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.     

Some features of solar cosmic ray penetration into the Earth’s magnetosphere

We compared fluxes of the 1–100 MeV solar energetic particles (SEP) measured in the interplanetary medium (ACE) and in the magnetosphere (Universitetsky-Tatiana, POES—in polar caps, and GOES-11—at geosynchronous orbit) during several SEP events of 2005–2006. Peak intensities of the SEP fluxes inside and outside the magnetosphere were compared for each event. It is shown that observed inside-outside difference depends mainly on direction of interplanetary magnetic field (IMF), on degree of the SEP anisotropy (pitch-angle distribution) in IMF, and on distance of the dayside magnetopause from the Earth.     

Ray Based Diffraction Tomography of the Ionosphere and Laboratory Inhomogeneous Plasma

A new procedure for restoration of the plasma inhomogeneities with improved resolution is suggested. The procedure deals with the double weighted Fourier transform (DWFT) of the observed wavefield in coordinates of both receivers = (x, y) and sources ₀ = (x ₀, y ₀) [1]. Phase increments between the sources and receivers, being found from DWFT representation, can be used for extracting information on small perturbations of the dielectric constant ~(, z) in a way similar to traditional radio tomography. The resulting resolution of the method is close to the diffraction limit = h/D in the horizontal direction and z = (h/D)² in the vertical direction, where h is the height of inhomogeneities and D is the length of the ground-based receiving system.     

The optimization of the orbital Hohmann transfer

There are four bi-impulsive distinct configurations for the generalized Hohmann orbit transfer. In this case the terminal orbits as well as the transfer orbit are elliptic and coplanar. The elements of the initial orbit a₁, e₁ and the semi-major axis a₂ of the terminal orbit are uniquely given quantities. For optimization procedure, minimization is relevant to the independent parameter e_T, the eccentricity of the transfer orbit. We are capable of the assignment of minimum rocket fuel expenditure by using ordinary calculus condition of minimization for |ΔV_A|+|ΔV_B|=S.We exposed in detail the multi-steps of the optimization procedure. We constructed the variation table of S(e_T) which proved that S(e_T) is a decreasing function of e_T in the admissible interval [e_Tmin,e_Tmax]. Our analysis leads to the fact that e₂=1 for e_T=e_Tmax, i.e. the final orbit is a parabolic trajectory.     

Characteristics of thermal ion outflows in the polar cap according to data of the <Emphasis Type="Italic">Interball-2</Emphasis> satellite

Characteristics of polar wind fluxes at a height of ∼20000 km measured by the Hyperboloid mass-spectrometer installed onboard the Interball-2 satellite are presented in the paper. The characteristics are presented for the upwelling flows of ionospheric ions H⁺, He⁺, and O⁺ from the sunlit polar cap in the period of solar activity minimum. Orbit segments with minimal precipitation of magnetospheric ions and electrons were preliminarily selected, and the measurements where the fluxes of ions coming from the cusp/cleft were excluded as carefully as possible. Thus, the densities, field-aligned velocities, and temperatures of ions in the regions where fluxes of polar wind could be detected with the maximal probability degree are presented in the paper. It is found that cases when only H⁺ ions are reaching the detector are with high probability the polar wind outflows. Their characteristics agree well with the Tube-7 hydrodynamic model and are as follows: n ≈ 1.5 cm⁻³, V _∥ ∼ 21 km/s; T _∥ = 3500 K, and T _⊥ = 2000 K. In cases when He⁺ and O⁺ ions are also detected, the temperatures are substantially higher than the model ones, and the measured field-aligned velocities of O⁺ fluxes are several times higher than the model ones. Moreover, it was revealed that the polar wind outflows are predominantly observed in the polar cap regions where the polar rain fluxes are very small.     

Ions with a Mass Number of Two in Mass-Spectrometric Experiments aboard Rockets and Satellites

Deuterium ions D⁺and doubly-charged helium ions He⁺⁺have the same mass-to- charge ratio (M/Z= 2) and are not distinguished by the mass-spectrometer. On the basis of analysis of published data, Interkosmos-24satellite data, and theoretical estimations, it is shown that in the ionosphere and plasmasphere the ion with a mass number of two is He⁺⁺and not D⁺, at least at altitudes of higher than 600–800 km. Arguments in favor of the validity of this assumption at lower altitudes are presented. Regularities of the dependence of the N(He⁺⁺)/N(He⁺) ratio on altitude, time of day, season, and solar activity are derived. It is found that in the daytime the N(He⁺⁺)/N(He⁺) ratio decreases with increasing solar activity. The seasonal dependence is most pronounced at nighttime in the altitude interval 1000–2000 km, where this ratio decreases in passing from winter to summer. Peculiarities of the latitude distribution of the absolute and relative values of the He⁺⁺concentration are found in the Interkosmos-24satellite data. On the basis of the same data, a strong longitude effect in the N(He⁺⁺) concentration occurring under certain heliogeophysical conditions is discovered, an effect amplitude attaining one order of magnitude on adjacent orbits. An interpretation of this effect is given.     

Theory of Singular Optimal Controls with Applications to Space Flight Mechanics

The problem of existence of solutions to the problems of optimum control with a singularity condition H(x, , u) const, u U is studied. The necessary conditions of appearance of the singular control, as well as time location and the numbers of singular sections of the trajectories of a controlled object under consideration, are obtained. The numerical algorithms of solving the problems with the condition of singularity of control are constructed. The widely known problem of optimum control of the motion of a high-altitude rocket probe is also considered, and it is proved that in this problem no intermediate section can exist in the law of variation of the thrust. The results of numerical experiments are presented together with their relative evaluation.     

Statistical analysis of turbulence in the foreshock region and in the Earth’s magnetosheath

Statistical properties of magnetic field and plasma flux fluctuations outside the Earth’s magnetosphere are studied on various time scales based on the INTERBALL-1 satellite data. The analysis of “rough” turbulence characteristics has shown that turbulence properties in various parts of the magnetosheath are distinct. The spectral density of the magnetic field undergoes a break at a frequency of ∼0.5 Hz. As a more “fine” characteristic of the fluctuations on various time scales, changes in the shape and parameters of the probability density function were studied. The analysis of the height of a maximum of the probability density function P(0) and of the kurtosis values have shown the presence of two asymptotic modes of P(0), which are characterized by different power laws. The critical scale, on which the properties of P(0) change, corresponds, presumably, to the scales of the Larmor radius of ions. Based on the results of studying structural functions of various orders, the conclusion is drawn that small-scale turbulence in the foreshock and magnetosheath is described by different phenomenological models.     

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.     

Empirical model of pitch-angle distributions of trapped protons on the inner boundary of the Earth’s radiation belt

We have made a generalization of experimental data on the fluxes of trapped protons that were detected by various instruments on three low-orbit satellites (NOAA-17, Universitetskii-Tatiana, and CORONAS-F) during April of 2005. Based on these data, a new quantitative model is suggested to describe the fluxes of trapped protons. It allows one, using analytical expressions, to predict the fluxes of protons with energy from 30 keV to 140 MeV under quiet geomagnetic conditions in the period close to the solar activity minimum at drift shells L = 1.14–1.4. The suggested model establishes differential directional fluxes of protons as a function of pitchangle on the geomagnetic equator and takes into account the anisotropy of trapped particles on the lower boundary of the Earth’s radiation belt.     

Dynamics of the 0.3–100 MeV Proton Energy Spectra in the Inner Heliosphere in Quiet Periods of 1974–1991

Variations of the proton spectra in the 0.3–100 MeV energy range based on the data of various instruments installed onboard the IMP-8 satellite are studied for very quiet, quiet, and quasi-stable solar activity periods during the years 1974–1991. As many as 118 spectra were approximated by two power laws: the left-hand and galactic branches of the spectrum were fitted by the AE ^– function and a dependence of the CE type, respectively, the sum J(E) = AE ^– + CE providing the total spectrum. It is shown that the spectra vary within a solar cycle with a shift of the minimum energy (E _min) to higher energies with increasing solar activity. It follows from the relations between the spectrum parameters thus obtained that, in particular periods of time, an increase (decrease) of the particle flux in the low-energy branch of the spectrum and an intensification (depression) of the GCR particle flux modulation take place simultaneously. This is manifested in a shift of the spectrum parallel to the energy axis. The study of the spectra in the most quiet time during three successive solar minima have shown that low-energy (0.3–10 MeV) protons, as well as GCR, are subject to the 22-year variation in the solar magnetic cycle.     

Stable spatial orbits around collinear libration points

A technique of generation of spatial periodic solutions to the restricted circular three-body problem from periodic orbits of the planar problem has been used for the families of orbits around collinear libration points L ₁ and L ₂. Developing the families obtained at the 1: 1 resonance, we have obtained stable solutions both in the Earth-Moon system and in the Sun-Earth system. Of course, the term “around the libration point” is rather conventional; the obtained orbits become more similar to the orbits around the smaller attracting body. The further development of the family of orbits “around” the libration point L ₂ in the Sun-Earth system made it possible to find the orbits satisfying the new, much more rigorous constraints on cooling the spacecraft of the Millimetron project.     

Application of LB-Planning for Designing the Programs of Trajectory Measurements

The LB-planning is a construction of the dependence between three variables k, m, and , where k is the number of parameters of the linear dynamic system (LDS) under study, m is the specified number of measurements (communication sessions), and (defect) is the maximum value of failure (set of all criterion functions) in a chosen m-point measurement program relative to the optimal program. The problem is reduced to the solution of an extremal problem, which, at m = k + 1, is found rather simply by maximization of the Tchebyshev determinant (TD-planning).     

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.     

An inversion approach for lunar regolith layer thickness using optical albedo data and microwave emission simulation

An approach to inversion of the lunar regolith layer thickness by using multi-channel brightness temperature observation in passive microwave remote sensing is developed. To first make simulation of brightness temperature from the lunar layered media, the lunar regolith layer thickness (d) is proposed being constructed by available lunar DEM (digital elevation mapping) and on site measurements. The physical temperature distribution (T) over the lunar surface is also empirically assumed as a monotonic function of the latitude. Optical albedo of the lunar nearside from the telescopic observation is employed to construct the spatial distribution of the FeO+TiO₂ content (S) in the lunar regolith layer. A statistic relationship between the DEM and S of the lunar nearside is further extended to construction of S of the lunar farside. Thus, the dielectric permittivity (ε) of global lunar regolith layer can then be determined. Based on all these conditions (d,T,ε), brightness temperature of the lunar regolith layer in passive microwave remote sensing, which is planned for China's Chang-E lunar project, is numerically simulated by a parallel layering model using the strong fluctuation theory of random media.Then, taking these simulations with random noise as observations, an inversion method of the lunar regolith layer thickness is developed by using three- or two-channels brightness temperatures. When the S is low, and the four channels brightness temperatures in China's Chang-E project are well distinguishable, the regolith layer thickness and physical temperature of the underlying lunar rock media can be inverted by the three-channels approach. When the S becomes high that the brightness temperature at high frequency channels such as 19.35, 37 GHz are saturated, the regolith layer thickness is alternatively inverted only by the two-channels approach.Numerical simulation and inversion approach in this paper make an evaluation of the performance for lunar passive microwave remote sensing, and for future data calibration and validation.     

Enhancements of fluxes of precipitating energetic electrons on the boundary of the outer radiation belt of the earth and position of the auroral oval boundaries

An analysis of enhancements in the fluxes of electrons with energies above 300 keV registered onboard of the Coronas-F satellite in the polar regions at the boundary of the outer radiation belt is performed. Cases are revealed when the increases in question were observed consequently during multiple crossings of the outer radiation belt boundary. Localization of the revealed events relative to the auroral oval using the data of almost simultaneous observations of electrons with energies of 0.1–10 keV on the Meteor-3M satellite and OVATION model is studied. It is shown that almost all studied increases in relativistic electrons are localized at latitudes of the auroral oval. Various mechanisms which could cause the observed increases are discussed, as well as a possibility of formation of local traps of energetic particles in the high-latitude magnetosphere.     

Gravitational Sensitivity of Solutions–Melts at the Crystallization of Two-Phase InSb–InBi Alloys under Space Conditions

Analyzing the results of space and ground-based experiments carried out in the Baikov Institute of Metallurgy and Materials Science to study the processes of the melting and crystallization of two-phase InSb–InBi alloys of an indium–antimony–bismuth (In–Sb– Bi) triple system, we have demonstrated the gravitational sensitivity of the InSb-based solution– melt. It manifests itself as a certain asymmetry of the boundary of the dissolution of the InSb ingot by the InSb–InBi melt and heterogeneity of the melt along this boundary depending on the magnitude and direction of the gravity force acceleration gin the range (1–10^–3–10^–5)g ₀, where g ₀is the acceleration of the gravity force on Earth. For the first time, it is established in the experiments under analysis that the homogeneity of melts of a complex composition with components of various densities can be reached only at magnitudes of quasistationary (residual) microaccelerations g< 10^–6 g ₀.     

Fluxes of low-energy particles in quiet periods of solar activity and the <Emphasis Type="Italic">MgII</Emphasis> index

Low fluxes of protons with energies 0.3–10 MeV were studied during 21–23 solar cycles as a function of the MgII index using the data of the instruments CPME, EIS (IMP8), and EPHIN (SOHO). It has been shown that a) during quiet time of solar activity the fluxes of protons (background protons) have a positive correlation with the MgII index value throughout the solar cycle, b) specific features of variations of the MgII index during the solar minima of 1986–1987 and 1996–1997 can be considered, as well as variations of background fluxes of low energy charged particles, to be manifestations of the 22-year magnetic cycle of the Sun, and c) periods of the lowest value of the MgII index are also characterized by the smaller values of the ratio of intensities of protons and helium nuclei than in other quiet periods. A hypothesis is put forward that acceleration in a multitude of weak solar flares is one of the sources of background fluxes of low energy particles in the interplanetary space.     

Relative occurrence rate and geoeffectiveness of large-scale types of the solar wind

We investigate the relative occurrence rate for various types of the solar wind and their geoeffectiveness for magnetic storms with Dst < —50 nT. Both integrated effect for the entire time 1976–2000 and variations during this period of 2.5 cycles of solar activity are studied As raw data for the analysis we have used the catalog of large-scale types of the solar wind for the period 1976-2000 (see ftp://ftp.iki.rssi.ru/omni/) created by us with the use of the OMNI database (http://omni.web.gsgc.nasa.gov) [1] and described in detail in [2]. The average annual numbers of different type of events are as follows: 124 ±81 for the heliospheric current sheet (HCS), 8 ±6 for magnetic clouds (MC), 99 ±38 for Ejecta, 46 ±19 for Sheath before Ejecta, 6 ±5 for Sheath before MC, and 63 ±15 for CIR. The measurements that allowed one to determine a source in the solar wind were available only for 58% of moderate and strong magnetic storms (with index Dst < —50 nT) during the period 1976–2000. Magnetic clouds (MC) are shown to be the most geoeffective (~61%). The CIR events and Ejecta with Sheath region are three times less geoeffective (~20–21 %). Variations of occurrence rate and geoeffectiveness of various types of the solar wind in the solar cycle are discussed.