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We analyze the nonlinear resonant interaction of energetic electrons with auroral kilometric radiation (AKR). The evolution of the electron distribution function in the energy range 1–150 keV is considered based on the numerical solution of the particle motion equations in a given field of a quasi-monochromatic AKR wave packet. It is shown that for realistic values of the wave amplitude 0.2–0.4 V/m, as a result of the interaction, the loss cone is filled with particles having the energies W

The correlation between the parameters of electromagnetic ion cyclotron waves in Earth’s magnetosphere and the parameters of trapped and precipitating ring current ions is analyzed using the example of a single event. It is shown that the observed energies and the degree of isotropy of proton fluxes at low altitudes correspond to the results from calculating the coefficient of pitch-angle diffusion using data on ion cyclotron wave parameters.

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.

We analyze the resonant interaction of energetic electrons with auroral kilometric radiation (AKR). Possible regimes of such an interaction are studied on the basis of a numerical solution of the particle motion equations in a given field of a quasi-monochromatic AKR wave packet. It is shown that for realistic wave amplitudes 0.2–0.4 V/m, the interaction can be highly nonlinear. As a result of nonlinear interaction, both a substantial (approximately twofold) acceleration of particles and a decrease in their energy (by about 20–50%) are possible. With realistic plasma and wave packet parameters, electrons with initial energies of the order of 10 keV are accelerated, and for electrons with initial energies of several tens of keV, the interaction leads to a decrease in energy.

This paper analyzes the effect of azimuthal proton drift from the nighttime sector of the Earth’s magnetosphere on the characteristics of the pitch-angle anisotropy of proton fluxes in the daytime sector. The drift in the magnetic field caused by curvature of the field lines and the magnetic field gradient, in the absence of external forces, has been considered. The external geomagnetic field has been described with Tsyganenko’s T96 model. The proton drift has been calculated in the approximation of the guiding center motion in the equatorial magnetosphere plane, i.e., after averaging over the bounce oscillations of particles between the mirror points. The influence of two effects on the anisotropy value has been studied. The first effect is related to changes in the proton pitch angle in the course of azimuthal drift. This effect can significantly (up to approximately six times, depending on the T96 model input parameters) increase the transverse anisotropy of protons when they drift from the nighttime to the daytime side. The second effect is caused by drift-shell splitting, as a result of which protons from the nighttime sector from different radial distances come to the same field line on the daytime side: the lower the pitch angle of the particle is, the larger is the distance it starts to drift from. As a result, the radial proton flux gradient on the magnetosphere nighttime side can lead to a pitch-angle anisotropy of fluxes in the daytime sector that is sufficient to generate electromagnetic ion cyclotron (EMIC) waves, even if the fluxes in the nighttime sector were isotropic in the pitch angles. The dependence of this anisotropy on the radial proton flux gradient on the nighttime side has been studied. The maximum anisotropy in the daytime sector due to the longitudinal drift in the geomagnetic field can be achieved at a distance of 5.3–10 RE depending on the Т96 model input parameters.

Simultaneous observations of ELF/VLF and EMIC waves from Van Allen Probe satellites in the daytime Earth’s magnetosphere and on the ground during multiple compressions of the magnetosphere due to the fluctuations of the dynamic pressure of the solar wind are considered. Each magnetospheric compression leads to the generation of a wave burst in these frequency ranges. Based on data on the spectral and amplitude characteristics of the waves, measurements of the magnetic field, and the cold plasma density, the pitch-angle diffusion coefficients of protons and electrons in the vicinity of the loss cone are calculated. It is shown that ELF waves with frequencies of 30 keV) electrons; VLF waves at frequencies of 2–5 kHz may be responsible for precipitation of electrons with energy of ~1 keV. The EMIC waves observed from satellites and on the ground are related to the precipitation of protons with energies of 10–100 keV. The particle energies that correspond to the maxima of the diffusion coefficient are compared with the energies of the charged particles precipitating into the ionosphere, which were determined based on data from low-orbit POES satellites, and it is shown that they are in a good agreement with each other.

We present a method for automatic search and parameterization of discrete elements of very low-frequency (VLF) chorus emissions. The method is based on the processing of dynamic spectrograms using a special scanning algorithm, which is intended for seeking the discrete elements of VLF chorus emissions and calculation of their parameters. We propose to create the optimal dynamic spectrograms for the scanning algorithm by using short-time Fourier transform. The paper gives general recommendations for calculation of spectrograms and their preprocessing. The scanning algorithm is based on processing of the dynamic-spectrogram images by using the methods of mathematical morphology. The developed method was tested for several cases of chorus emissions observed by the Van Allen Probes spacecraft. It is shown that the total errors related to “false positive” detection and missing the target are about 10% of the elements visible to the human eye when the optimal parameters of the scanning algorithm are used and intense discrete elements are processed. The method can be applied to both spacecraft and ground-based wave data. The results of using the method can be employed for verification of physical theories of the formation of chorus emissions and determining their statistical properties.

In our previous paper [1] it was shown, using the theory of antennas in plasmas, that the effective length leff of a receiving dipole antenna can be much larger than its geometric length in case quasielectrostatic chorus emissions propagating close to the resonance cone are received. In order to simplify calculations of leff, it was proposed to use a model (“effective”) source of such emissions because taking into account all of the real source properties (that are determined by the nonlinear processes of interaction between waves and charged particles in a wide region of space) would lead to unreasonably cumbersome calculations. The present paper analyzes how the effective length of the spacecraft-borne receiving antenna depends on the parameters of the space charge distribution in the model source of quasi-electrostatic chorus emissions. It is found that the length leff decreases as a power function (with exponent −1/2) with increasing distance (along the group velocity resonance cone) between the model source and the receiving antenna. This relationship is correct up to the distance at which the effective length becomes of the order of the geometric length. At longer distances, the radiation field loses its resonance nature because of the excitation of an electromagnetic (quasi-longitudinal) wave. It is shown that under conditions of the Earth’s magnetosphere, the approximation we used can remain valid up to distances of the order of the geomagnetic field line length, which confirms the importance of the discussed effect for correct interpretation of the electric wave measurement data in the whistler-mode frequency range. It is also shown that the length leff changes by less than 10% when the characteristic scale of spectrum of the charge distribution along the model source varies as Δ ∼ (0.1–1.0) kobs, where the wave number kobs corresponds to the observed spectral maximum of radiation at a given frequency.

We study the dynamics of the spectra of multiband sporadic magnetic pulsations in the Pc1 range (0.2–5.0 Hz) during the event of 5–6 March 2011 by using ground-based magnetic measurements at stations largely spaced from each other in latitude and longitude. The event is characterized by a long duration (about 16 h), the presence of several bands with varying frequencies, splitting of these bands into narrower subbands, significant variations in the amplitude and polarization of the signals on the ground, and their observation in a wide range of latitudes and longitudes. On the basis of a joint analysis of the Pc1 pulsation properties and the data of low-orbiting spacecraft detecting localized precipitations of energetic protons into the ionosphere, we infer the possible generation regions of these waves in the magnetosphere and conclude that they are multiple. The results of analysis allowed us to determine the mechanisms of broadening and splitting of Pc1 frequency bands even in the absence of direct wave observations in the magnetosphere. We also propose an explanation of the atypical (for ground-based detection) character of two-band Pc1 spectra when the signal at frequencies above the helium ion gyrofrequency has a higher amplitude than at lower frequencies. We also explain the inhomogeneous frequency profile of polarization in different frequency bands. Possible variations in the magnetospheric plasma parameters that resulted in the observed dynamics of amplitude and polarization spectra of Pc1 pulsations are revealed by using calculations of the wave cyclotron amplification by energetic protons in the magnetosphere.

We present the results of a multi-point and multi-instrument study of electromagnetic ion cyclotron (EMIC) waves and related energetic proton precipitation during a substorm. We analyze the data from Arase (ERG) and Van Allen Probes (VAPs) A and B spacecraft for an event of 16 and 17 UT on December 1, 2018. VAP-A detected an almost dispersionless injection of energetic protons related to the substorm onset in the night sector. Then the proton injection was detected by VAP-B and further by Arase, as a dispersive enhancement of energetic proton flux. The proton flux enhancement at every spacecraft coincided with the EMIC wave enhancement or appearance. This data show the excitation of EMIC waves first inside an expanding substorm wedge and then by a drifting cloud of injected protons. Low-orbiting NOAA/POES and MetOp satellites observed precipitation of energetic protons nearly conjugate with the EMIC wave observations in the magnetosphere. The proton pitch-angle diffusion coefficient and the strong diffusion regime index were calculated based on the observed wave, plasma, and magnetic field parameters. The diffusion coefficient reaches a maximum at energies corresponding well to the energy range of the observed proton precipitation. The diffusion coefficient values indicated the strong diffusion regime, in agreement with the equality of the trapped and precipitating proton flux at the low-Earth orbit. The growth rate calculations based on the plasma and magnetic field data from both VAP and Arase spacecraft indicated that the detected EMIC waves could be generated in the region of their observation or in its close vicinity.

We study the influence of real structure of electromagnetic ion-cyclotron wave packets in the Earth’s radiation belts on precipitation of relativistic electrons. Automatic algorithm is used to distinguish isolated elements (wave packets) and obtain their amplitude and frequency profiles from satellite observations by Van Allen Probe B. We focus on rising-tone EMIC wave packets in the proton band, with a maximum amplitude of 1.2–1.6 nT. The resonant interaction of the considered wave packets with relativistic electrons 1.5–9 MeV is studied by numerical simulations. The precipitating fluxes are formed as a result of both linear and nonlinear interaction; for energies 2–5 MeV precipitating fluxes are close to the strong diffusion limit. The evolution of precipitating fluxes is influenced by generation of higher-frequency waves at the packet trailing edge near the equator and dissipation of lower-frequency waves in the $$\text {He}^+$$ He + cyclotron resonance region at the leading edge. The wave packet amplitude modulation leads to a significant change of precipitated particles energy spectrum during short intervals of less than 1 minute. For short time intervals about 10–15 s, the approximation of each local amplitude maximum of the wave packet by a Gaussian amplitude profile and a linear frequency drift gives a satisfactory description of the resonant interaction.

We present simultaneous observations of very low-frequency emissions with periodic bursts by Van Allen Probe near geomagnetic equator and Kannuslehto and Lovozero ground-based sites. The repetition period and ground–spacecraft delay are consistent with guided whistler wave propagation between conjugate ionospheres. In contrast to lightning whistlers, the group velocity dispersion is not accumulated from one burst to another, thus implying a nonlinear mechanism of its compensation. Two regimes are observed. In one regime, Poynting flux direction alternates in the magnetosphere, and the burst period (2 s) is half of that detected on the ground (4 s), corresponding to single-wave packet bouncing along the field line. This regime is switched to the other one, with burst period unchanged in the magnetosphere but halved on the ground. In this second regime, no alternating Poynting flux direction is observed. The second regime corresponds to two symmetrically propagating wave packets synchronously meeting at the equator.

The data of simultaneous observation of the energetic electron flux by ARASE satellite and aurora by ground-based all-sky imager in Murmansk region (Russia) have been analyzed for the time interval 00:00-01:00 UT on March 31, 2017. The energy spectra of middle-energy (7-90 keV) electrons observed by MEPe detectors in and near the loss cone have been used for simulation of the auroral emissions in the atmosphere. The temporal evolution of the simulated emission intensity has been compared with the observed emission in the magnetic field-aligned footprint point for the satellite. It was found that the projection along magnetic field has been distorted by the developing disturbance.

A specialized ground-based system has been developed for simultaneous observations of pulsating aurora (PsA) and related magnetospheric phenomena with the Arase satellite. The instrument suite is c...

We study quasi-periodic VLF emissions observed simultaneously by Van Allen Probes spacecraft and Kannuslehto and Lovozero ground-based stations on 25 December 2015. Both Van Allen Probes A and B de...

International audience; Quasiperiodic emissions are magnetospheric whistler mode waves at frequencies between about 0.5 and 4 kHz which exhibit a nearly periodic time modulation of the wave intensity. We use large data sets of events observed by the Van Allen Probes in the equatorial region at larger radial distances and by the low-altitude DEMETER spacecraft. While Van Allen Probes observe the events at all local times and longitudes, DEMETER observations are limited nearly exclusively to the daytime and significantly less frequent at the longitudes of the South Atlantic Anomaly. Further, while the events observed by Van Allen Probes are smoothly distributed over seasons with only mild maxima in spring/autumn, DEMETER occurrence rate has a single pronounced minimum in July. The apparent inconsistency is explained by considering a nondipolar Earth's magnetic field and significant background wave intensities which in these cases prevent the quasiperiodic events from being identified in DEMETER data.

Using Poynting vector measurements of whistler mode chorus emissions detected by the THEMIS spacecraft within the source region, that is, close to the magnetic field minimum, we found both in individual events and statistically that chorus elements propagating equatorward had systematically higher frequencies and smaller amplitudes compared with simultaneously observed elements propagating away from the equator. We demonstrate similar features in the results of numerical simulations based on backward wave oscillator equations. It can be qualitatively explained by the nonlinear evolution of the energetic electron distribution function during wave generation. The motion of electrons from the equator is accompanied by a decrease in their velocity component along the magnetic field line due to both the adiabatic mirror force and nonlinear wave-particle interactions. Thus, the frequency of the chorus elements generated by such electrons and propagating equatorward is higher compared with the elements propagating away from the equator.

We use numerical simulations to study the resonant interaction of relativistic electrons with rising-frequency EMIC wave packets in the H band. We find that precipitation fluxes are formed by quasi...

We analyze the integral parameters of resonant interaction of relativistic electrons in the Earth’s radiation belts with electromagnetic ion–cyclotron waves. The analysis is based on numerical simulations. Wave packets of finite length with varying frequency and various amplitude profiles propagating from the equator are considered. The roles of three nonlinear interaction regimes, analyzed in the first part of our paper [1] for single particle trajectories, are compared. It is shown that interaction characteristics depend stronger on the electron energy and wave packet position for the wave packet with Gaussian amplitude profile than for the wave packet with constant amplitude. For the wave packet with Gaussian amplitude profile, the directed and diffusive transfer of particles in the phase space are comparable, while for the wave packet with constant amplitude the mean change in the equatorial pitch angle can be considerably (a factor of 3 to 5) greater than the standard deviation. The most significant decrease in the equatorial pitch angle and the largest fraction of the corresponding particles are obtained for particles with energies of about 1 MeV for the wave packet close to the equator. The fraction of particles which can be scattered into the loss cone after a single pass through the wave packet is 1.0–1.7%.

Different types of proton auroras observed by the IMAGE satellite equatorward of the proton aurora oval are briefly reviewed. These auroras are caused by the precipitation of energetic protons from the Earth’s magnetosphere during the development of the ion-cyclotron instability. In addition to the previously considered types of proton auroras (spots, evening arcs, and dayside flashes), a new type is described: longlasting proton auroras on the dayside. The scheme of interrelation between different proton auroras equatorward of the oval with the distribution of cold plasmaspheric plasma is given.

Regions of the detection of electromagnetic ion-cyclotron (EMIC) waves on the THEMIS satellites near the equatorial plane and the precipitation of energetic protons on POES low Earth orbiting satellites are compared with the magnetospheric magnetic field model. It is confirmed that low Earth orbiting satellites detect the precipitation of energetic protons in the regon associated with observations of EMIC waves in the magnetosphere. This is consistent with the idea that protons are scattered in the loss cone as a result of ioncyclotron interaction. Thus, observations of fluxes of energetic protons in low Earth orbits can be used to monitor ion-cyclotron instability regions in the magnetosphere. Simultaneous observations at high and low Earth orbits contribute to the construction of a spatiotemporal pattern of the interaction region of EMIC waves and energetic protons. In addition, it is shown that proton precipitation associated with EMIC waves can cause errors in determining the latitude of the isotropic boundary (the equatorial boundary of isotropic fluxes of energetic protons), which is an indicator of the configuration of the magnetic field in the magnetosphere.

We analyze the resonant interaction of relativistic electrons with ion-cyclotron waves in the Earth radiation belts. Finite-length wave packets with variable frequencies and different amplitude profiles are considered. Specific features of the nonlinear interaction regimes are analyzed on the basis of solving numerically a system of equations of the particle motion along with the efficiency of this interaction for a single pass of the particle through the wave packet. In the first part of this work, the peculiarities of the trajectories of individual particles are analyzed. The influence of the shape of the wave packet on the well-known regimes, such as particle trapping by the wave field and particle phase bunching, which leads to a non-zero average variation in the pitch angle in an inhomogeneous medium, are considered. It is shown that a long stay of a particle near the separatrix on the phase plane in the region far from the saddle leads to a strong decrease in the pitch angle of the particle in the absence of the trapping as well. This nonlinear regime (directed scattering) is possible for comparatively low initial pitch angles. In this case, the value of the pitch angle decrease depends on the initial phase of the particle. It is shown that the trajectories corresponding to the directed scattering can be regarded as a transitional type of trajectories, between the trajectories of the untrapped and trapped particles. Quantitative estimates of variations in the pitch angle are obtained, and it is confirmed that the directed scattering and trapping of particles by the wave field can lead to electron precipitation into the loss cone.

We generalize the equations, which describe the backward-wave oscillator regime in the magnetized plasma in the presence of a jump (“step”) in the velocity distribution function of energetic charged particles, to the case of an arbitrary direction of the wave relative to an external magnetic field and an arbitrary wave mode. The dependence of instability threshold on the angle χ between the wave vector k and the external magnetic field B0 for whistler-mode waves and a slow extraordinary wave (Z-mode) is determined.

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.