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Using the statistical wave power spectral profiles obtained from CRRES wave data within the 0000–0600 MLT sector under different levels of geomagnetic activity and a modeled latitudinal variation of wave normal angle distribution, we examine quantitatively the effects of lower band and upper band chorus on resonant diffusion of plasma sheet electrons for diffuse auroral precipitation in the inner magnetosphere. Whistler mode chorus‐induced resonant scattering of plasma sheet electrons is geomagnetic activity dependent, varying from above the strong diffusion limit (timescale of an hour) during active times (AE* > 300 nT) with peak wave amplitudes of >50 pT to weak scattering (timescale of a day) during quiet conditions (AE* < 100 nT) with typical wave amplitudes of ≤10 pT. Chorus waves present at different magnetic latitudes make distinct contributions to the net diffusion rates of plasma sheet electrons, largely depending on the latitudinal variation of wave power. Upper band chorus is the controlling scattering process for electrons from ∼100 eV to ∼2 keV, and lower band chorus is most effective for precipitating the higher energy (>∼2 keV) plasma sheet electrons in the inner magnetosphere. Efficient scattering by the combination of active time lower band and upper band chorus can cover a wide energy range from ∼100 eV to >100 keV and a broad interval of equatorial pitch angle, thereby accounting for the formation of observed electron pancake distribution. Decreased chorus scattering during less disturbed times can also modify the magnetic local time distribution of plasma sheet electrons. Compared to the effects of chorus waves, electron cyclotron harmonic wave‐induced resonant diffusion coefficients are at least 1 order of magnitude smaller and are negligible under any geomagnetic condition, indicating that chorus waves act as the major contributor dominantly responsible for diffuse auroral precipitation in the inner magnetosphere. Chorus‐driven momentum diffusion and mixed diffusion are also important. Lower band and upper band chorus can cause strong momentum diffusion of plasma sheet electrons in the energy ranges of ∼500 eV to ∼2 keV and ∼2 keV to ∼3 keV, respectively, which can significantly result in energization of the electrons and attenuation of the waves. Key Points Chorus can cause both efficient pitch angle scattering and momentum diffusion Chorus dominates over ECH waves to account for diffuse auroral precipitation Chorus scattering can also explain the formation of electron pancake distribution

The scattering of charged particles by oxygen ion cyclotron harmonic (OCH) waves in the inner magnetosphere is investigated by evaluating the relevant quasi‐linear diffusion coefficients. Recent studies demonstrated that OCH waves are oxygen ion Bernstein modes and their complex kinetic dispersion relation has made it challenging to assess their role in scattering charged particles. The present study calculates the quasi‐linear diffusion coefficients for the scattering of electrons and ions by OCH waves using their kinetic dispersion relation. The results show that OCH waves can effectively scatter electrons between ∼100 eV and 100s keV via Landau resonance. They are also capable of heating cold helium and oxygen ions through cyclotron resonances. Specially, it is found that the 4th harmonic of OCH waves can lead to effective heating of helium ions, while oxygen ions would interact more efficiently with lower harmonics of OCH waves. Plain Language Summary Oxygen ion cyclotron harmonic (OCH) waves observed in the inner magnetosphere often have multiple spectral peaks at harmonics of the local oxygen ion cyclotron frequency. They have been shown to be excited by hot oxygen ion loss‐cone or ring/ring‐like distributions and follow a complicated kinetic dispersion relation for oxygen ion Bernstein waves. Since OCH waves cannot be described by the relatively simple cold plasma dispersion relation, it has been difficult to calculate their diffusion coefficients in scattering charged particles in quasi‐linear theory. The present study numerically solves the kinetic dispersion relation for OCH waves and then uses the results to calculate the corresponding quasi‐linear diffusion coefficients for electrons and ions. The diffusion coefficients obtained show that OCH waves can effectively interact with ∼100 eV to 100s keV electrons and are capable of heating cold helium and oxygen ions. Thus, OCH waves have their own unique contribution to the particle dynamics in the inner magnetosphere. Key Points Quasi‐linear diffusion coefficients are evaluated for particle scattering by oxygen ion cyclotron harmonic (OCH) waves for the first time OCH waves can scatter electrons in a wide energy range (∼100 eV–100s keV) via Landau resonance OCH waves are capable of heating cold helium and oxygen ions through cyclotron resonance

When assessing the scattering of radiation belt electrons by fast magnetosonic (MS) waves, it is traditionally assumed that the waves follow the MS/whistler branch of the cold plasma dispersion relation (CPDR) in magnetohydrodynamics. However, MS waves are essentially ion Bernstein modes following a distinct kinetic dispersion relation. This study calculates the MS wave‐induced electron diffusion rates with the kinetic dispersion relation for the first time and compares the results with that obtained with the CPDR. It is found that the kinetic effects lead to a lower minimum resonant energy around 100 eV and a broader resonant pitch angle range. Kinetic effects also result in power spectral density attenuation when transforming wave frequency spectra into wavenumber spectra, so the diffusion rates are overall smaller than the ones obtained using the CPDR. Our results demonstrate that kinetic effects can significantly affect the role that MS waves play in the radiation belt dynamics. Plain Language Summary Magnetosonic (MS) waves belong to the kinetic ion Bernstein modes essentially. But when the cold plasma is dominating, the waves also approximately follow the MS/whistler branch of the cold plasma dispersion relation (CPDR) in magnetohydrodynamics. Subsequently, studies of the electron scattering by MS waves have traditionally assumed the CPDR for simplicity. Motivated by recent studies which involved both satellite observations and kinetic theory revealing that the lower harmonic MS waves clearly follow the kinetic dispersion relation, we assess how the differences between the kinetic and cold plasma dispersion relations affect the MS wave‐induced electron scattering rates. Our results indicate that the kinetic dispersion relation produces relatively lower parallel phase speeds for MS waves, leading to a lower minimum resonant energy and subsequently a broader resonant pitch angle range for electrons (of a given energy). The kinetic effects also decrease the overall diffusion rates by attenuating the wave power spectral density in wavenumber space when mapped from a given frequency spectrum. Key Points Linear kinetic dispersion relation indicates lower phase speeds and a broader range of group speeds for fast magnetosonic (MS) waves The lower phase speeds of MS waves result in a broader range of resonant pitch angles and lower minimum resonant energies of electrons Kinetic effects reduce the wavenumber power spectral density and thus result in smaller electron diffusion rates

The temporal evolution of the phase space density of plasma sheet electrons (100 eV–30 keV) injected into the nightside at L = 6 during moderate geomagnetic activity is investigated using a quasi‐linear diffusion formulation. Scattering in energy and pitch angle during interactions with both whistler mode chorus waves and electron cyclotron harmonic waves are included using an improved wave model recently obtained using CRRES spacecraft data. We compare our simulation results with observations from the THEMIS spacecraft and demonstrate that the formation of the observed electron pitch angle distributions is mainly due to resonant interactions with a combination of upper and lower band chorus waves. The pancake distributions at low energies (E < 2 keV), the flattened pitch angle distributions at medium energies (between 2–3 keV), and the distributions with enhanced pitch angle anisotropy at high energies (E > 3 keV) are explained using the banded chorus wave structure with a power minimum at half the electron cyclotron frequency. Results of the current work can be used to model the dynamical evolution and resultant global distribution of plasma sheet electrons. Key Points Evolution of the electron pitch angle distribution Plasma sheet electron dynamics following injections Roles of chorus and ECH waves in keV electron dynamics

The sensitivity of quasi‐linear scattering rates to the wave normal distribution of chorus waves is studied using the Full Diffusion Code newly developed at the University of California, Los Angeles. Scattering rates are computed for field‐aligned, oblique (∼20° wave normal angles), and highly oblique (∼40° wave normal angles) cases. For radiation belt electrons, scattering rates are relatively insensitive to the assumed distribution of wave normal angles at high energies; while when the energy is smaller, in the range of tens of keV, knowledge of the wave normal distribution becomes important. It is shown that Landau resonance becomes very important for the scattering of electrons with energies of tens of keV as waves become more oblique. Scattering rates for various order resonances and energies are presented. Our results show that, for a fixed ratio of plasma to gyrofrequency and fixed spectral properties of waves, scattering rates scale as an inverse of magnitude of the magnetic field. We also show that resonant scattering of 10 keV and 100 keV occurs within 10° and 20° latitude of the geomagnetic equator, respectively. At 1 MeV, dominant scattering occurs above 20° latitude. We also present local scattering rates as a function of energy and latitude. Implications of the presented results for the upcoming satellite mission's planning, future measurements, and radiation belt modeling are discussed.

Using statistical wave power spectral profiles obtained from CRRES and the latitudinal distributions of wave propagation modeled by the HOTRAY code, a quantitative analysis has been performed on the scattering of plasma sheet electrons into the diffuse auroral zone by multiband electrostatic electron cyclotron harmonic (ECH) emissions near L = 6 within the 0000–0600 MLT sector. The results show that ECH wave scattering of plasma sheet electrons varies from near the strong diffusion rate (timescale of an hour or less) during active times with peak wave amplitudes of an order of 1 mV/m to very weak scattering (on the timescale of >1 day) during quiet conditions with typical wave amplitudes of tenths of mV/m. However, for the low‐energy (∼100 eV to below 2 keV) electron population mainly associated with the diffuse auroral emission, ECH waves are only responsible for rapid pitch angle diffusion (occasionally near the limit of strong diffusion) for a small portion of the electron population with pitch angles αeq < 20°, dependent on electron energy and geomagnetic activity level. ECH scattering alone cannot account for the rapid loss of plasma sheet electrons during transport from the nightside to the dayside, nor can it explain the formation of the pancake electron distributions strongly peaked at αeq > 70°. Computations of the bounce‐averaged coefficients of momentum diffusion and (pitch angle, momentum) mixed diffusion indicate that both mixed diffusion and energy diffusion of plasma sheet electrons due to ECH waves are very small compared to pitch angle diffusion and that ECH waves have little effect on local electron acceleration. Consequently, the multiple harmonic ECH emissions cannot play a dominant role in the occurrence of diffuse auroral precipitation near L = 6, and other wave‐particle interaction mechanisms, such as whistler mode chorus‐driven resonant scattering, are required to explain the global distribution of diffuse auroral precipitation and the formation of the pancake distribution in the inner magnetosphere. Key Points ECH scattering varies from strong diffusion limit to weak diffusion ECH scattering is confined to a small electron population with low pitch angles ECH scattering alone cannot account for the diffuse auroral precipitation

The loss of relativistic electrons from the Earth's radiation belts can be described in terms of the quasi‐linear pitch angle diffusion by cyclotron‐resonant waves, provided that their frequency spectrum is broad enough. Chorus waves at large wave‐normal angles with respect to the magnetic field are often present in CLUSTER and THEMIS measurements in the outer belt at moderate to high latitudes. An approximate analytical formulation of diffusion coefficients has been derived in the low‐frequency limit, leading to a simplified analytical expression of diffusion coefficients and lifetimes for energetic trapped electrons. Large values of the wave‐normal angles between the Gendrin and resonance angles are shown to induce important increases in diffusion, thereby strongly reducing the particle lifetimes (by almost two orders of magnitude). The analytical diffusion coefficients and lifetimes obtained here are found to be in a good agreement with full numerical calculations based on CLUSTER chorus waves measurements in the outer belt for electron energies ranging from 100 keV to 2 MeV. Such very oblique chorus waves could contribute to a predominantly perpendicular anisotropy of the global equatorial electron population on the dayside and to a relative isotropization at low energy under disturbed conditions. It is also suggested that they might play a significant role in pulsating auroras. Key Points Reduced electron lifetimes due to oblique chorus waves Analytical estimates of electron lifetimes Explanation of decreased lifetimes

Wave–particle interactions are a fundamental driver of electron radiation belt dynamics. Quantifying their effects through quasi‐linear theory requires diffusion coefficients, but their direct evaluation involves nested integrations and is computationally expensive, limiting their use in real‐time applications. Here we develop a fully connected neural network to efficiently estimate diffusion coefficients using a data‐driven approach. The model produces coefficients more than an order of magnitude faster than conventional numerical methods on a single CPU core, and achieves significantly larger speedup when run on a GPU commonly used in modern machine‐learning workflows. To validate its reliability, we use the model‐predicted coefficients in a quasi‐linear simulation, which produces results in close agreement with those obtained using precisely calculated values. These results demonstrate that data‐driven approaches provide a practical path for incorporating diffusion coefficients into real‐time radiation belt forecasting, and more broadly illustrate how such approaches can accelerate computationally intensive physics‐based models.

Using the statistical CRRES measurements of the electric field intensities of lower band chorus (LBC) and upper band chorus (UBC) around L = 6 under geomagnetically moderate conditions, we evaluate the variations in modeled magnetic field spectral intensity and the resultant changes in resonant scattering rates of plasma sheet electrons caused by different choices of the wave normal distribution. UBC scattering rates inferred from electric field measurements show a common trend of decreasing scattering with increasing peak wave normal angle, θm, for the plasma sheet electrons at all resonant pitch angles. This trend is mainly due to the lower power of magnetic field as derived from the electric field measurements for oblique waves. The LBC resonant diffusion inferred from electric field measurements shows a considerable increase in scattering rates with increasing θm for ∼1 keV electrons at all resonant pitch angles and for 3–30 keV electrons over certain ranges of pitch angles, which is contrary to the decrease in wave magnetic field amplitude and results mainly from the decrease in resonant energy and redistribution of the majority of wave power at large wave normal angles for increased peak wave normal angle. LBC‐induced scattering rates of 3–10 keV electrons decrease with increasing θm at low pitch angles, consistent with the decrease in wave magnetic field amplitude when θm increases. Our investigation demonstrates that the knowledge of the wave normal distribution of LBC and UBC is essential for an accurate quantification of the net resonant scattering rates and loss timescales of the plasma sheet electrons for an improved global simulation of diffuse auroral precipitation and the evolution of plasma sheet electron pitch angle distribution if only measurements of wave electric field intensity are available. In contrast, the diffuse auroral scattering rates calculated from magnetic field measurements are much less sensitive to the assumption on wave normal angle distribution. While UBC scattering with constant magnetic field power is roughly insensitive to the assumed wave normal distribution, LBC scattering with constant magnetic field power becomes more dependent on the assumed wave normal angle distribution, especially for ∼1 keV electrons. Key Points Importance of wave normal distribution to electric and magnetic field conversion Impact of wave normal distribution on chorus‐driven diffuse auroral scattering Relative roles of magnetic amplitude and wave power distribution over normal angle

The redistribution of energy during the recovery phase of geomagnetic storms related to the acceleration of electrons in the Earth's outer radiation belt by cyclotron‐resonant chorus waves is an important and challenging topic of magnetospheric plasma physics. An approximate analytical formulation of energy diffusion coefficients is derived in this paper, on the basis of a quasi‐linear formalism valid for large enough bandwidths or for successive random scatter by uncorrelated waves of different frequencies and moderate average amplitudes. We make use of chorus wave parameterizations derived from CLUSTER measurements to show that oblique whistler waves can significantly increase the energy diffusion rate of small pitch angle electrons on the dayside. On the other hand, the energization rate of the more numerous high pitch angle electrons is typically reduced by a factor of 2 on the dayside, while it remains nearly unchanged on the nightside where high‐intensity waves are less oblique. Besides, lifetimes are strongly reduced on the dayside, which could also impact the long‐term time‐integrated acceleration rates of injected electrons. Comparison between the analytical formulas and full numerical results demonstrates a good agreement and provides new scaling laws as a function of whistler mean frequency, plasma density and particle energy. It is also suggested that the enhancement of energy diffusion of low energy electrons (<100 keV) at small pitch angles with oblique waves could result in an intensification of wave growth at latitudes higher than 15°. This might contribute to explain high chorus intensities measured by CLUSTER on the dayside at high latitudes. Key Points Electron acceleration modified with oblique chorus waves Chorus QL growth possibly enhanced with oblique chorus waves Most intense waves control long‐term timescales