the THEMIS satellites between 2007 and 2011 to identify regions with very low plasma pressure gradients (pressure plateaus), which could be responsible for the appearance of these gaps. It was found that the pressure profiles with low radial gradients are typically located between 8 and 10 Radii around the Earth. Projections of pressure plateau regions onto ionospheric altitudes, for both individual events and on a statistical basis, coincide with the locations of gaps between Iijima and Potemra field‐aligned currents. The role played by identified pressure plateaus in shaping the pattern of large‐scale field‐aligned currents is discussed.

Variations of relativistic electron fluxes ( E ≥ 1 MeV) and wave activity in the Earth magnetosphere are studied to determine the contribution of different acceleration mechanisms of the outer radiation belt electrons: ULF mechanism, VLF mechanism, and adiabatic acceleration. The electron fluxes were measured by Arase satellite and geostationary GOES satellites. The ULF power index is used to characterize the magnetospheric wave activity in the Pc5 range. To characterize the VLF wave activity in the magnetosphere, we use data from PWE instrument of Arase satellite. We consider some of the most powerful magnetic storms during the Arase era: May 27–29, 2017; September 7–10, 2017; and August 25–28, 2018. Also, non-storm intervals with a high solar wind speed before and after these storms for comparison are analyzed. Magnitudes of relativistic electron fluxes during these magnetic storms are found to be greater than that during non-storm intervals with high solar wind streams. During magnetic storms, the flux intensity maximum shifts to lower L-shells compared to intervals without magnetic storms. For the considered events, the substorm activity, as characterized by AE index, is found to be a necessary condition for the increase of relativistic electron fluxes, whereas a high solar wind speed alone is not sufficient for the relativistic electron growth. The enhancement of relativistic electron fluxes by 1.5–2 orders of magnitude is observed 1–3 days after the growth of the ULF index and VLF emission power. The growth of VLF and ULF wave powers coincides with the growth of substorm activity and occurs approximately at the same time. Both mechanisms operate at the first phase of electron acceleration. At the second phase of electron acceleration, the mechanism associated with the injection of electrons into the region of the magnetic field weakened by the ring current and their subsequent betatron acceleration during the magnetic field restoration can work effectively. Graphical Abstract

Проведен анализ наземных оптически наблюдений на обс. Баренцбург (арх. Шпицберген) 22 декабря 2003 г. в период регистрации спутником DMSP F16 дневного полярного каспа. Характеристики высыпающихся частиц, наблюдаемые спутником F16, позволили определить широтное положение приполюсной и экваториальной границ каспа и широтную структуру авроральных высыпаний в полуденном секторе. Данные OMNI Web показывают, что Bz-компонента ММП повернулась на север примерно за 12 мин до пролета спутника и оставалась северной примерно в течение 30 мин. Наземные оптические наблюдения показывают, что ионосферная проекция дневного каспа совпадает с областью свечения в эмиссии 630.0 нм с максимумом интенсивности в приполюсной части каспа. С приполюсной стороны касп окаймляет лучистая дуга (RA), положение которой совпадает с максимумом потока энергии электронных высыпаний. Средняя энергия высыпающихся электронов в каспе составляла ~ 0.13 кэВ, а в RA ~ 0.24 keV со спектральным пиком на энергиях около 0.4 кэВ. Яркость RA при северной ориентации ММП изменялась в пределах 1-2 кР в хорошем соответствии с вариациями AL-индекса магнитной активности.

We analyzed the applicability of a hydrodynamic approach to the analysis of large-scale magnetospheric dynamics in the conditions of quiet geomagnetic activity. The main parameter, determining the applicability of the ideal MHD, is the ratio between the Alfvén and plasma velocities. We obtained the 2D distribution of this parameter using data of the THEMIS mission at geocentric distances <20 RE, and showed that not only the ring current region can be described suggesting full pressure balance. The external part of the ring current, which is localized in the surrounding the Earth plasma ring and earlier considered as a plasma sheet continuation, can be regarded as a stress balance region as well. Azimuthal plasma pressure gradients in this region create a system of large-scale field-aligned currents. Their closing in the ionosphere generates a large-scale convection in the ionosphere and magnetosphere. The mechanism of the large-scale convection control due to "penetration" of large-scale solar wind magnetic field is discussed. We discuss the role of turbulent transport in the analysis of magnetospheric regions, in which high level of turbulence is observed simultaneously with large-scale stress balance.

The most recent findings on the dynamics of the outer radiation belt (ORB) and the physics of magnetospheric substorms are examined. Specifically, we investigate the relationship between storm time substorms and the energetic electron population that forms the ORB. Traditionally, storm time substorms have been considered as the primary source of energetic electrons, which are further accelerated during storms to contribute to the formation of the ORB. However, several observations have demonstrated that large magnetospheric substorms can generate high-energy electrons even in the absence of magnetic storms. Substorms introduce dispersionless injections of energetic electrons deep into the magnetosphere from the geosynchronous orbit during storm times. The injected electrons undergo additional acceleration via the betatron mechanism during the storm recovery phase, thus increasing the ORB population. To gain a better understanding of this process, it is crucial to study plasma sheet turbulence, substorm onset processes, and the brightening of auroral arcs. By analyzing the aforementioned findings, this study aims to highlight the need for reanalyzing of the role of auroral processes in the formation of the ORB.

In this paper, we consider the behavior of the radial distribution of the plasma pressure, magnetic field, and plasma parameter in the night sector of the Earth's magnetosphere at geocentric distances from 7 to 12 R-E that are obtained using the THEMIS mission measurements. The results of measurements on the THEMIS-D and THEMIS-A satellites on February 2009 when the satellites were near the equatorial plane were analyzed. Time intervals are identified when the plasma pressure actually did not change with a change in the distance from the Earth. It is shown that profiles with a pressure plateau can exist stably during the day are destroyed during the period of disturbance and are restored after destruction. The role of the pressure plateau in the formation of the structure of magnetospheric current systems is discussed.

The data from the DMSP spacecraft were used to study the characteristics of ion and electron precipitation in the nightside sector of the auroral zone during magnetically quiet periods at extreme values of the solar wind dynamic pressure ( Psw ). It was shown that the ion pressure at the isotropy boundary (IB) increases with Psw and can reach a level of 4–6 nPa at Psw = 20–22 nPa. The latitude profiles of the ion pressure obtained at different levels of Psw indicate that the increase in Psw is accompanied by an expansion of the ion precipitation region and a shift of the IB to lower latitudes. At 〈 Psw 〉 = 0.5 nPa, the IB latitude is ~70.4° CGL, while at 〈 Psw 〉 = 16.3 nPa, it shifts toward the equator to ~64.6° CGL. As the Psw level decreases, the energy fluxes of precipitating electrons decrease significantly. At Psw < ~ 2.0 nPa, auroras in the region of the auroral oval can be considered subvisual. At extremely low values of dynamic pressure, Psw = ~ 0.2 nPa, it becomes very problematic to identify the zone of electron and ion precipitation.

One of the main problems of modern magnetospheric physics is the lack of a self-consistent explanation of the main physical processes based on the laws of plasma physics. Among all the traditionally studied phenomena, the polar aurora stands out for being key to our understanding of several magnetospheric processes. In this manuscript, I would like to share with the younger generation my view about main auroral processes which I have developed during my career over the past 50 years.