Near-Equatorial Electrons as Measured onboard the MirSpace Station

Some results of studying the electrons with energies of tens to hundreds of keV at the low and near- equatorial geomagnetic latitudes by using the instruments Sprut-V and Ryabina-2 onboard the Mirspace station in 1991 are presented. It is found that at L< 1.2 the enhanced electron fluxes are sporadically detected, being localized within three longitudinal intervals, 180° W–0°–15° E, 90°– 120° E, and 160° E–180°–135° W. The most intense electron fluxes are observed at the lower edge of the near-equatorial boundary of the inner radiation belt on longitudes of the South Atlantic Anomaly between 14 and 20 h MLT. The occurrence of electron bursts does not depend on the geomagnetic disturbance level. A hardening of the electron spectra is observed near the geomagnetic equator. At L< 1.1, the more energetic particles are located closer to the geomagnetic equator. The results are compared with the data on the low-frequency waves and fields at low and near-equatorial latitudes obtained by the Ariel-4and San Marco Dsatellites, as well as by the spacecraft and ground-based observations of the thunderstorm global distribution. The thunderstorms are considered as a possible source of electron production near the geomagnetic equator.     

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.     

Sources and Losses of Energetic Electrons at Low Altitudes from Satellite Data

Fluxes and differential spectra of 0.04–2.0 MeV electrons at low altitudes in the Earth's magnetosphere are considered in comparison with the model spectra AE-8 MAX and AE-8 MIN. Possible causes of the discrepancy between the observational and model spectra are discussed. The coefficients of radial diffusion at various L-shells are estimated for the maximum of solar activity (using the Interkosmos-19 data) and for the minimum of solar activity (using the Kosmos-1686 data) and are derived from the model AE-8. A quantitative evaluation of the electron yield from radial diffusion at low L shells is derived. Ionization losses, Coulomb angle scattering, and resonant wave–particle interaction are considered as the loss mechanisms. A calculation of these losses at the low L-shells is given. The electron distribution at low L-shells is best fitted by a combination of dissipative terms from different models: Coulomb scattering dominates at the lower L-shells (L = 1.2–1.4) and the resonant wave–particle interaction controls the radiation belt maximum and the gap (L = 1.4–2.0).     

Invariance of Charged Particle Time Profiles at Late Stages of SCR Events from the Data of Multisatellite Observations

Based on the data obtained in simultaneous measurements on the Helios-1 and Helios-2 spacecraft, the properties of the spatial and temporal invariance of spectra of protons with energies more than 4 MeV and electrons with energies more than 0.3 MeV are studied during the phase of intensity decay in events initiated by the following associations: a flare—coronal mass ejection—coronal and interplanetary shock waves. Emphasis is placed on research into the fluxes of electrons, whose possibility to be accelerated by shock waves is problematic. It is shown that the spectra and decay times of both protons and electrons are approximately invariant relative to the flare coordinates in a wide angular range. Depending on the western or eastern spacecraft position in relation to the front part of a shock wave, one observes a delay or advance of the onset of the invariant mode relative to the shock wave arrival, which increases with the growth of the corresponding angular distance.     

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).     

Fluxes of Quasi-trapped Electrons with Energies >0.08 MeV in the Near-Earth Space on Drift Shells <Emphasis Type="Italic">L</Emphasis> < 2

We study the characteristics of fluxes of electrons with energy >80 keV in the near-Earth space regions corresponding to the drift shells L = 1.7, 1.4, and 1.1 observed during the entire period of the GRIF experiment onboard the Spectr module of the Mir orbital station from October 1995 to June 1997. The obtained geographic maps of the distribution of electron fluxes at the height of the station flight (400 km) and, also, the estimates of the spectra indicate that the South-Atlantic Anomaly provides for a mechanism of stable replenishment for shells with L < 1.5. The mechanism of stable replenishment of shells with L < 1.5 may be due to the scattering, in the residual atmosphere, of electrons from the inner radiation belt precipitating into the region of the South-Atlantic Anomaly.     

Short increases of the fluxes of electrons with energies > 0.08 MeV at low-latitude (<Emphasis Type="Italic">L</Emphasis> < 2) regions of near-Earth space

We present the characteristics of short (duration less than 1 min) increases of the counting rate of electrons with energies >0.08 MeV observed in low-latitude (L < 2.0) regions of near-Earth space in the course of the GRIF experiment on the Spektr module of the Mir orbital station. The measurements were carried out using a set of instruments including X-ray and gamma-ray spectrometers, as well as detectors of electrons, protons, and nuclei with large and small geometrical factors, which allowed one to detect the fluxes of charged particles both in the region of the Earth’s radiation belts and in regions close to the geomagnetic equator. As a result of more than 1.5 years of observation, it is demonstrated that short increases in the intensity of electrons of subrelativistic energies are detected not only in the regions of the near-Earth space known as “precipitation zones” (1.7 < L < 2.5), but in high-latitude regions (up to the geomagnetic equator, L < 1.1) as well. Two types of increases of the electron counting rate are found: either fairly regular increases repeating on successive orbits or increases local in time. The latter type of increases can be caused by a short enhancement of electron flux on a given drift shell. The results of our measurements have shown that the duration of the detected increases in intensity can be rather short, as little as 20–30 s. Therefore, in the case of large amplitudes, such increases of the counting rate of electrons can imitate astrophysical events of the type of cosmic gamma-ray bursts in the detectors of hard X-ray and gamma radiation.     

Relationship between the fluxes of relativistic electrons at geosynchronous orbit and the level of ULF activity on the Earth’s surface and in the solar wind during the 23rd solar activity cycle

We present the results of a cross-correlation analysis made on the basis of Spearman’s rank correlation method. The quantities to correlate are daily values of the fluence of energetic electrons at a geosynchronous orbit, intensities of ground and interplanetary ultra-low-frequency (ULF) oscillations in the Pc5 range, and parameters of the solar wind. The period under analysis is the 23rd cycle of solar activity, 1996–2006. Daily (from 6 h to 18 h of LT) magnetic data at two diametrically opposite observatories of the Intermagnet network are taken as ground-based measurements. The fluxes of electrons with energies higher than 2 MeV were measured by the geosynchronous GOES satellites. The data of magnetometers and plasma instruments installed on ACE and WIND spacecraft were used for analysis of the solar wind parameters and of the oscillations of the interplanetary magnetic field (IMF). Some results elucidating the role played by interplanetary ULF waves in the processes of generation of magneospheric oscillations and acceleration of energetic electrons are obtained. Among them are (i) high and stable correlation of ground ULF oscillations with waves in the solar wind; (ii) closer link of mean daily amplitudes of both interplanetary and ground oscillations with ‘tomorrow’ values of the solar wind velocity than with current values; and (iii) correlation of the intensity of ULF waves in the solar wind, normalized to the IMF magnitude, with fluxes of relativistic electrons in the magnetosphere.     

Design of transfer trajectories between resonant orbits in the Earth–Moon restricted problem

The application of dynamical systems techniques to mission design has demonstrated that employing invariant manifolds and resonant flybys enables previously unknown trajectory options and potentially reduces the ΔV$\mathrm{\Delta }V$ requirements. In this investigation, planar and three-dimensional resonant orbits are analyzed and cataloged in the Earth–Moon system and the associated invariant manifold structures are computed and visualized with the aid of higher-dimensional Poincaré maps. The relationship between the manifold trajectories associated with multiple resonant orbits is explored through the maps with the objective of constructing resonant transfer arcs. As a result, planar and three-dimensional homoclinic- and heteroclinic-type trajectories between unstable periodic resonant orbits are identified in the Earth–Moon system. To further illustrate the applicability of 2D and 3D resonant orbits in preliminary trajectory design, planar transfers to the vicinity of L₅ and an out-of-plane transfer to a 3D periodic orbit, one that tours the entire Earth–Moon system, are constructed. The design process exploits the invariant manifolds associated with orbits in resonance with the Moon as transfer mechanisms.     

Disturbance in the lower ionosphere that accompanied the reentry of the Chelyabinsk cosmic body

The paper describes quasi-periodic and aperiodic variations in the phase and amplitude of radio waves of LF and VLF ranges, which accompanied the flight and explosion of the Chelyabinsk meteoroid. Quasi-periodic variations in the phase have been explained by the generation of acoustic-gravity waves in the atmosphere, which modulate the electron density in the ionosphere and the phase of radio waves. Aperiodic variations in the phase and amplitude of radio waves are associated with an increase in the electron density in the lower ionosphere (at altitudes of 65–70 km). This increase was most likely caused by the interactions of subsystems in the Earth–atmosphere–ionosphere–magnetosphere system or, more correctly, by the precipitation of high-energy electrons from the magnetosphere into the lower ionosphere, which was stimulated by the flight and explosion of a cosmic body. According to the estimates, the density of the flux of electrons with energies of 100 KeV should be on the order of 106 m^–2 s^–1.     

Nonlinear Evolution of a Balloon Satellite Orbit

The motion of a spherically symmetric balloon satellite near the equatorial plane is considered. Taking the Earth's oblateness and solar light pressure into account, the integral of motion can be obtained under certain simplifications. The eccentricity is related to the solar angle which represents an angle between pericenter and the Sun. This analytical approximation describes a large and complicated evolution of the eccentricity in corresponding areas of the phase space and the space of parameters. Phase portraits contain fixed saddle points and separatrices that divide different types of oscillations of the eccentricity. In the unsimplified problem, separatrices break down, and specific stochastic motions arise. The aims of the present study are (1) evaluation of the accuracy of analytical approximation with the help of numerical integration using a sufficiently complete model of motion and (2) numerical investigation of stochastic motions and dimensions of stochastic zones in the region of broken separatrices for an adequate model of motion. For a balloon satellite with a semimajor axis of 2.15 Earth's radii and a windage of 30 cm²/g the dimensions of a stochastic zone in eccentricity and solar angle are 10^–5and 0.1°, respectively. The analytical approximation describes the orbit evolution in the right way, except for the cases of large eccentricities, e> 0.4, which corresponds to a pericenter height of less than 1400 km, where the atmospheric drag is already significant.     

On the belt of energetic electrons at <Emphasis Type="Italic">L</Emphasis> = 2.75 in the Earth’s magnetosphere

In 1964, during flights of the ELECTRON satellites the narrow belts of energetic electrons (E _e ≈ 6MeV) have been discovered in the Earth’s magnetosphere at L ≈ 2.75. The same structures approximately at the same magnetic shells were found in 2004 by the CORONAS-F and SERVIS-1 satellites. A comparison of the results of these experiments is presented. It is shown that the additional narrow belts of energetic electrons occur after intense magnetic storms (D _st > 100 nT), in our cases, having a double-triple structure. The lifetime of these belts is a few months and their disappearance had a gradual character. The obtained results separated in time by 40 years suggest the constancy of the sources of particles of the Earth’s radiation belts and processes occurring in the magnetosphere, which ensures not only existence of the radiation belts, but also the recurrence of various exotic phenomena in the belts similar to the belt of energetic electrons at the inner magnetic shells.     

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.     

Periodic solutions in three-dimensional restricted three-body problem: 2. Loss of symmetry at the 1:1 resonance

Within the framework of the circular restricted three-body problem a family of inverse periodic orbits around the two attracting bodies (the Egorov’s family) and families generated by it at the 1:1, 2:1, and 3:1 resonances for three-dimensional orbits in the Sun-Earth and Earth-Moon systems are considered. Their relationship with families generated by orbits around the libration points L ₁, L ₂ and L ₃ is investigated. One of the families contains periodic solutions that seem promising as possible orbits for the space radio telescope of the Millimetron project.     

Acceleration of solar cosmic rays and the fine spectral structure of type II radio bursts

On the basis of data, obtained by means of the ground-based solar service RSTN (Radio Solar Telescope Network) and the geostationary satellite system GOES, the relationship between the solar cosmic rays (SCR) intensity I _p with the proton energy E _p > 1 MeV and parameters of meter-decameter type II radio bursts in the frequency range of 25–180 MHz is studied. The process of proton acceleration by shock waves was characterized by the frequency drift velocity of radio bursts V _mII and the relative difference between radio emission frequencies at the first two harmonics b. It is shown that the coefficient of correlation between I _p and b increases with E _p growing from 0.40 to 0.70, while a similar coefficient between I _p and V _mII does not exceed 0.30. Indications in favor of the two-stage SCR acceleration model are obtained.     

Radiation Electrification of Spacecraft Leeward Surfaces by Auroral Electrons in the Ionosphere

A methodology of the physical modeling of radiation electrification of the leeward surfaces of the materials used to construct space vehicles by auroral electrons, when the vehicles are flown supersonically around by the ionospheric plasma at low and middle heights, is developed. Based on laboratory modeling, numerical experiments, and in situ observations, the dependencies of charging levels and equilibrium potentials on the ratio of the auroral electron density to the positive ions in the near wake behind the body and in the undisturbed plasma are determined.     

Variation of the trapped proton flux in the inner radiation belt of the earth as a function of solar activity

Fluxes of trapped protons with energies above 70 MeV measured onboard the NOAA-15 satellite during the 23rd solar activity cycle (from 1999 to 2006) are analyzed. Comparing to similar experimental data obtained for 1976–1996, regularities of changes in the proton flux at low drift shells (L = 1.14–1.20) of the Earths’s radiation belt caused by changes in the solar activity are discussed.     

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.     

On Saturn’s rotation relative to a center of mass under the action of the gravitational moments of the Sun and Jupiter

Saturn’s rotation relative to a center of mass is considered within an elliptic restricted three-body problem. It is assumed that Saturn is a solid under the action of gravity of the Sun and Jupiter. The motions of Saturn and Jupiter are considered elliptic with small eccentricities e_S and e_J, respectively; the mean motion of Jupiter n_J is also small. We obtain the averaged Hamiltonian function for a small parameter of ε = n_J and integrals of evolution equations. The main effects of the influence of Jupiter on Saturn’s rotation are described: (α) the evolution of the constant parameters of regular precession for the angular momentum vector I₂; (β) the occurrence of new libration zones of oscillations I₂ near the plane of the celestial equator parallel to the plane of the Jupiter’s orbit; (γ) the occurrence of additional unstable equilibria of vector I₂ at the points of the north and south poles of the celestial sphere and, as a result, the existence of homoclinic trajectories; and (δ) the existence of periodic trajectories with arbitrarily large periods near the homoclinic trajectory. It is shown that the effects of (β), (γ), and (δ) are caused by the eccentricity e of the Jupiter’s orbit and are practically independent of Jupiter’s mass (within satellite approximation).     

遥测天线升降机构谐振频率测试方法的研究

研究设计一套遥测天线升降机构谐振频率的测试方法。经测试,遥测天线升降机构不会与天线发生共振,遥测天线谐振频率约为18Hz,升降机构垂直方向的最低谐振频率为12.82Hz,侧向方向的最低谐振频率为25.64Hz,前后方向的最低谐振频率为38.46Hz。