Polarization of ULF waves in the earth’s magnetosphere

Conditions for the realization of ULF waves with different polarization are formulated and verified with the use of observational data from the spacecrafts which performed measurements in the earth’s magnetosphere. It is shown that the conditions formulated are in good agreement with observed wave parameters.     

Toroidal quarter waves in the Earth’s magnetosphere: theoretical studies

An analytic model has been developed for toroidal quarter wave (QW) oscillations in the Earth’s magnetosphere using idealistic and highly asymmetric ionospheric boundary condition. The background magnetic field is dipolar and plasma density distribution is governed by a power law 1/r ^m where r is the geocentric distance of any point along the field line and m is the density index. The solution thus obtained has been compared with the numerical solutions. Earlier workers had developed the analytic model for trivial 1/r ⁶ (m=6) type of plasma density distribution along the field line for which the period of the fundamental is twice that of corresponding half wave (i.e. toroidal oscillation in the symmetric ionospheric boundary). The present analytic model does reproduce this feature. In addition, it is seen that this ratio decreases for lower values of m. Moreover, for a particular value of m, this ratio shows a decreasing trend with increased harmonic number. The spatial characteristics of QW obtained from present analytic model are in excellent agreement with those computed numerically, thereby validating the model. The departure of frequency computed analytically from that obtained numerically is significant only for the fundamental and this departure reduces sharply with the increased harmonic number. It should be noted that there is no such departure for 1/r ⁶ type of plasma density distribution and spatial structures as well as frequency computed from the present analytic model match perfectly with those computed numerically.     

On one mechanism for the generation of a reverse solar wind shock in the magnetosheath in front of the Earth’s magnetosphere

A possible mechanism for the generation of a reverse fast shock in the magnetosheath in the solar wind flow around the Earth’s magnetosphere is considered. It is shown that such a shock can emerge through the breaking of a nonlinear fast magnetosonic compression wave reflected from the magnetopause toward the bow shock rear. In this case, the magnetopause is represented as a tangential discontinuity with a zero normal magnetic field component at it and the mechanism under consideration is assumed to be secondary with respect to the sudden disturbance of the bow shock-Earth’s magnetosphere system by a nonstationary solar wind shock. A possible confirmation of the process under study by in-situ SC3 experimental observations of the bow shock front motion on the Cluster spacecraft is pointed out.     

Specific features of VLF wave propagation in the earth’s inner magnetosphere

The ray trajectories of waves in the very low frequency (VLF) range in the case of nonducted propagation in the earth’s inner magnetosphere are studied as functions of location of their source region, frequency, and initial angle between the vector of wave normal and intensity vector of external magnetic field. Simulation is performed on the basis of geometric ray tracing approach in multicomponent plasma. The parameters of the magnetospheric medium were calculated using a diffusion model of the concentration distribution of plasma components and the International Geomagnetic Reference Field (IGRF) model. It is shown that the magnetospheric wave reflection can occur if the lower hybrid resonance frequency is greater than its own wave frequency (ω _LHF > ω), i.e., at the latitudes λ ≈ 50°. The simulation results confirm that the quasi-longitudinal approximation cannot be used to describe the magnetospheric whistler propagation. We present simulations of propagation of chorus-type wave magnetospheric emissions that were performed using realistic wave distributions over initial parameters. In particular, we present distributions of chorus waves over directions of wave vector as functions of geomagnetic latitude; these distributions are required to study the particle scattering and acceleration processes in the radiation belts. Our results well agree with CLUSTER satellite measurements.     

Peculiarities of the variations in the coordinates of the Earth’s pole

The appearance of features with cusp points on the diagrams of changes in the coordinates of the Earth’s instantaneous pole (polhodes) is considered as the result of mapping onto the plane of its displacement over the surface during the Earth’s rotational-translational motion. The results of qualitative and quantitative analyses of the data on the coordinates of the Earth’s instantaneous pole are discussed. The basic principles of the theory of Whitney singularities and their application for explaining the bifurcations of the equilibrium positions for the Zeeman catastrophe machine (Arnold 1990) are used in the analyses.     

The effect of the Earth’s oblateness on the Moon’s physical libration in latitude

The Moon’s physical libration in latitude generated by gravitational forces caused by the Earth’s oblateness has been examined by a vector analytical method. Libration oscillations are described by a close set of five linear inhomogeneous differential equations, the dispersion equation has five roots, one of which is zero. A complete solution is obtained. It is revealed that the Earth’s oblateness: a) has little effect on the instantaneous axis of Moon’s rotation, but causes an oscillatory rotation of the body of the Moon with an amplitude of 0.072″ and pulsation period of 16.88 Julian years; b) causes small nutations of poles of the orbit and of the ecliptic along tight spirals, which occupy a disk with a cut in a center and with radius of 0.072″. Perturbations caused by the spherical Earth generate: a) physical librations in latitude with an amplitude of 34.275″; b) nutational motion for centers of small spiral nutations of orbit (ecliptic) pole over ellipses with semi-major axes of 113.850″ (85.158″) and the first pole rotates round the second one along a circle with radius of 28.691″; c) nutation of the Moon’s celestial pole over an ellipse with a semi-major axis of 45.04″ and with an axes ratio of about 0.004 with a period of T = 27.212 days. The principal ellipse’s axis is directed tangentially with respect to the precession circumference, along which the celestial pole moves nonuniformly nearly in one dimension. In contrast to the accepted concept, the latitude does not change while the Moon’s poles of rotation move. The dynamical reason for the inclination of the Moon’s mean equator with respect to the ecliptic is oblateness of the body of the Moon.     

Properties of acoustic-gravity waves in the Earth’s polar thermosphere

The properties of acoustic-gravity waves in the polar regions of the Earth’s thermosphere have been studied. It has been shown that the change in AGW amplitudes occurs against the background of large-scale rotational movements of the medium in the polar thermosphere. The amplitudes of waves increase with AGW propagation against the motion of the medium and decrease when AGW propagate along rotation. An analytical expression for the gain coefficient of AGW perturbations is obtained; the wave’s amplification effect in the opposite wind given the characteristic parameters of the thermosphere is estimated. The results are consistent with the measurements of AGW parameters in the polar regions from the “Dynamic Explorer 2” satellite.)     

Statistical Characteristics of Meteoroid Parameters in the Earth’s Atmosphere

Statistical characteristics of meteoroids with kinetic energy from 0.1 to 440 kt TNT are estimated based on NASA satellite observations made in 1994–2016. The distributions of the number of falling meteoroids are constructed and analyzed based on the values of their initial kinetic energy, initial velocity, initial mass, altitude, geographic coordinates of the maximum total radiated energy region, and the year of the fall. Correlation dependences “mass–initial kinetic energy,” “maximum total radiated energy region altitude–initial kinetic energy,” and “maximum total radiated energy region altitude–initial velocity (the square of the initial velocity)” are constructed.     

Minicomets in the Solar system and in the Earth’s atmosphere and related phenomena

We consider the history of discovery and justify the existence in the Solar system of a new class of bodies—minicomets, i.e., bodies of cometary nature and composition but of low mass. Two classes of minicomets are distinguished: icy ones similar to the Tunguska meteorite, and snow ones, which break up at high altitudes.     

Gamma-ray bursts and the production of cosmogenic radionuclides in the Earth’s atmosphere

An explanation is offered for the impulsive increase in the concentration of cosmogenic radiocarbon in annual tree rings (Δ¹⁴C ～ 12‰) from AD ?775. A possible cause of such an increase could be the high-energy emission from a Galactic gamma-ray burst. It is shown that such an event should not lead to an increase in the total production of ¹⁰Be in the atmosphere, as distinct from the effect of cosmic-ray fluxes on the atmosphere. At the same time, the production of an appreciable amount of ³⁶Cl, which can be detected in Greenland and Antarctica ice samples of the corresponding age, should be expected. This allows the effects caused by a gamma-ray burst and anomalously powerful proton events to be distinguished.     

Probing the Earth’s Interior with the LENA Detector

A future large-volume liquid scintillator detector such as the proposed 50 kton LENA (Low Energy Neutrino Astronomy) detector would provide a high-statistics measurement of terrestrial antineutrinos originating from β-decays of the uranium and thorium chains. Additionally, the neutron is scattered in the forward direction in the detection reaction . Henceforth, we investigate to what extent LENA can distinguish between certain geophysical models on the basis of the angular dependence of the geoneutrino flux. Our analysis is based on a Monte-Carlo simulation with different levels of light yield, considering an unloaded PXE scintillator. We find that LENA is able to detect deviations from isotropy of the geoneutrino flux with high significance. However, if only the directional information is used, the time required to distinguish between different geophysical models is of the order of severals decades. Nonetheless, a high-statistics measurement of the total geoneutrino flux and its spectrum still provides an extremely useful glance at the Earth’s interior.     

A Simulation Study of the Plasma Wave Enhancements in the Earth’s Equatorial Plasmasphere

In the equatorial plasmasphere, plasma waves are frequently observed. To improve our understanding of the mechanism generating plasma waves from instabilities, a comparison of observations, linear growth-rate calculations, and simulation results is presented. To start the numerical experiments from realistic initial plasma conditions, we use the initial parameters inferred from observational data obtained around the plasma-wave generation region by the Akebono satellite. The linear growth rates of waves of different modes are calculated under resonance conditions, and compared with simulation results and observations. By employing numerical experiments by a particle code, we first show that upper hybrid-, Z-, and whistler-mode waves are excited through instabilities driven by a ring-type velocity distribution. The simulation results suggest a possibility that energetic electrons with energies of some tens of keV confined around the geomagnetic equator are responsible for the observed enhancements of Z- and whistler-mode waves. While the comparison between linear growth-rate calculations and observations shows the different tendency of wave amplitude of Z-mode and whistler-mode waves, the wave amplitude of these wave modes in the simulation results is consistent with the observation.     

On constructing the general Earth’s rotation theory

In the present paper the equations of the orbital motion of the major planets and the Moon and the equations of the three–axial rigid Earth’s rotation in Euler parameters are reduced to the secular system describing the evolution of the planetary and lunar orbits (independent of the Earth’s rotation) and the evolution of the Earth’s rotation (depending on the planetary and lunar evolution). Hence, the theory of the Earth’s rotation can be presented by means of the series in powers of the evolutionary variables with quasi-periodic coefficients with respect to the planetary–lunar mean longitudes. This form of the Earth’s rotation problem is compatible with the general planetary theory involving the separation of the short–period and long–period variables and avoiding the appearance of the non–physical secular terms.     

Study of the interannual variations of the Earth’s rotation

In this work we investigate the variations of the Earth’s rotation in the interval of periods from 2 to 8 years using the longest available observational series obtained both by means of astrometry and space geodesy. We found an abrupt change of the variation pattern in the middle of the 1980s, when classical ground-based astrometric facilities for studying the Earth Rotation Parameters (ERP) were replaced with space geodesy methods. Variations with a 6-year periodicity and ∼0.2-ms amplitude practically disappeared (space geodesy instruments did not detect these variations right from the start), but the 2- to 4-year periodicities increased in amplitude and began to dominate in this frequency range under consideration. In this study, we analyze some possible excitation sources and possible causes of the change in the variability pattern.     

On the origin of energetic particles in the foreshock region of the Earth’s bow shock

We consider the processes related to the formation of the so-called foreshock region upstream of the Earth’s bow shock. We suggest a model based on the surfing of pick-up ions in the bow shock front in terms of which the ion acceleration mechanism in the front can be explained. We ascertain the physical conditions under which the accelerated ions lie upstream of the shock front and determine the direction of motion of the energetic ions. We conclude that it is this population of energetic ions (longitudinal beams) that plays a major role in forming the ion foreshock boundary.     

Influence of the hot oxygen corona on the satellite drag in the Earth’s upper atmosphere

Calculation results on the possible influence of the hot oxygen fraction on the satellite drag in the Earth’s upper atmosphere on the basis of the previously developed theoretical model of the hot oxygen geocorona are presented. Calculations have shown that for satellites with orbits above 500 km, the contribution from the corona is extremely important. Even for the energy flux Q ₀ = 1 erg cm⁻² s⁻¹, the contribution of the hot oxygen can reach tens of percent; and considering that real energy fluxes are usually higher, one can suggest that for extreme solar events, the contribution of hot oxygen to the atmospheric drag of the satellite will be dominant. For lower altitudes, the contribution of hot oxygen is, to a considerable degree, defined by the solar activity level. The calculations imply that for the daytime polar atmosphere, the change of the solar activity level from F _10.7 ∼ 200 to F _10.7 ∼ 70 leads to an increase in the ratio of the hot oxygen partial pressure to the thermal oxygen partial pressure by a factor of almost 30, from 0.85 to 25%. The transition from daytime conditions to nighttime conditions almost does not change the contribution from suprathermal particles. The decrease of the characteristic energy of precipitating particles, i.e., for the case of charged particles with a softer energy spectrum, leads to a noticeable increase of the contribution of the suprathermal fraction, by a factor of 1.5–2. It has been ascertained that electrons make the main contribution to the formation of the suprathermal fraction; and with the increase of the energy of precipitating electrons, the contribution of hot oxygen to the satellite drag also increases proportionally. Thus, for a typical burst, the contribution of the suprathermal fraction is 30% even at relatively high solar activity F _10.7 = 135.     

Role of the solar wind parameters in changing orbital motion of the Earth’s satellites

The investigation of the solar wind and geomagnetic activity parameters' effect on variations of the orbital motion periods of artificial satellites has been continued. The periods of orbital motion of uncontrolled satellites from the database of the Ukrainian network of optical stations (UNOS) for 2012–2014 was used. The data have been compared with the values of geomagnetic planetary index K and the energy spectra of protons and electrons obtained by the GEOS satellites in events during which the orbital periods have changed. It is shown that, in the energy spectra of the proton and electron fluxes, there is no effect of softening the spectrum with time at the time of the flare appearance. This indicates the possibility of particle accumulation above the active region (AR), which entails further continuous energy emission of the solar flare from AR. Dependences have been obtained between the geomagnetic activity and the solar wind speed at a given interplanetary magnetic field strength during the periods under study for the changes in the orbital motion periods of satellites. The corresponding correlation coefficients are 0.93–0.96.     

Solar-Terrestrial Relations: Magnetic Turbulence in the Earth’s Magnetosphere and Geomagnetic Activity

Recent spacecraft observations of magnetic turbulence in the ion foreshock, in the magnetosheath, in the polar cusp regions, and in the magnetotail will be reviewed. Turbulence features like the fluctuation level, the spectral power law index, the turbulence anisotropy and intermittency, and the turbulence driver will be addressed.