Radial profile of pressure in a storm ring current as a function of D st

Using satellite data obtained near the equatorial plane during 12 magnetic storms with amplitudes from ?61 down to ?422 nT, the dependences of maximum in L-profile of pressure (L _m) of the ring current (RC) on the current value of D _st are constructed, and their analytical approximations are derived. It is established that function L _m(D _st ) is steeper on the phase of recovery than during the storm’s main phase. The form of the outer edge of experimental radial profiles of RC pressure is studied, and it is demonstrated to correspond to exponential growth of the total energy of RC particles on a given L shell with decreasing L. It is shown that during the storms’ main phase the ratio of plasma and magnetic field pressures at the RC maximum does not practically depend on the storm strength and L _m value. This fact reflects resistance of the Earth’s magnetic field to RC expansion, and testifies that during storms the possibilities of injection to small L are limited for RC particles. During the storms’ recovery phase this ratio quickly increases with increasing L _m, which reflects an increased fraction of plasma in the total pressure balance. It is demonstrated that function L _m(D _st ) is derived for the main phase of storms from the equations of drift motion of RC ions in electrical and magnetic fields, reflecting the dipole character of magnetic field and scale invariance of the pattern of particle convection near the RC maximum. For the recovery phase it is obtained from the Dessler-Parker-Sckopke relationship. The obtained regularities allow one to judge about the radial profile of RC pressure from ground-based magnetic measurements (data on the D _st variation).     

Distribution of Plasma Pressure in the Geomagnetic Tail in the Transition Region from Dipole to Quasidipole and Stretched Magnetic Field Lines: Events on October 13, 1995 and March 13, 1996

The results of an analysis of the pressure distribution of the hot magnetosphere plasma and transverse currents in the plasma at distances from 8R _E to 12R _E are presented. The data were taken in the vicinity of the equatorial plane onboard the Interball-1 satellite during its passages on October 13, 1995 and March 13, 1996. The pressure was determined from the measurements of particle fluxes by the CORALL, DOK-2, and SKA-2 instruments. The specific features of this experiment made it possible to calculate the pressure with a high accuracy and to determine the distribution of the magnetostatically equilibrium currents in the plasma. It is shown that at the parts of the monotonous increase of the pressure in the earthward direction one can detect regions of plateau in the plasma pressure. A possible origin of the small-scale variations and regions with plateau are discussed. A comparison of the measured pressure profiles with the pressure profiles in the Tsyganenko and Mukai-2003 model is performed. Transverse currents flowing in the plasma are calculated assuming magnetostatic equilibrium.     

Plasma flow disturbances in the magnetospheric plasma sheet during substorm activations

We have considered variations in fields and particle fluxes in the near-Earth plasma sheet on the THEMIS-D satellite together with the auroral dynamics in the satellite-conjugate ionospheric part during two substorm activations on December 19, 2014 with K _p = 2. The satellite was at ~8.5R_E and MLT = 21.8 in the outer region of captured energetic particles with isotropic ion fluxes near the convection boundary of electrons with an energy of ~10 keV. During substorm activations, the satellite recorded energetic particle injections and magnetic field oscillations with a period of ~90 s. In the satellite-conjugate ionospheric part, the activations were preceded by wavelike disturbances of auroral brightness along the southern azimuthal arc. In the expansion phase of activations, large-scale vortex structures appeared in the structure of auroras. The sudden enhancements of auroral activity (brightening of arcs, auroral breakup, and appearance of NS forms) coincided with moments of local magnetic field dipolarization and an increase in the amplitude Pi2 of pulsations of the B_z component of the magnetic field on the satellite. Approximately 30–50 s before these moments, the magnetosphere was characterized by an increased rate of plasma flow in the radial direction, which initiated the formation of plasma vortices. The auroral activation delays relative to the times when plasma vortices appear in the magnetosphere decreased with decreasing latitude of the satellite projection. The plasma vortices in the magnetosphere are assumed to be responsible for the observed auroral vortex structures and the manifestation of the hybrid vortex instability (or shear flow ballooning instability) that develops in the equatorial magnetospheric plane in the presence of a shear plasma flow in the region of strong pressure gradients in the Earthward direction.     

The Structure of Ion Spectra in Outer Regions of the Ring Current: The November 13, 1995 Event

We present the results on variations of ion spectra in the energy range from 1 keV to 3 MeV. The spectra measured onboard the INTERBALL Tail Probe satellite on November 13, 1995, during the satellite's passage from the dipole field lines to the lines stretched into the magnetotail are analyzed. The data of the CORALL, DOK-2, and SKA-2 instruments are used to reconstruct the ion spectra. It is shown that, when the ion spectrum along the satellite trajectory is averaged over 2-min intervals, it is smooth up to geocentric distances of 6R _E. With decreasing distances, the form of the particle spectra in the region under consideration remained virtually unchanged (region from L = 11R _E down to L= 6R _E) and only insignificant variations of the energy of the spectral maxima are observed. Possible reasons for the observed regularities are discussed.     

Verification of the Accuracy of the Magnetopause Empirical Models Using the INTERBALL-1 Satellite Data

A statistical analysis of the shape and location of the magnetopause according to the INTERBALL-1 satellite data for the period 1995–1997 is carried out. The instants of crossing the magnetosphere boundaries obtained by the plasma and magnetic data are compared with computations based on three empirical models, namely, Petrinec and Russel, 1996; Shue et al., 1997; and Shue et al., 1998. The state of the interplanetary medium (dynamic pressure of the solar wind plasma P _d and the B _z component of the interplanetary magnetic field) was determined by the measurements onboard the WIND spacecraft. We estimate the accuracy of the considered models for different groups of boundary crossings: single, multiple with small duration (less than 40 min), and multiple with large duration (more than 40 min). It is demonstrated that the small-scale motions of the boundary (<1R _E) are observed more often in the dayside magnetosphere, especially near the cusp region. Large-scale boundary oscillations (>1R _E) are more common in the tail region of the magnetosphere, namely, its flanks. Various models give similar results: about 50% of all events have deviations by more than 1R _E from the model locations. In some cases, the deviation of the measured location of the magnetosphere boundary from the model prediction may be as large as 5–6R _E for all three models considered, the actual boundary being more often located nearer to the Earth than the result of model computations. The best model is that of Shue et al., 1998, but it does not differ significantly from the other models.     

Energy dependence of the fraction of protons of ionospheric origin in the ring current

The energy dependence of a fraction of ring current protons of ionospheric origin is calculated using the AMPTE/CCE data for a typical strong magnetic storm (max|D _st | ≈ 120 nT). It is shown that this fraction monotonically decreases from ～ 83 to 25–30% with an increase in proton energy from 5 to 315 keV at L = 6–7 (L is the McIlwain parameter) and is 30–40% at energy 40–50 keV corresponding to the maximum of proton energy density at L = 6–7. It is demonstrated that the core of the ring current (L = 3.7–4.7) was enriched by solar protons with E ≈ 10–200 keV during the active phase of the storm (the maximum effect is reached at E ≈ 20–50 keV).     

Structure of current and plasma in current sheets depending on the conditions of sheet formation

The structure of current sheets created under laboratory conditions is characterized by a large variety, which depends substantially on the conditions under which the sheet if formed. In this work, we present the results of an experimental study of the structure and evolution of current sheets that were formed in magnetic configurations with a singular line of the X type. It has been shown that the change in the transverse magnetic field gradient, the strength of the longitudinal magnetic field, and the mass of the ions in plasma makes it possible to significantly vary the main parameters of the current sheets. This offers the challenges of using laboratory experimental results for analyzing and simulating the cosmophysical processes.     

Lorentz-force-perturbed orbits with application to J2-invariant formation

The Lorentz force acting on an electrostatically charged spacecraft in the Earth's magnetic field provides a new propellantless means for controlling a spacecraft's orbit. Assuming that the Lorentz force is much smaller than the gravitational force, the perturbation of a charged spacecraft's orbit by the Lorentz force in the Earth's magnetic field, which is simplified as a titled rotating dipole, is studied in this article. Our research starts with the derivation of the equations of motion in geocentric equatorial inertial Cartesian coordinates using Lagrange mechanics, and then derives the Gauss variational equations involving Lorentz-force perturbation using a set of nodal inertial coordinates as an intermediate step. Subsequently, the approximate averaged changes in classical orbital elements, including single-orbit-averaged and one-day-averaged changes, are obtained by employing orbital averaging. We have found that the approximate analytic one-day-averaged changes in semi-major axis, eccentricity, and inclination are nearly zero, and those in the other three angular orbital elements are affected by J₂ and Lorentz-force perturbations. This characteristic is applied to model bounded relative orbital motion in the presence of the Lorentz force, which is termed Lorentz-augmented J₂-invariant formation. The necessary condition for J₂-invariant formation is derived when the chief spacecraft's reference orbit is either circular or elliptical. It is shown that J₂-invariant formation is easier to implement if the deputy spacecraft is capable of establishing electric charge. All conclusions drawn from the approximate analytic solutions are verified by numerical simulation.     

Storm deviations of the geomagnetic trap core from dipole configuration deduced from data on relativistic electrons

Satellite data on the position of maximum L _m of the belt of relativistic electrons during strong storms, obtained at low altitudes (∼500 km) and at high altitudes (near the geomagnetic equator plane), are compared (L is the McIlwain parameter). Both at low and high altitudes the maximum of the storm belt of relativistic electrons is formed on the outer edge of the ring current. It is shown that the geomagnetic field can substantially deviate from dipole configuration not only at the geomagnetic trap periphery, but at its core as well (at L ∼ 2.5–3.5), and these deviations are nonlinear. Simultaneous measurements of the fluxes of relativistic electrons at low and high altitudes can serve for estimation of the real shape of magnetic field lines at L < 4 during geomagnetic disturbances.     

Large and sharp changes of solar wind dynamic pressure and disturbances of the magnetospheric magnetic field at geosynchronous orbit caused by these variations

The large and sharp changes of solar wind dynamic pressure, found from the INTERBALL-1 satellite and WIND spacecraft data, are compared with simultaneous magnetic field disturbances in the magnetosphere measured by geosynchronous GOES-8, GOES-9, and GOES-10 satellites. For this purpose, about 200 events in the solar wind, associated with sharp changes of the dynamic pressure, were selected from the INTERBALL-1 satellite data obtained during 1996–1999. The large and sharp changes of the solar wind dynamic pressure were shown to result in rapid variations of the magnetic field strength in the outer magnetosphere, the increase (drop) of the solar wind dynamic pressure always lead to an increase (drop) of the geosynchronous magnetic field magnitude. The value of the geomagnetic field variation strongly depends on the local time of the observation point, reaching a maximum value near the noon meridian. It is shown that the direction of the B _z component of the interplanetary magnetic field has virtually no effect on the geomagnetic field variation because of a sharp jump of pressure. The time shift between an event in the solar wind and its response in the magnetosphere at a geosynchronous orbit essentially depends on the inclination of the front of a solar wind disturbance to the Sun-Earth line.     

On the Accuracy of the Conjugation of High-Orbit Satellites with Small-Scale Regions in the Ionosphere

The degree of uncertainty that arises when mapping high-orbit satellites of the Cluster type into the ionosphere using three geomagnetic field models (T89, T98, and T01) has been estimated. Studies have shown that uncertainty is minimal in situations when a satellite in the daytime is above the equatorial plane of the magnetosphere at the distance of no more than 5 R_E from the Earth’s surface and is projected into the ionosphere of the northern hemisphere. In this case, the dimensions of the uncertainty region are about 50 km, and the arbitrariness of the choice of the model for projecting does not play a decisive role in organizing satellite support based on optical observations when studying such large-scale phenomena as, e.g., WTS, as well as heating experiments at the EISCAT heating facility for the artificial modification of the ionosphere and the generation of artificial fluctuations in the VLF band. In all other cases, the uncertainty in determining the position of the base of the field line on which the satellite is located is large, and additional information is required to correctly compare the satellite with the object in the ionosphere.     

INTERBALL-1 Observations of the Kilometric “Continuum” of the Earth's Magnetosphere

The electromagnetic radio-frequency emission of the inner region of the Earth's plasmasphere discovered recently by the GEOTAIL satellite [4] and referred to as the kilometric continuum was observed by the INTERBALL-1 satellite (1995–2000) in the 100–500 kHz band in the AKR-X experiment. During a period of low solar activity (1995–1997), this continuum was found leaving the inner plasmasphere at geocentric distances of 2–4R _E as isolated pencil-like (1°–6°) beams located in the magnetic equator plane. During a time of high solar activity (1999–2000), the occurrence of the emission was extremely rare (it was observed only at a considerable fall of this activity). If detected, at the same geocentric distances (2–4R _E) the continuum demonstrated a strongly variable and perturbed character, as well as a considerably larger extension of the beam over the geomagnetic latitude (10°–20° and more). In addition, quasi-periodic (QP) signals, similar to the observed QP emissions of Jupiter, were sometimes detected in this period. The probable nature of the observed features of the kilometric continuum is briefly discussed.     

Large and Fast Variations of Parameters in the Magnetosheath: 3. Amplitudes and Transverse Profiles of Low and High Frequency Variations of the Plasma and Magnetic Field

We present the results of experimental studies of high frequency (with periods of seconds and tens of seconds) and low frequency (with periods of minutes and tens of minutes) large variations of the ion flux and magnetic field magnitude in the magnetosheath. It is shown that, on average, the relative amplitudes of these variations are approximately two times higher than similar values characteristic for the undisturbed solar wind. The averaged spatial profile of these values and their variations across the magnetosheath is obtained, as are the dependencies of normalized plasma fluxes and their variations on the place of entrance of a given plasma element into the magnetosheath. Using one particular example, a good coincidence between the time profiles of ion fluxes measured aboard two spacecraft separated by a distance of 10R _E along the magnetosheath is demonstrated.     

Fine structure of interplanetary shock fronts from the data of the BMSW instrument of the PLASMA-F experiment

The paper is concerned with studying the thickness of fronts of 38 interplanetary shocks detected by the BMSW instrument, which is a part of the scientific payload of the SPEKTR-R spacecraft, which was launched into a highly elliptical orbit in 2011. The main parameters of the interplanetary shocks have been calculated as follows: the ratio of thermal pressure to magnetic pressure before the front β, the angle between the shock front normal and the undisturbed magnetic field θ_Bn, the ratio of the shock propagation velocity to the magnetosonic velocity in the undisturbed region M_ms, and the shock front velocity relative to the Earth. It has been shown that the front thickness determined from the plasma parameters approximately matches the front thickness obtained from the magnetic field measurements and lies between 0.5 and 5 proton inertial lengths. In some events, the oscillations have been observed (upstream and downstream of the shock) in plasma parameters and in the magnetic field data. The length has been found to be between 0.5 and 6 proton inertial lengths for the preceding oscillations and between 0.5 and 10 proton inertial lengths for the following oscillations. The average value of the proton inertial length is 62 km.     

Peculiarities of the formation of a thin current sheet in the Earth’s magnetosphere

We investigate the process of the self-consistent formation of a thin current sheet with a thickness close to the ion Larmor gyroradius in the presence of decreasing magnetic field’s normal component B_n. This behavior is typical of the current sheet of the Earth’s magnetospheric tail during geomagnetic substorms. It has been shown that, in a numerical model of the current sheet, based on the particle-in-cell method, the appearance of self-consistent electric field component E_y in the current sheet vicinity can lead to its significant thinning and, eventually, to the formation of a multiscale configuration with a thin current sheet (TCS) in the central region supported by transient particles. The structure of the resulting equilibrium is determined by the initial parameters of the model and by the particle dynamics during the sheet thinning. Under certain conditions, the particle drift in the crossed electric and magnetic fields leads to a significant portion of ions becoming trapped near the neutral sheet and, in this way, to the formation of a wider configuration with an embedded thin current sheet. The population of trapped particles produces diamagnetic negative currents that manifest in the form of negative wings at the periphery of the sheet. Correspondingly, in the direction perpendicular to the sheet, a nonmonotonic coordinate dependence of the magnetic field appears. The mechanisms of the evolution of the current sheet in the Earth’s magnetotail and the formation of a multiscale structure are discussed.     

Turbulent fluctuations of plasma and magnetic field parameters in the magnetosheath and the low-latitude boundary layer formation: Multisatellite observations on March 2, 1996

The results of simultaneous analysis of plasma and magnetic field characteristics measured on the INTERBALL/Tail Probe, WIND and Geotail satellites on March 2, 1996, are presented. During these observations the INTERBALL/Tail Probe crossed the low-latitude boundary layer, and the WIND and Geotail satellites measured the solar wind’s and magnetosheath’s parameters, respectively. The plasma and magnetic field characteristics in these regions have been compared. The data of the Corall, Electron, and MIF instruments on the INTERBALL/Tail Probe satellite are analyzed. Fluctuations of the magnetic field components and plasma velocity in the solar wind and magnetosheath, measured onboard the WIND and Geotail satellites, are compared. The causes resulting in appearance of plasma jet flows in the low-latitude boundary layer are analyzed. The amplitude of magnetic field fluctuations in the magnetosheath for a studied magnetosphere boundary crossing is shown to exceed the magnetic field value below the magnetopause near the cusp. The possibility of local violation of pressure balance on the magnetopause is discussed, as well as penetration of magnetosheath plasma into the magnetosphere, as a result of magnetic field and plasma flux fluctuations in the magnetosheath.     

Observation of the Near Plasma Sheet,Ring Current,and Energetic Electrons from Radiation Belts at a Geosynchronous Orbit,March 11–25, 1992

The dynamics of near plasma sheet electrons and ions (E 0.1–12.4 keV), ring current protons (E _i 41–133 keV), and energetic electrons from the Earth's radiation belts (E _e 97–1010 keV) is considered using the data from the Gorizont-34and Gorizont-35geosynchronous satellites from March 11–25, 1992. Peculiarities of this period are a long (more than 4 days) interval of the northward interplanetary magnetic field (B _z> 0) and a high-speed stream of the solar wind with an enhanced particle density. The SC and compression of the magnetosphere to the geosynchronous orbit (GMC) preceded this interval. Under quiet and moderately disturbed geomagnetic conditions and under a prolonged northward interplanetary magnetic field, we observed a significant decrease of fluxes and softening of spectra of the electron component of plasma in the energy ranges of 0.1–12.4 keV and 97–1010 keV, and of the ion component of plasma at energies of 0.1–4 keV, while the intensity of 5–12.4 keV ion fluxes increases by about one order of magnitude. The peculiarities of distributions of energetic particle fluxes observed in the period under consideration can be associated with significant variations of the convection conditions and a decreased or fully suppressed injection of energetic electrons into the geosynchronous orbit region.     

Radial propagation velocity of energetic particle injections according to measurements onboard the <Emphasis Type="Italic">Cluster</Emphasis> satellites

Injections of energetic electrons with a dispersion over energies were observed during the February 23, 2004 (at about 03:20 UT) substorm onboard the Cluster satellites in the vicinity of perigee near the midnight meridian. The delays in the particle observation caused by the energy dependence of the magnetic drift velocities made it possible to determine the position and time of the beginning of the drift, tracing the trajectories of the leading center of particles back in time in the magnetospheric model. The comparisons of the measurements of four satellites allowed us to determine the radial propagation of the injection front with a velocity of 100–150 km/s at a distance of 7–9 R _E. The comparison with a few previous measurements shows a substantial slowing down of injections as they approached the Earth, and this confirms the prospects of this method for more detailed study of propagation of plasma injection into the inner magnetosphere.     

Variations of the magnetopause position versus the level of geomagnetic activity (according to data of the INTERBALL-1 Satellite for 1995–1997)

The variations in the deviation of the observed position of the magnetosphere boundary from its mean position predicted by the Shue at al., 1997 (Sh97) model [7] are studied as a function of the substorm activity level (the AE-index value) and magnetic storm intensity (the value of the corrected D _st ^* index). The results obtained make it possible to state that the amplitude of motion of the magnetospheric boundary on the dayside and in the low-latitude tail is small. It is likely that the position of the boundary is either independent of the AE and D _st ^* indices or this dependence is weak. At the same time, the boundary of the high-latitude tail shifts inward on the average by 1.5R _E with an increase of the AE-index in the case of absence of magnetic storms (contraction of the magnetospheric tail). On the contrary, in the presence of magnetic storms, this boundary shifts outward by up to 3R _E with an increase of the AE-index (inflation of the magnetospheric tail). It is also shown that the boundary of the high-latitude tail moves outward with an increase of the D _st ^* index, both at low substorm activity and in periods of high substorm activity. The amplitude of the outward motion of the high-latitude tail of the magnetosphere is by a factor of two higher for moderate magnetic storms with strong substorms than for moderate magnetic storms with weak substorms.     

Long-term variations of asymmetry of the solar magnetic field and geometry of the interplanetary magnetic field

A comparative analysis of variations of the mean solar magnetic field and the interplanetary magnetic field over all history of their measurements is performed. Asymmetry of the solar magnetic field and its manifestation in the heliosphere is investigated. Long-term variations of the solar magnetic field and the heliosphere, which manifest themselves in alternation of dominating magnetic polarities of different sign, are discovered. On the basis of the analysis of cumulative sums of the IMF components, long-term variations of the IMF geometry and of the solar wind spiral angle are found. The cumulative sum of the IMF B _z component perpendicular to the ecliptic plane also shows long-term variations. Time intervals are revealed, in which negative values of the IMF B _z component dominate, and an increased geomagnetic activity is observed.