Estimation of the current density and analysis of the geometry of the current system surrounding the Earth

The results of an investigation of the distribution of plasma pressure, pressure gradients, and magnetic field near the equatorial plane in the plasma ring surrounding the Earth under magneto-quiet conditions are presented. Observational data obtained during the international THEMIS mission are used. The picture of the distribution of transverse-current density near the equatorial plane was obtained under assumption of observing the magnetostatic balance condition at geocentric distances from 6 to 12R _E. In estimating the integral transverse current it was accepted that in daytime sector the magnetic-field minima on magnetic field lines are not localized in the equatorial plane. Estimates of the integral transverse current were obtained, which demonstrate the possibility of closing nighttime transverse currents at geocentric distances of up to ～12R _E inside the magnetosphere, which form a high-latitudinal continuation of the ring current.     

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.     

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.     

Sporadic structures and small-scale irregularity in the nighttime polar ionosphere in the period of high solar activity according to the data of radio occultation measurements on satellite-to-satellite paths

Results of the analysis of 327 sessions of radio occultation on satellite-to-satellite paths are presented. The data are taken in the nighttime polar ionosphere in the regions with latitudes of 67°–88°, and in the period of high solar activity from October 26, 2003 to November 9, 2003. Typical ionospheric changes in the amplitude and phase of decimeter radio waves on paths GPS satellites-CHAMP satellite are presented. It is demonstrated that these data make it possible to determine characteristics of the sporadic E _s structures in the lower ionosphere at heights of 75–120 km. Histograms of distribution of the lower and upper boundaries, thickness, and intensity of the E _s structures are presented. Dispersion and spectra of amplitude fluctuations of decimeter radio waves caused by small-scale irregularity of the ionospheric plasma are analyzed. The relation of the polar E _s structures and intensity of small-scale plasma irregularity to various manifestations of solar activity is discussed. The efficiency of monitoring the ionospheric disturbances caused by shock waves of the solar wind by the radio occultation method on satellite-to-satellite paths is demonstrated.     

Statistical Approach to the Evaluation of the Mean Correlation Length and the Propagation Velocity of Middle-Scale Plasma Structures in the Earth's Foreshock

Based on simultaneous measurements of ion fluxes made onboard the closely separated satellites Interball-1and Magion-4, the propagation velocity of middle-scale plasma structures in the Earth's foreshock relative to the solar wind flow is estimated. The derived value of this velocity allows these structures to be identified as a fast magnetosonic wave propagating upstream of the solar wind inflowing the Earth's bow shock. An evaluation is also made of the correlation length of these disturbances in the plane perpendicular to the Sun–Earth line. This length is approximately equal to 2R _E.     

Geosynchronous magnetopause crossings on October 29–31, 2003

During the period October 29–31, 2003, geosynchronous magnetopause crossings (GMC) have been identified based on the magnetic data of the GOES series spacecraft and plasma data of the LANL series spacecraft. It is shown that most of the time the size of the dayside magnetosphere was highly decreased under the effect of very high pressure associated with high velocities and densities of the solar wind plasma, as well as high negative values of the B_z component of the interplanetary magnetic field (IMF). For tens of hours the subsolar magnetopause was deep inside the geosynchronous orbit. During the main phase and at the maximum of the strong geomagnetic storms that occurred in the period under consideration, the dayside magnetosphere was characterized by a strong dawn-dusk asymmetry, so that its size in the postnoon sector considerably exceeded the size in the pre-noon sector. The geomagnetic disturbances in the morning on October 30 and 31, 2003 were accompanied by global magnetospheric pulsations with periods of 5–10 min and high amplitude (up to 0.8 R_E).Translated from Kosmicheskie Issledovaniya, Vol. 42, No. 6, 2004, pp. 574–584.Original Russian Text Copyright © 2004 by Dmitriev, Suvorova.     

Relationship between ionospheric electric fields and magnetic activity indices

The relations between electric fields in the daytime and nighttime sectors of the polar ionosphere and magnetic activity indices of auroral region (AL) and northern polar cap (PCN) are studied. It is found that the above relations do exist and are described by: a) equations U _pc⁽¹⁾ (kV) = 27.62 + 21.43PCN with a correlation coefficient R = 0.87 and U _pc⁽¹⁾ (kV) = 4.06 + 49.21PCN - 6.24 PCN² between the difference in the electric potentials across the polar cap in the daytime sector U _pc⁽¹⁾ and PCN and b) regression equation U _pc⁽²⁾ (kV) = 23.33 + 0.08|AL| with R = 0.86 between the difference in the electric potentials across the polar cap in the nighttime sector U _pc⁽²⁾ and |AL|. It is shown that: a) it is possible to use the AL and PCN indices for real-time diagnostics of instantaneous values of the electric fields in the daytime and nighttime sectors of the polar ionosphere in the process of a substorm development; b) at the expansion phase of a substorm, due to calibration of PCN values by the values of the solar wind electric field E _sw, the PCN index does not feel the contribution of the western electrojet and, accordingly, the contribution of the nighttime ionospheric electric field U _pc⁽²⁾, governed by the reconnection in the magnetospheric tail.     

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.     

Precipitating Protons and Their Role in Ionization of the Polar Ionosphere

Spatial distributions of the electron density in the latitude range 60°–90° N were calculated on the basis of a physical model of the E and lower Fregions of the high-latitude ionosphere using statistical models of auroral proton and electron precipitation. It is shown that precipitating protons can play the key role in the ionization of the Eregion in the dusk and midnight sectors of the auroral oval. However, quantitative estimates of the contribution of protons to the ionization depend on the used statistical models of electron precipitation. Comparison of the electron density profiles calculated for two incoherent scatter radars, EISCAT (Tromsö) and ESR (Svalbard), for simultaneous precipitation of electrons and protons and for electron precipitation only show that the influence of protons is the most significant in the dusk sector over the EISCAT radar and in the midnight sector over the ESR radar. The results presented indicate the need to take protons into account when radar data are used to derive precipitating electron spectra.     

Radio Occultation Measurements of the Radio Wave Absorption and the Sulfuric Acid Vapor Content in the Atmosphere of Venus

The results of the determination of centimeter ( = 5 cm) radio waves absorption in the radio occultation experiments, carried out using the Venera-15and Venera-16spacecraft, are presented. The altitude distribution of the absorber substance is analyzed. The absorbing layer is shown to exist at altitudes of 64 to 58 km in the near-polar regions of the planet. At middle latitudes such an absorbing layer was not found. In the altitude range from 56 to 46 km the radio wave absorption by the sulfuric acid (H₂SO₄) vapor is observed. The content of the sulfuric acid vapor is shown to increase with decreasing altitude: in the mid-latitude region at altitudes of 56.7 and 53 km it equals 5 and 20 ppm, respectively, and at polar latitudes the same content of H₂SO₄vapor is observed at altitudes of 51.2 and 47 km, respectively. A comparison of these results with the data of radio wave absorption in the = 13 cm band, obtained in the Pioneer Venus Orbiterradio occultation experiments, leads to the conclusion that the obtained values of the sulfuric acid vapor content well agree in the regions of overlap of the data.     

Nonlinear Localized Electrostatic Structures and Their Experimental Diagnostics in the Magnetosphere Plasma

The theoretical models of the formation of the three-dimensional quasi-stationary structures of variations of density and electrostatic potential in a multicomponent magnetosphere plasma are considered. On the basis of the perturbation method, we have studied the domains of the parametric space, where the occurrence of nonlinear quasi-stationary ion-acoustic and electron-acoustic structures are possible. For these structures, the velocities of motion along the direction of the magnetic field are estimated, together with the longitudinal and transverse scales with respect to the direction of the Earth's magnetic field. The calculated dependences of the scales l and l _|| of the structures on the plasma parameters in the three-component plasma allow one to compare the results of the considered theoretical models with new experimental data of measuring the form of soliton structures onboard the FAST, POLAR, and GEOTAIL satellites.     

Transfer orbits to/from the Lagrangian points in the restricted four-body problem

The well-known Lagrangian points that appear in the planar restricted three-body problem are very important for astronautical applications. They are five points of equilibrium in the equations of motion, what means that a particle located at one of those points with zero velocity will remain there indefinitely. The collinear points (L₁, L₂ and L₃) are always unstable and the triangular points (L₄ and L₅) are stable in the present case studied (Earth–Sun system). They are all very good points to locate a space-station, since they require a small amount of ΔV (and fuel), the control to be used, for station-keeping. The triangular points are especially good for this purpose, since they are stable equilibrium points.In this paper, the planar restricted four-body problem applied to the Sun–Earth–Moon–Spacecraft is combined with numerical integration and gradient methods to solve the two-point boundary value problem. This combination is applied to the search of families of transfer orbits between the Lagrangian points and the Earth, in the Earth–Sun system, with the minimum possible cost of the control used. So, the final goal of this paper is to find the magnitude of the two impulses to be applied in the spacecraft to complete the transfer: the first one when leaving/arriving at the Lagrangian point and the second one when arriving/living at the Earth.The dynamics given by the restricted four-body problem is used to obtain the trajectory of the spacecraft, but not the position of the equilibrium points. Their position is taken from the restricted three-body model. The goal to use this model is to evaluate the perturbation of the Sun in those important trajectories, in terms of fuel consumption and time of flight. The solutions will also show how to apply the impulses to accomplish the transfers under this force model.The results showed a large collection of transfers, and that there are initial conditions (position of the Sun with respect to the other bodies) where the force of the Sun can be used to reduce the cost of the transfers.     

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.     

The Role of Wave–Particle Interactions in the Dynamics of Plasma in the Polar Cusp

This paper presents a review of observations of low-frequency plasma waves together with plasma particles performed by Interball 1 and its subsatellite Magion 4 and by the Freja satellite in different cusp regions. The detailed study of the wave spectra together with the electron distribution functions indicates the correlation between the presence of lower-hybrid waves and of particles with energies higher than in the surrounding space. These experimental facts suggest that strong coupling between waves and particles is responsible for plasma heating. The Freja data with a high time resolution allow identification of the process of energy transport via a cascade from low frequency waves to high frequency waves accompanied by electron energization.     

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.     

Surface temperature distribution along a thin liquid layer due to thermocapillary convection

The surface temperature distributions due to thermocapillary convections in a thin liquid layer with heat fluxes imposed on the free surface are investigated. The nondimensional analysis predicts that, when convection is important, the characteristic length scale in the flow direction L, and the characteristic temperature difference ΔT₀, can be represented by and , respectively, where L_R and ΔT_T are the reference scales used in the conduction-dominant situations with A denoting the aspect ratio and Ma the Marangoni number. Having had L and ΔT₀ defined, the global surface-temperature gradient ( ), the global thermocapillary driving-force, and other interesting features can then be readily determined. Finally, numerical calculations involving a Gaussian heat flux distribution are presented to justify these two relations.     

Protons with energy of E P ≥ MeV under the earth’s radiation belts

Variations in fluxes of quasi-trapped energetic protons were studied on the basis of the data of the CORONAS-I satellite. These variations are characterized by an increase in the proton fluxes with E _P ≥ 1 MeV both in the vicinity of the geomagnetic equator and in the high-latitude region of the magnetosphere. The analysis of structural features of the proton distributions in the regions at L ～ 1–1.1; 3 < L < 4; and L > 4, was performed and made it possible to detect reliably the type of the proton flux increase in this region. The mechanisms of particle scattering leading to the precipitation of energetic protons under conditions of various types of geomagnetic disturbances are considered.     

Observations of electromagnetic emissions inside the Earth’s plasmasphere from the <Emphasis Type="Italic">Interball-1</Emphasis> satellite

The spectrum analyzer AKR-X onboard the Interball-1 satellite at the beginning (August–October 1995) and at the end (August–October 2000) of satellite operation in perigees of its orbital motion recorded and analyzed electromagnetic emissions of the inner regions of the Earth’s plasmasphere in the frequency band 100–1500 kHz at distances of 1.1–1.8 R _E. The observations have shown that the electromagnetic modes (the Z and LO modes escaping the magnetosphere) which are formed at the altitudes 600–4000 km are associated with the subauroral nonthermal continuum and with the recently discovered kilometric continuum. There are noticeable differences in the spectral character of these emissions during the minimum (1996) and maximum (2000) solar activity, when, as a rule, the LO mode escaping the plasmaphere and the continua are not present.     

An Empirical Model of the Radiation Belt of Helium Nuclei

Based on satellite data, we present the results of modeling the spatial and energy distributions of integral fluxes of He nuclei (α particles) with E > 1, 2, 4, and 7 MeV at L = 1.1–6.6 in a broad range of B/B ₀ (E is the kinetic energy of particles, L is the drift shell parameter, and B/B ₀ is the magnetic field ratio). Some ways of practically applying the model are considered. The results of calculation of α-particle fluxes for a circular orbit with a height of 300 km and an inclination of 50° are presented.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 243–247.Original Russian Text Copyright © 2005 by Getselev, Sosnovets, Kovtyukh, Dmitriev, Podzolko, Vlasova, Reizman.