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We study the properties of the cyclotron amplification of whistler-mode waves during their propagation in the Earth’s magnetosphere in the presence of large-scale density inhomogeneities such as the plasmapause or density ducts. Wave propagation is considered within the framework of the geometrical optics with the use of cold plasma density profiles measured onboard the Van Allen Probes satellites. Wave amplitude variation due to the cyclotron interactions with energetic electrons having an anisotropic distribution function is studied. The cyclotron growth rate is calculated along the wave trajectory taking into account the wave vector variation for a given analytical distribution function of energetic electrons. We show that in the case of guided propagation in a density duct or near the plasmapause the frequency dependences of the one-hop wave gain and the local growth rate in the equatorial region approximately coincide with each other for low initial wave normal angles (|Θ0| ≲ 30°) and relatively low energies (W0 ≲ 15 keV). The amplification band expands towards the higher frequencies for higher initial propagation angles and electron energies. In the case of nonducted propagation, the efficiency of cyclotron interactions is notably lower, and the frequency dependences of the one-hop wave gain and the equatorial growth rate differ: the waves having the initial wave angle directed towards the Earth are stronger amplified, and this asymmetry increases with increasing electron energy.

In the framework of the approximation of geometric optics, the peculiarities of VLF-wave propagation in the Earth’s ionosphere and magnetosphere during the creation of large-scale artificial plasma irregularities by heating facilities such as HAARP and “Sura” in the ionosphere are studied. For calculation of ray trajectories, the profile of the concentration and ion composition of plasma is taken by calculating the SAMI2 ionospheric model, which was modified to take the influence on the ionosphere of the HF emissions of heating facilities into account. As a result of the influence of the heating facilities on the ionosphere, a region could occur with an increased plasma concentration that is stretched out along the geomagnetic field (up to heights on the order of the Earth’s radius) with small dimensions across the field (∼1°). The ray trajectories of waves that propagate from heights of about 100 km from different initial points in the region where such a disturbance has been created with different initial inclination angles of the wave normal are studied in this paper. Both lightning discharges and modulated HF heating of the ionosphere could be the sources of such waves. It is shown on the basis of the performed analysis that the presence of such disturbances in density can lead to a substantial changes in wave-propagation trajectories, in particular, to efficient channeling of VLF waves in the disturbance region and an increase in the interval of the initial propagation angles of waves, which can reach the ionosphere in the opposite hemisphere.

The properties of quasiperiodic (QP), extremely low-frequency (ELF), and very low-frequency (VLF) emissions detected at a ground-based station in northern Finland between 15:00 UT and 22:00 UT on December 24, 2011 were studied. Characteristic periods in the spectra of QP emissions at different timescales and their dynamics during the considered event were analyzed. Two types of period variations of the QP emissions were observed: a regular increase of periods on timescales of 1 min to 2.5 min and appreciable period variations on a timescale of 1–10 min during substorms. These period variations are explained based on the properties of a self-oscillating cyclotron-instability regime in the magnetosphere. The analysis of the fine structure of the spectra of QP elements indicated that short-periodic modulations with periods of approximately 3 and 6 s were detected in the low-frequency part of the spectrum (f 2.5 kHz), respectively. The 6 s period corresponded to the period of two-hop propagation of whistling atmospherics. The presence of this short-periodic modulation may be related to the passive mode locking in a magnetospheric cyclotron maser.

We present analytical and numerical estimations of the value and frequency dependence of the impedance and noise electromotive force (EMF) in the context of the conditions which correspond to the trajectories and parameters of the antennas borne by geophysical monitoring satellites. The estimations were obtained for two circular orbits at altitudes of 600 and 1200 km over the Earth’s surface in the frequency range from 20 to 120 kHz, which corresponded to the area of the lower-hybrid resonance, where a higher level of noise emissions is observed at the altitudes under consideration. It is shown that near the lower-hybrid resonance frequency, the real part of the antenna impedance is determined by the resonant “monopole” loss by radiation of quasipotential waves. In the nonresonant frequency band (at the frequencies below the frequency of the lowerhybrid resonance), the antenna reactance is determined by the transit loss, which is, however, low as compared with the resonant loss. When the noise was calculated, the medium was assumed to be a two-temperature plasma. The spectral density of the power of the noise EMF lies in the range $$ V_{\omega}^2\approx \left( {2-4} \right)\cdot {10^{-12 }}-{10^{-13 }}\;{V^2}\cdot H{z^{-1 }} $$ and is determined mainly by suprathermal electrons. In the nonresonant frequency band, the efficient temperature of noise radiation is equal to the temperature of the “cold” plasma component, and the antenna reactance is determined by the transit loss, i.e., the level of the noise EMF is low as compared with the EMF in the resonant frequency band.

We study theoretically the propagation of lower-hybrid resonance (LHR) waves in the auroral ionospheric plasma. The ray-tracing technique is used to study the properties of LHR wave propagation with account of a large-scale inhomogeneity both along and across the geomagnetic field. It is shown that wave refraction in such an inhomogeneous medium can result in direct transformation of LHR waves whose wave normals make large angles with the geomagnetic field into whistler-mode waves, whose wave vectors are close to the geomagnetic-field direction and which can therefore pass through the ionosphere to the ground. The parameters of LHR waves which can thus be transformed into whistler-mode waves are found. The transformation process considered can be important for interpreting ground-based observations of ELF waves.

Numerical analysis of the model for cyclotron instability in the Earth's magnetosphere is performed. This model, based on the self-consistent set of equations of quasi-linear plasma theory, describes different regimes of wave generation and related energetic particle precipitation. As the source of free energy the injection of energetic electrons with transverse anisotropic distribution function to the interaction region is considered. A parametric study of the model is performed. The main attention is paid to the analysis of generation regimes for different characteristics of energetic electron source, such as the shape of pitch angle distributions and its intensity. Two mechanisms of removal of energetic electrons from a generation region are considered, one is due to the particle precipitation through the loss cone and another one is related to the magnetic drift of energetic particles. It was confirmed that two main regimes occur in this system in the presence of a constant particle source, in the case of precipitation losses. At small source intensity relaxation oscillations were found, whose parameters are in good agreement with simplified analytical theory developed earlier. At a larger source intensity, transition to a periodic generation occurs. In the case of drift losses the regime of self-sustained periodic generation regime is realized for source intensity higher than some threshold. The dependencies of repetition period and dynamic spectrum shape on the source parameters were studied in detail. In addition to simple periodic regimes, those with more complex spectral forms were found. In particular, alteration of spikes with different spectral shape can take place. It was also shown that quasi-stationary generation at the low-frequency band can coexist with periodic modulation at higher frequencies. On the basis of the results obtained, the model for explanation of quasi-periodic whistler wave emissions is verified.

We study the cyclotron interaction of energetic electrons and whistler waves in plasma waveguides formed by inhomogeneous distribution of cold plasma. Such waveguides can be formed in the Earth's magnetosphere, e.g., by the plasmapause or by ducts with enhanced background-plasma density. In this paper, we consider a cylindrically symmetric model of a magnetospheric duct with enhanced cold-plasma density in a homogeneous magnetic field. The spatial structure of the eigenmodes of such a waveguide is found. We obtain a set of self-consistent quasilinear equations for cyclotron instability with eigenmode structure taken into account, thus generalizing the quasilinear theory of a magnetospheric cyclotron maser.

Further analysis of energetic electron precipitation at the evening sector of magnetosphere is performed. In the framework of the quantitative model of cyclotron wave-particle interactions developed in the previous Pasmanik et al. paper, the case of finite spread over energies of initial energetic electron distribution is studied. The solution for distribution function of energetic electron is found. The energetic spectrum of trapped and precipitating electrons and whistler wave spectrum are analysed.Key words. Magnetospheric physics (energetic particles · precipitating; energetic particles · trapped); · Space plasma physics (wave-particle interactions).

Whistler-mode wave propagation in magnetospheric ducts of enhanced cold plasma density is studied. The case of the arbitrary ratio of the duct radius to the whistler wavelength is considered, where the ray-tracing method is not applicable. The set of duct eigenmodes and their spatial structure are analysed and dependencies of eigenmode propagation properties on the duct characteristics are studied. Special attention is paid to the analysis of the group delay time of one-hop propagation of the whistler wave packet along the duct. We found that, in contrast to the case of a wide duct, the group delay time in a rather narrow duct decreases as the eigenmode number increases. The results obtained are suggested for an explanation of some types of multi-component whistler signals.

The formation of a zone of energetic electron precipitation by the plasmapause, a region of enhanced plasma density, following energetic particle injection during a magnetic storm, is analyzed. Such a region can also be formed by detached cold plasma clouds appearing in the outer magnetosphere by restructuring of the plasmasphere during a magnetic storm. As a mechanism of precipitation, wave-particle interactions by the cyclotron instability between whistler-mode waves and electrons are considered. In the framework of the self-consistent equations of quasi-linear plasma theory, the distribution function of trapped electrons and the electron precipitation pattern are found. The theoretical results are compared with experimental data obtained from NOAA satellites.Key words. Magnetospheric physics · Energetic particles · Precipitating and trapped · Plasma waves and instabilities