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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.

This paper presents the results of simultaneous observations of narrow-band noise VLF emissions in the frequency range 4–10 kHz at Kannuslehto ground station in Northern Finland and by Van Allen Probes (previously RBSP) in the equatorial part of the magnetosphere. The event of December 25, 2015, is considered. During the event, narrow-band noise VLF emissions were detected on the Earth in two frequency ranges, f = 3.5–6 kHz and f = 8–10 kHz, between 1100 and 1300 UT. Narrow-band VLF emissions in the equatorial zone were also observed during that time by the RBSP-B satellite; their frequency was close to the electron equatorial half-gyrofrequency and gradually increased from 3 to 11 kHz during the satellite motion from L = 5.0 to L = 3.0. Analysis of the fine structure of the emissions on the ground showed that their spectral and temporal characteristics corresponded to emissions by the satellites in localized zones at different L-shells. The ground-based observations at lower frequencies correlated with the satellite observations at larger L-shells. In order to localize the regions of the generation of the VLF emissions observed at Kannuslehto auroral station at different frequencies, we calculated the ray trajectories of waves from the equator for the plasma density distributions detected by Van Allen Probes. The calculations of the trajectories showed that the VLF waves detected at Kannuslehto station could travel to the ground only if they propagated in the large-scale density ducts (700–900 km) observed by Van Allen Probes.

We study specific features of VLF waves propagation in the Earth's ionosphere and magnetosphere in the presence of large-scale field-aligned plasma inhomogeneities (ducts). These inhomogeneities can, e.g., be formed during the ionosphere heating by high-power HF facilities such as HAARP and “Sura.” They can extend up to altitudes of several thousand km along geomagnetic field lines and have transverse scales of about 1 degree determined by the heated region scale. We analyze ray trajectories of VLF waves with frequencies of 1 to 15 kHz starting from about 100 km altitude, and use the plasma parameters obtained within the framework of the SAMI2 simulation model [Huba et al., 2000]. This model employs MHD equations for thermal plasma and allows one to obtain the plasma parameters along the entire magnetic flux tube in a fixed meridional plane. By knowing the ray trajectories we calculate and compare the amplitude variation along the ray paths for the cases of unperturbed and heated ionosphere. We show that the presence of a large-scale density disturbance produced by the HF heating can lead to significant changes of wave propagation trajectories. In particular, efficient guiding of VLF waves in this region can take place, which in turn can result in the appearance of several wave focusing regions and a drastic local increase of the VLF wave amplitude in these regions (up to ∼10-times as compared to the case of unperturbed plasma). The number of focusing regions is determined by an extension of an artificial duct along the geomagnetic field.

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.

We present the results of a case study of quasi-periodic (QP) ELF/VLF hiss emissions detected on board the Freja and Magion5 satellites. Detailed analysis of available QP events revealed certain specific features of their dynamic spectra, which have not been reported earlier. In particular, we found an event with an increase in the frequency drift rate during the generation of a single element of QP emission, and an event with alteration of QP elements having different frequency drift rates. Another event demonstrates the possible relationship between QP hiss emissions and discrete VLF emissions. Properties of QP events are compared with parameters of energetic electrons and cold plasma, and other available data. Possible scenarios for the formation of these emissions are discussed on the basis of self-consistent simulations of the cyclotron instability, employing the information obtained experimentally. It is shown that the generation regime of self-sustained pulsations can explain consistently our data set. We show that our numerical model is capable of explaining the mentioned specific features of the dynamic spectrum of QP emissions. Comparison of the modeling results with experimental data yields an estimate for the parameters not measured directly. Key words. Magnetospheric physics (plasma waves and instabilities; energetic particles, precipitating; energetic particles, trapped)

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.

The work considers the highly anisotropic electron distribution functions observed by Bell and co-workers at Stanford in the magnetosphere. IOt is maintained that Bells' observations provide evidence for the existence of step like deformations in electron distribution function, and that his observations may be due to such steps. The origin of such steps at the top of hiss band emissions is explained, and the implications for triggering of emissions and chorus is explained.

[1] We present ground-based observations of banded structures (BS) in auroral hiss. This BS hiss was detected at Porojarvi station in Northern Finland, mainly in the local evening from 19 to 23 MLT, during magnetically quiet periods; half of all the events observed corresponded to AE < 50 nT. The structures, which resemble those observed by low-altitude satellites, can be related to the cyclotron resonant interaction of VLF waves at frequencies near the lower-hybrid resonance with suprathermal protons in the upper ionosphere and magnetosphere. The maximum probability distribution of band spacing for the events observed at Porojarvi is reached in the frequency range 200–300 Hz, which corresponds to proton gyrofrequencies at L ∼ 6 at altitudes of 4000–3000 km. We found that the BS hiss was detected in the region of evening-side downward field-aligned currents and rather intense precipitation of ions with energies 1–30 keV, detected by DMSP spacecraft. We propose that the observed BS hiss can be formed not only due to absorption at the proton gyroharmonics, as is usually assumed for similar structures observed onboard satellites, but also due to generation by energetic protons with an anisotropic velocity distribution.

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.

[1] We study the amplification of ducted whistler-mode waves in the Earth’s magnetosphere by the cyclotron instability for different types of energetic electron distributions in velocity space. Particular attention is paid to the comparison between cases of smooth distribution functions and those with sharp gradients (‘‘steps’’) in velocity space, which arise naturally owing to interactions with noise-like VLF emissions. We show that step-like features greatly favor the amplification of whistler-mode waves propagating along the Earth’s magnetic field line and hence the generation of narrowband VLF emissions even if the electron anisotropy is only moderate. The results obtained are discussed in light of observations of discrete VLF emissions from the magnetosphere, in particular those of Bell et al. [2000]. INDEX TERMS: 2720 Magnetospheric Physics: Energetic particles, trapped; 2730 Magnetospheric Physics: Magnetosphere—inner; 0654 Electromagnetics: Plasmas; 2772 Magnetospheric Physics: Plasma waves and instabilities; KEYWORDS: whistlers, amplification, anisotropic, electrons, step-like, chorus

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