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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.

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).

[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.

[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