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Energetic electron losses in the Earth's inner magnetosphere are dominated by outward radial diffusion and scattering into the atmosphere by various electromagnetic waves. The two most important wave modes responsible for electron scattering are electromagnetic ion cyclotron (EMIC) waves and whistler‐mode waves (whistler waves) that, acting together, can provide rapid electron losses over a wide energy range from few keV to few MeV. Wave‐particle resonant interaction resulting in electron scattering is well described by quasi‐linear diffusion theory using the cold plasma dispersion, whereas the effects of nonlinear resonances and hot plasma dispersion are less well understood. This study aims to examine these effects and estimate their significance for a particular event during which both wave modes are quasi‐periodically modulated by ultra‐low‐frequency (ULF) compressional waves. Such modulation of EMIC and whistler wave amplitudes provides a unique opportunity to compare nonlinear resonant scattering (important for the most intense waves) with quasi‐linear diffusion (dominant for low‐intensity waves). The same modulation of plasma properties allows better characterization of hot plasma effects on the EMIC wave dispersion. Although hot plasma effects significantly increase the minimum resonant energy,E_min, for the most intense EMIC waves, such effects become negligible for the higher frequency part of the hydrogen‐band EMIC wave spectrum. Nonlinear phase trapping of 300–500 keV electrons through resonances with whistler waves may accelerate and make them resonant with EMIC waves that, in turn, quickly scatter those electrons into the loss‐cone. Our results highlight the importance of nonlinear effects for simulations of energetic electron fluxes in the inner magnetosphere.

 

In the radiation belts, energetic and relativistic electron precipitation into the atmosphere is expected to be mainly controlled over the long term by quasilinear pitch‐angle scattering by whistler‐mode and electromagnetic ion cyclotron waves. Accordingly, statistical electron lifetimes have been derived from quasilinear diffusion theory on the basis of multi‐year wave statistics. However, the full consistency of such statistical quasilinear models of electron lifetimes with both measured electron lifetimes, spectra of trapped and precipitated electron fluxes, and wave‐driven diffusion rates inferred from electron flux measurements, has not yet been verified in detail. In the present study, we use data from Electron Loss and Fields Investigation (ELFIN) mission CubeSats, launched in September 2018 in low Earth orbit, to carry out such comparisons between quasi‐linear diffusion theory and observed electron flux variations. We show that statistical theoretical lifetime models are in reasonable agreement with electron pitch‐angle diffusion rates inferred from the precipitated to trapped 100 keV electron flux ratio measured by ELFIN after correction for atmospheric backscatter, as well as with timescales of trapped electron flux decay independently measured over several days by ELFIN. The present results demonstrate for the first time a broad consistency between timescales of trapped electron flux decay, the pitch‐angle distribution of precipitated electrons, and quasilinear models of wave‐driven electron loss, showing the reliability of such statistical electron lifetime models parameterized by geomagnetic activity for evaluating electron precipitation into the atmosphere during not too disturbed periods.

 

Resonant interactions of energetic electrons with electromagnetic whistler‐mode waves (whistlers) contribute significantly to the dynamics of electron fluxes in Earth's outer radiation belt. At low geomagnetic latitudes, these waves are very effective in pitch angle scattering and precipitation into the ionosphere of low equatorial pitch angle, tens of keV electrons and acceleration of high equatorial pitch angle electrons to relativistic energies. Relativistic (hundreds of keV), electrons may also be precipitated by resonant interaction with whistlers, but this requires waves propagating quasi‐parallel without significant intensity decrease to high latitudes where they can resonate with higher energy low equatorial pitch angle electrons than at the equator. Wave propagation away from the equatorial source region in a non‐uniform magnetic field leads to ray divergence from the originally field‐aligned direction and efficient wave damping by Landau resonance with suprathermal electrons, reducing the wave ability to scatter electrons at high latitudes. However, wave propagation can become ducted along field‐aligned density peaks (ducts), preventing ray divergence and wave damping. Such ducting may therefore result in significant relativistic electron precipitation. We present evidence that ducted whistlers efficiently precipitate relativistic electrons. We employ simultaneous near‐equatorial and ground‐based measurements of whistlers and low‐altitude electron precipitation measurements by ELFIN CubeSat. We show that ducted waves (appearing on the ground) efficiently scatter relativistic electrons into the loss cone, contrary to non‐ducted waves (absent on the ground) precipitating onlykeV electrons. Our results indicate that ducted whistlers may be quite significant for relativistic electron losses; they should be further studied statistically and possibly incorporated in radiation belt models.

 

Intense lower band chorus waves are ubiquitous in the inner magnetosphere. Their properties have been modeled by various codes and investigated using measurements of many spacecraft missions. This study aims to compare simulated and observed properties of chorus waves. We present detailed comparisons between results from four different codes of nonlinear chorus wave generation and statistical observations from satellites, focusing on the fine structure of such chorus waves. We show that simulations performed with these different codes well reproduce the observed wave packet characteristics, although in somewhat complementary parameter domains as concerns wave packets sizes, amplitudes, and frequency sweep rates. In particular, simulations generate both the frequently observed short wave packets with high positive and negative frequency sweep rates, and the more rare long and intense packets with mainly rising tones. Moreover, simulations reproduce quantitatively both the increase of the size of the observed chorus wave packets with their peak amplitude, and the fast decrease of their frequency sweep rate as their size increases. This confirms the reliability of the main existing codes for accurately modeling chorus wave generation, although we find that initial conditions should be carefully selected to reproduce a given parameter range.

 

We present a global survey of energetic electron precipitation from the equatorial magnetosphere due to hiss waves in the plasmasphere and plumes. Using Van Allen Probes measurements, we calculate the pitch angle diffusion coefficients at the bounce loss cone, and evaluate the energy spectrum of precipitating electron flux. Our ∼6.5‐year survey shows that, during disturbed times, hiss inside the plasmasphere primarily causes the electron precipitation atL > 4 over 8 h < MLT < 18 h, and hiss waves in plumes cause the precipitation atL > 5 over 8 h < MLT < 14 h andL > 4 over 14 h < MLT < 20 h. The precipitating energy flux increases with increasing geomagnetic activity, and is typically higher in the plasmaspheric plume than the plasmasphere. The characteristic energy of precipitation increases from ∼20 keV atL = 6–∼100 keV atL = 3, potentially causing the loss of electrons at several hundred keV.

 

We investigate relativistic electron precipitation events detected by Polar Environmental Satellites (POES) in low‐Earth orbit in close conjunction with Van Allen Probe A observations of electromagnetic ion cyclotron (EMIC) waves near the geomagnetic equator. We show that the occurrence rate of >0.7 MeV electron precipitation recorded by POES during those times strongly increases, reaching statistically significant levels when the minimum electron energy for cyclotron resonance with hydrogen or helium band EMIC waves at the equator decreases below ≃1.0–2.5 MeV, as expected from the quasi‐linear theory. Both hydrogen and helium band EMIC waves can be effective in precipitating MeV electrons. However, >0.7 MeV electron precipitation is more often observed (at statistically significant levels) when the minimum electron energy for cyclotron resonance with hydrogen band waves is low (E_min = 0.6–1.0 MeV), whereas it is more often observed when the minimum electron energy for cyclotron resonance with helium band waves is slightly larger (E_min = 1.0–2.5 MeV). This is indicative of the warm plasma effects for waves approaching the He⁺gyrofrequency. We further show that most precipitation events had energies > 0.7–1.0 MeV, consistent with the estimated minimum energy (E_min ∼ 0.6 − 2.5 MeV) of cyclotron resonance with the observed EMIC waves during the majority of these events. However, 4 out of the 12 detected precipitation events cannot be explained by electron quasi‐linear scattering by the observed EMIC waves, and 12 out of 20 theoretically expected precipitation events were not detected by POES, suggesting the possibility of nonlinear effects likely present near the magnetic equator, or warm plasma effects, and/or narrowly localized bursts of EMIC waves.

 

In this study we consider the Hamiltonian approach for the construction of a map for a system with nonlinear resonant interaction, including phase trapping and phase bunching effects. We derive basic equations for a single resonant trajectory analysis and then generalize them into a map in the energy/pitch-angle space. The main advances of this approach are the possibility of considering effects of many resonances and to simulate the evolution of the resonant particle ensemble on long time ranges. For illustrative purposes we consider the system with resonant relativistic electrons and field-aligned whistler-mode waves. The simulation results show that the electron phase space density within the resonant region is flattened with reduction of gradients. This evolution is much faster than the predictions of quasi-linear theory. We discuss further applications of the proposed approach and possible ways for its generalization.