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This paper considers a method for estimating bounce-averaged quasi-linear diffusion coefficients due to whistler-mode waves for a specified ratio of plasma frequency to gyrofrequency, ω p / Ω e , using values precomputed for a different value of that ratio. This approach was recently introduced to facilitate calculations associated with the "POES technique," generalized to infer both wave intensity and cold plasma density from measurements of particle fluxes near the loss cone. The original derivation was justified on the basis of parallel-propagating waves but applied to calculations with much more general models of the waves. Here, we justify the estimates, which are based on equating resonant frequencies for differing values of ω p / Ω e and energy, for wide ranges of wave normal angle, resonance number, energy, and equatorial pitch angle. Refinements of the original estimates are obtained and tested numerically against full calculations of the diffusion coefficients for representative wave models. The estimated diffusion coefficients can be calculated rapidly and generally give useful estimates for energies in the 30-keV–300-keV range, especially when both relevant values of the ratio ω p / Ω e are large. [ABSTRACT FROM AUTHOR]

We analyze the properties of relativistic (>700 keV) electron precipitation (REP) events measured by the low-Earth-orbit (LEO) POES/MetOp constellation of spacecraft from 2012 through 2023. Leveraging the different profiles of REP observed at LEO, we associate each event with its possible driver: waves or field line curvature scattering (FLCS). While waves typically precipitate electrons in a localized radial region within the outer radiation belt, FLCS drives energy-dependent precipitation at the edge of the belt. Wave-driven REP is detected at any MLT sector and L shell, with FLCS-driven REP occurring only over the nightside–a region where field line stretching is frequent. Wave-driven REP is broader in radial extent on the dayside and accompanied by proton precipitation over 03–23 MLT, either isolated or without a clear energy-dependent pattern, possibly implying that electromagnetic ion cyclotron (EMIC) waves are the primary driver. Across midnight, both wave-driven and FLCS-driven REP occur poleward of the proton isotropic boundary. On average, waves precipitate a higher flux of >700 keV electrons than FLCS. Both contribute to energy deposition into the atmosphere, estimated of a few MW. REP is more associated with substorm activity than storms, with FLCS-driven REP and wave-driven REP at low L shells occurring most often during strong activity (SML* < −600 nT). A preliminary analysis of the Solar Wind (SW) properties before the observed REP indicates a more sustained (∼5 h) dayside reconnection for FLCS-driven REP than for wave-driven REP (∼3 h). The magnetosphere appears more compressed during wave-driven REP, while FLCS-driven REP is associated with a faster SW of lower density. These findings are useful not only to quantify the contribution of >700 keV precipitation to the atmosphere but also to shed light on the typical properties of wave-driven vs FLCS-driven precipitation which can be assimilated into physics-based and/or predictive radiation belt models. In addition, the dataset of ∼9,400 REP events is made available to the community to enable future work. [ABSTRACT FROM AUTHOR]

The Earth’s electron radiation belts typically exhibit a two-belt structure. However, observations from the Van Allen Probes revealed the existence of a three-belt structure. This structure consists of an inner belt, a slot region, a remnant belt, a “second slot,” and a new outer belt (or the “third belt”). The formation of the structure involves both the partial loss of the original outer belts and the formation of the third belts. These processes are likely associated with radial diffusion induced by ultra-low-frequency (ULF) waves. In this study, we mainly analyzed electron flux data from medium Earth orbit (MEO) navigation satellites M17–M19 to supplement the observational evidence for the sub-relativistic electron (~100–500 keV) three-belt structure. Evidence of substorm injections and ULF waves during the three-belt event was identified, suggesting they played significant roles in the formation and evolution of the third belt. Substorm injections may introduce new electron populations to the third belt, whereas ULF waves may influence the evolution of the third belt through radial diffusion. Toward the end of the three-belt event, the compression of the magnetosphere by shocks may lead to the dropout of the third belt because of the magnetopause shadowing effect and outward radial diffusion, ultimately disrupting the three-belt structure. This study provides more evidence for the presence of a sub-relativistic electron three-belt structure and offers an analysis of the evolutionary mechanisms of the third belt, which may contribute to a comprehensive understanding of the electron three-belt structure in the radiation belts.

Plasmaspheric hiss plays an important role in the loss of radiation belt electrons via cyclotron resonant interactions. The cold plasma approximation is widely used in the evaluation of hiss‐driven electron losses, which however can break down during disturbed periods of geomagnetic storms and substorms. The kappa particle velocity distribution, characterized by a pronounced high‐energy tail, is well‐established to model the profile of superthermal plasma under disturbed geomagnetic conditions. In the present study, by calculating the electron bounce‐averaged pitch angle diffusion coefficients with kappa plasma dispersion relations, we investigate the sensitivity of hiss‐induced cyclotron‐resonant electron scattering loss to the spectral index κ under a variety of superthermal plasma conditions. Our results demonstrate that, with increasing κ, the diffusion coefficients of ∼20–100 keV radiation belt electrons significantly decrease at lower pitch angles and increase at higher pitch angles. In contrast, for electrons at higher energies, the diffusion coefficients tend to increase at lower pitch angles and decrease at relatively higher pitch angles. We also find that decrease of L‐shell and increase of α* and temperature anisotropy tend to weaken the hiss‐driven pitch angle scattering efficiency of electrons at energies from tens to hundreds of keV with a dip at ∼30–50 keV, while the scattering of higher energy electrons can be enhanced. This study confirms the important role of superthermal plasmas in the hiss‐driven electron loss processes and should be carefully incorporated in future modeling of radiation belt electron dynamics. Key Points: We calculate electron pitch angle diffusion coefficients due to plasmaspheric hiss in a kappa‐distribution plasmaAn increase in κ causes significant decreases in hiss‐induced diffusion coefficients of ∼20–100 keV electrons at low pitch anglesIncreasing α*, temperature anisotropy and decreasing L‐shell weaken the scattering efficiency of tens to hundreds of keV electrons [ABSTRACT FROM AUTHOR]

This paper considers a method for estimating bounce-averaged quasi-linear diffusion coefficients due to whistler-mode waves for a specified ratio of plasma frequency to gyrofrequency, ωp/Ωe, using values precomputed for a different value of that ratio. This approach was recently introduced to facilitate calculations associated with the “POES technique,” generalized to infer both wave intensity and cold plasma density from measurements of particle fluxes near the loss cone. The original derivation was justified on the basis of parallel-propagating waves but applied to calculations with much more general models of the waves. Here, we justify the estimates, which are based on equating resonant frequencies for differing values of ωp/Ωe and energy, for wide ranges of wave normal angle, resonance number, energy, and equatorial pitch angle. Refinements of the original estimates are obtained and tested numerically against full calculations of the diffusion coefficients for representative wave models. The estimated diffusion coefficients can be calculated rapidly and generally give useful estimates for energies in the 30-keV–300-keV range, especially when both relevant values of the ratio ωp/Ωe are large.

We analyze the properties of relativistic (>700 keV) electron precipitation (REP) events measured by the low-Earth-orbit (LEO) POES/MetOp constellation of spacecraft from 2012 through 2023. Leveraging the different profiles of REP observed at LEO, we associate each event with its possible driver: waves or field line curvature scattering (FLCS). While waves typically precipitate electrons in a localized radial region within the outer radiation belt, FLCS drives energy-dependent precipitation at the edge of the belt. Wave-driven REP is detected at any MLT sector and L shell, with FLCS-driven REP occurring only over the nightside–a region where field line stretching is frequent. Wave-driven REP is broader in radial extent on the dayside and accompanied by proton precipitation over 03–23 MLT, either isolated or without a clear energy-dependent pattern, possibly implying that electromagnetic ion cyclotron (EMIC) waves are the primary driver. Across midnight, both wave-driven and FLCS-driven REP occur poleward of the proton isotropic boundary. On average, waves precipitate a higher flux of >700 keV electrons than FLCS. Both contribute to energy deposition into the atmosphere, estimated of a few MW. REP is more associated with substorm activity than storms, with FLCS-driven REP and wave-driven REP at low L shells occurring most often during strong activity (SML* < −600 nT). A preliminary analysis of the Solar Wind (SW) properties before the observed REP indicates a more sustained (∼5 h) dayside reconnection for FLCS-driven REP than for wave-driven REP (∼3 h). The magnetosphere appears more compressed during wave-driven REP, while FLCS-driven REP is associated with a faster SW of lower density. These findings are useful not only to quantify the contribution of >700 keV precipitation to the atmosphere but also to shed light on the typical properties of wave-driven vs FLCS-driven precipitation which can be assimilated into physics-based and/or predictive radiation belt models. In addition, the dataset of ∼9,400 REP events is made available to the community to enable future work.

The editorial discusses the dynamics of Earth's radiation belts, focusing on relativistic electron fluxes and magnetospheric plasma waves. Various processes, such as radial diffusion and wave-particle interactions, influence the variability of the radiation belts. Different models and simulations are used to study and forecast the behavior of energetic particles and plasma waves in the magnetosphere. The research topic collected several articles that address theoretical, observational, and modeling aspects of radiation belt dynamics, aiming to advance understanding and prediction capabilities. [Extracted from the article]

This research examines the plasma processes under penetration of the plasma clouds (plasmoids) across the magnetopause which is modeled as a tangential discontinuity (TD). Cases with the parallel magnetic field in both sides out of the TD are under investigation. Plasma parameters and magnetic field were chosen from the MMS mission and other spacecraft observations. The results are important for understanding the following basic space plasma physics problems: (a) plasma cloud deformation and strong phase mixing with magnetospheric plasma; (b) the transfer of mass, momentum and energy of magnetosheath and magnetic cloud plasma into magnetospheric plasmas; (c) necessary conditions for plasma cloud penetration via the magnetopause; (d) wave generation by plasma clouds inside the magnetopause. Key Points: Plasma clouds (fragments) experience a significant slowdown when moving through magnetosheath plasmasWave‐particle interactions provide a strong phase mixing between plasma cloudsand magnetosheath, and magnetospheric plasmas3‐D hybrid modeling and spacecraft observations provethe mass, momentum and energy transport from the magnetosheath tomagnetosphere [ABSTRACT FROM AUTHOR]

Relativistic electrons in the radiation belts can be transported as a result of wave‐particle interactions (WPI) with ultra‐low frequency (ULF) waves. Such WPI are often assumed to be diffusive, parametric models for the radial diffusion coefficient often being used to assess the rates of radial transport. However, these WPI transition from initially coherent interactions to the diffusive regime over a finite time, this time depending on the ULF wave power spectral density, and local resonance conditions. Further, in the real system on the timescales of a single storm, interactions with finite discrete modes may be more realistic. Here, we use a particle‐tracing model to simulate the dynamics of outer radiation belt electrons in the presence of a finite number of discrete frequency modes. We characterize the point of the onset of diffusion as a transition from separate discrete interactions in terms of wave parameters by using the "two‐thirds" overlap criterion (Lichtenberg & Lieberman, 1992, https://doi.org/10.1007/978‐1‐4757‐2184‐3), a comparison between the distance between, and the widths of, the electron's primary resonant islands in phase space. Further, we find the particle decorrelation time in our model system with typical parameters to be on the timescale of hours, which only afterward can the system be modeled by one‐dimensional radial diffusion. Direct comparison of particle transport rates in our model with previous analytic diffusion coefficient formulations show good agreement at times beyond the decorrelation time. These results are critical for determining the time periods and conditions under which ULF wave radial diffusion theory can be applied. Plain Language Summary: The dynamics of Earth's outer Van Allen radiation belt electrons have up to now been almost exclusively modeled using statistical methods. However, such approaches may not be valid for all scenarios. In this work, we defined a criterion separating the regimes where the dynamics of the outer radiation belt electrons can and cannot be modeled statistically, and in particular using a model based around the concepts of diffusion where averaging over many individual interactions leads to an assessment for the overall behavior of a set, or ensemble, of electrons. We use a test particle‐tracing model to assess the actual dynamics of particle ensembles when perturbed by a type of plasma waves with ultra‐low frequency in space. We showed that there is a distinctive qualitative and quantitative difference between diffusive and the more coherent regimes and identified their point of transition. We further verified that once the system has evolved beyond our derived transition criteria it does indeed match the common statistical predictions, verifying the applicability of a diffusion model after that time. Significantly, however, at earlier times the more correlated system behaves differently and may be characterized by a much faster and coherent transport. Key Points: We derive analytic expressions required for the transition from coherent to diffusive transport applied to ultra‐low frequency (ULF) wave‐particle interactionsWe characterize the behavior using an equivalent dynamical system model, highlighting the importance of the particle decorrelation timeFor decorrelation times longer than typical ULF wavetrains, particle transport rates cannot be estimated under a radial diffusion paradigm [ABSTRACT FROM AUTHOR]

Dissipation processes derived from the kinetic theory of gases (shear viscosity and heat conduction) are employed to examine the solar wind that interacts with planetary ionospheres. The purpose of this study is to estimate the mean free path of wave-particle interactions that produce a continuum response in the plasma behavior. Wave-particle interactions are necessary to support the fluid dynamic interpretation that accounts for the interpretation of various features measured in a solar wind–planet ionosphere region; namely, (i) the transport of solar wind momentum to an upper ionosphere in the presence of a velocity shear, and (ii) plasma heating produced by momentum transport. From measurements conducted in the solar wind interaction with the Venus ionosphere, it is possible to estimate that in general terms, the mean free path of wave-particle interactions reaches λH ≥ 1000 km values that are comparable to the gyration radius of the solar wind particles in their Larmor motion within the local solar wind magnetic field. Similar values are also applicable to conditions measured by the Mars ionosphere and in cometary plasma wakes. Considerations are made in regard to the stochastic trajectories of the plasma particles that have been implied from the measurements made in planetary environments. At the same time, it is as possible that the same phenomenon is applicable to the interaction of stellar winds with the ionosphere of exoplanets, and also in regions where streaming ionized gases reach objects that are subject to rotational motion in other astrophysical problems (galactic flow–plasma interactions, black holes, etc.). [ABSTRACT FROM AUTHOR]

Electromagnetic ion cyclotron (EMIC) waves can very rapidly and effectively scatter relativistic electrons into the atmosphere. EMIC‐driven precipitation bursts can be detected by low‐altitude spacecraft, and analysis of the fine structure of such bursts may reveal unique information about the near‐equatorial EMIC source region. In this study, we report, for the first time, observations of EMIC‐driven electron precipitation exhibiting energy, E, dispersion as a function of latitude (and hence L‐shell): two predominant categories exhibit dE/dL > 0 and dE/dL < 0. We interpret precipitation with dE/dL < 0 as due to the typical inward radial gradient of cold plasma density and equatorial magnetic field (∼65% of the statistics). Precipitation with dE/dL > 0 is interpreted as due to an outward radial gradient of the equatorial magnetic field, likely produced by energetic ions freshly injected into the ring current (∼35% of the statistics). The observed energy dispersion of EMIC‐driven electron precipitation was reproduced in simulations. Plain Language Summary: Relativistic electron precipitation from the equatorial magnetosphere deposits significant energy fluxes to the atmosphere below 50 km, and thus naturally alters the atmosphere ionization and contributes to ozone destruction in the mesosphere. This precipitation is, in good part, due to electron resonant interactions with electromagnetic ion cyclotron (EMIC) waves. Although basic theories of this interaction have been well understood, the detailed electron precipitation pattern, which depends on the background plasma and magnetic field conditions in the wave source regions, are not well studied. In this study, we demonstrate a new property of electron precipitation driven by EMIC waves—the dispersion in energy versus latitude as observed by the low‐altitude ELFIN CubeSats. Such dispersion can provide information about the EMIC wave source region and, as it turns out, connect relativistic electron precipitation with one of the most powerful phenomena in the magnetosphere, substorm plasma injections. Key Points: We report two types of energy versus latitude (or L‐shell) dispersion of relativistic electron precipitation observed at ELFINBoth types of dispersion signatures can be attributed to electron scattering by electromagnetic ion cyclotron (EMIC) wavesEnergy dispersion is controlled by the magnetic field radial profile in the EMIC wave source region [ABSTRACT FROM AUTHOR]

This paper presents a new Monte Carlo algorithm intended for use in orbit following Monte Carlo codes (OFMC) to describe resonant interaction of ions with Radio Frequency (RF) waves in axi-symmetric toroidal plasmas. The algorithm is based on a quasi-linear description of the wave–particle interaction and its effect on the distribution function of a resonating ion species. The algorithm outlined in the present paper utilises a two-step approach for the evaluation of the Monte Carlo operator that has better efficiency and a stronger convergence than the standard Euler–Maruyama scheme. The algorithm preserves the reciprocity of the diffusion process. Furthermore, it simplifies how the displacement of the resonance position, as a result of wave–particle interaction, is accounted for. Such displacements can have a noticeable effect on the deterministic part of the Monte Carlo operator. The fundamental nature of guiding centre displacements of resonant ions as a result of wave–particle interaction is reviewed.

Theoretical analysis has revealed a specific resonance that shares the same condition as Landau resonance, but instead involves wave electromagnetic fields rather than traditionally electrostatic fields. While this resonance, referred to as electromagnetic Landau resonance due to its properties, is considered significant for magnetospheric dynamics, rare reports or evaluations based on observations have been made thus far. Here, we present an event detected by the Magnetospheric Multiscale mission near the dayside magnetopause. During this event, ∼748‐eV protons are observed to be in resonance with a wave. Detailed data analysis demonstrates the resonant velocity closely matches the wave's parallel phase speed, which, combined with the significant work done by wave perpendicular electric field, confirms this interaction as electromagnetic Landau resonance. Further investigation indicates these protons are being secularly accelerated within this resonance. Consequently, our observations provide the first empirical evidence supporting the previously suggested theoretical importance of the electromagnetic Landau resonance. Plain Language Summary: The electromagnetic Landau resonance shares the same resonance condition as the normal Landau resonance, but differs in that it involves the electromagnetic components of wave fields instead of the electrostatic components found in the case of the latter. Although it has been examined in theories and confirmed to occur in space plasmas experimentally, this resonance, especially the accompanying evolution of particle velocity distributions, has yet to be evaluated quantitatively through spacecraft observations. In this paper, we report the first observation of this resonance obtained by the Magnetospheric Multiscale mission near the dayside magnetosphere. In the reported case, protons of ∼400–1,000 eV are found to be in resonance with a wave. A more detailed examination of the observed fields and protons shows the corresponding resonant velocity is nearly identical to the wave's parallel phase speed. This observation, combined with the significant work done by wave perpendicular electric field, conclusively confirms the observed interaction as the electromagnetic Landau resonance. Further investigation indicates the protons are secularly accelerated by the wave via this resonance. Hence, our observations provide empirical evidence supporting the previously suggested theoretical significance of the electromagnetic Landau resonance. Key Points: MMS observations of electromagnetic Landau resonance near the dayside magnetopause are presentedThis resonance follows the same condition as the Landau resonance, but modulates particles via the electromagnetic components of wave fieldsAnalysis of the observed fields and protons provide conclusive evidence for this resonance accelerating protons [ABSTRACT FROM AUTHOR]

Quasilinear theories have been shown to well describe a range of transport phenomena in magnetospheric, space, astrophysical and laboratory plasma "weak turbulence" scenarios. It is well known that the resonant diffusion quasilinear theory for the case of a uniform background field may formally describe particle dynamics when the electromagnetic wave amplitude and growth rates are sufficiently "small", and the bandwidth is sufficiently "large". However, it is important to note that for a given wave spectrum that would be expected to give rise to quasilinear transport, the quasilinear theory may indeed apply for given range of resonant pitch-angles and energies, but may not apply for some smaller, or larger, values of resonant pitch-angle and energy. That is to say that the applicability of the quasilinear theory can be pitch-angle dependent, even in the case of a uniform background magnetic field. If indeed the quasilinear theory does apply, the motion of particles with different pitch-angles are still characterised by different timescales. Using a high-performance test-particle code, we present a detailed analysis of the applicability of quasilinear theory to a range of different wave spectra that would otherwise "appear quasilinear" if presented by e.g., satellite survey-mode data. We present these analyses as a function of wave amplitude, wave coherence and resonant particle velocities (energies and pitch-angles), and contextualise the results using theory of resonant overlap and small amplitude criteria. In doing so, we identify and classify five different transport regimes that are a function of particle pitch-angle. The results in our paper demonstrate that there can be a significant variety of particle responses (as a function of pitch-angle) for very similar looking survey-mode electromagnetic wave products, even if they appear to satisfy all appropriate quasilinear criteria. In recent years there have been a sequence of very interesting and important results in this domain, and we argue in favour of continuing efforts on: (i) the development of new transport theories to understand the importance of these, and other, diverse electron responses; (ii) which are informed by statistical analyses of the relationship between burst-and survey-mode spacecraft data. [ABSTRACT FROM AUTHOR]

The significant role of nonlinear wave–particle interactions in the macrodynamics and microdynamics of the Earth's outer radiation belt has long been recognised. Electron dropouts during magnetic storms, microbursts in atmospheric electron precipitation, and pulsating auroras are all associated with the rapid scattering of energetic electrons by the whistler-mode chorus, a structured electromagnetic emission known to reach amplitudes of about 1 % of the ambient magnetic field. Despite the decades of experimental and theoretical investigations of chorus and the recent progress achieved through numerical simulations, there is no definitive theory of the chorus formation mechanism, not even in the simple case of parallel (one-dimensional) propagation. Here we follow the evolution of these theories from their beginnings in the 1960s to the current state, including newly emerging self-consistent excitation models. A critical review of the unique features of each approach is provided, taking into account the most recent spacecraft observations of the fine structure of chorus. Conflicting interpretations of the role of resonant electron current and magnetic field inhomogeneity are discussed. We also discuss the interplay between nonlinear growth and microscale propagation effects and identify future theoretical and observational challenges stemming from the two-dimensional aspects of chorus propagation. [ABSTRACT FROM AUTHOR]

Energetic electron dynamics in the Earth's radiation belts and near‐Earth plasma sheet are controlled by multiple processes operating on very different time scales: from storm‐time magnetic field reconfiguration on a timescale of hours to individual resonant wave‐particle interactions on a timescale of milliseconds. The most advanced models for such dynamics either include test particle simulations in electromagnetic fields from global magnetospheric models, or those that solve the Fokker‐Plank equation for long‐term effects of wave‐particle resonant interactions. The most prospective method, however, would be to combine these two classes of models, to allow the inclusion of resonant electron scattering into simulations of electron motion in global magnetospheric fields. However, there are still significant outstanding challenges that remain regarding how to incorporate the long term effects of wave‐particle interactions in test‐particle simulations. In this paper, we describe in details two approaches that incorporate electron scattering in test particle simulations: stochastic differential equation (SDE) approach and the mapping technique. Both approaches assume that wave‐particle interactions can be described as a probabilistic process that changes electron energy, pitch‐angle, and thus modifies the test particle dynamics. To compare these approaches, we model electron resonant interactions with field‐aligned whistler‐mode waves in dipole magnetic fields. This comparison shows advantages of the mapping technique in simulating the nonlinear resonant effects, but also underlines that more significant computational resources are needed for this technique in comparison with the SDE approach. We further discuss applications of both approaches in improving existing models of energetic electron dynamics. Key Points: We discuss two approaches to incorporate resonant effects into test particle simulation modelsDetailed approaches have been shown for continuous stochastic differential equations (SDEs) and the mapping technique, respectivelyIn contrast to continuous SDE, the mapping technique allows one to simulate nonlinear resonant effects [ABSTRACT FROM AUTHOR]

Abstract Energetic electron precipitation (EEP) from the radiation belts into Earth's atmosphere leads to several profound effects (e.g., enhancement of ionospheric conductivity, possible acceleration of ozone destruction processes). An accurate quantification of the energy input and ionization due to EEP is still lacking due to instrument limitations of low‐Earth‐orbit satellites capable of detecting EEP. The deployment of the Electron Losses and Fields InvestigatioN (ELFIN) CubeSats marks a new era of observations of EEP with an improved pitch‐angle (0°–180°) and energy (50 keV–6 MeV) resolution. Here, we focus on the EEP recorded by ELFIN coincident with electromagnetic ion cyclotron (EMIC) waves, which play a major role in radiation belt electron losses. The EMIC‐driven EEP (∼200 keV–∼2 MeV) exhibits a pitch‐angle distribution (PAD) that flattens with increasing energy, indicating more efficient high‐energy precipitation. Leveraging the combination of unique electron measurements from ELFIN and a comprehensive ionization model known as Boulder Electron Radiation to Ionization (BERI), we quantify the energy input of EMIC‐driven precipitation (on average, ∼3.3 × 10−2 erg/cm2/s), identify its location (any longitude, 50°–70° latitude), and provide the expected range of ion‐electron production rate (on average, 100–200 pairs/cm3/s), peaking in the mesosphere—a region often overlooked. Our findings are crucial for improving our understanding of the magnetosphere‐ionosphere‐atmosphere system as they accurately specify the contribution of EMIC‐driven EEP, which serves as a crucial input to state‐of‐the‐art atmospheric models (e.g., WACCM) to quantify the accurate impact of EMIC waves on both the atmospheric chemistry and dynamics.

Abstract Electromagnetic ion cyclotron (EMIC) waves can very rapidly and effectively scatter relativistic electrons into the atmosphere. EMIC‐driven precipitation bursts can be detected by low‐altitude spacecraft, and analysis of the fine structure of such bursts may reveal unique information about the near‐equatorial EMIC source region. In this study, we report, for the first time, observations of EMIC‐driven electron precipitation exhibiting energy, E, dispersion as a function of latitude (and hence L‐shell): two predominant categories exhibit dE/dL > 0 and dE/dL 0 is interpreted as due to an outward radial gradient of the equatorial magnetic field, likely produced by energetic ions freshly injected into the ring current (∼35% of the statistics). The observed energy dispersion of EMIC‐driven electron precipitation was reproduced in simulations.

Recent work has shown that ElectroMagnetic Ion Cyclotron (EMIC) waves tend to occur in four distinct regions, each having their own characteristics and morphology. Here, we use nonlinear test-particle simulations to examine the range of energetic electron scattering responses to two EMIC wave groups that occur at low L-shells and overlap the outer radiation belt electrons. The first group consists of low-density, H-band region b waves, and the second group consists of high-density, He-band region c waves. Results show that while low-density EMIC waves cannot precipitate electrons below ∼16 MeV, the high density EMIC waves drive a range of linear and nonlinear behaviors including phase bunching and trapping. In particular, a nonlinear force bunching effect can rapidly advect electrons at low pitch-angles near the minimum resonant energy to larger pitch angles, effectively blocking precipitation and loss. This effect contradicts conventional expectations and may have profound implication for observational campaigns.

Plasmaspheric hiss waves at the Earth are well known for causing losses of electrons from the radiation belts through wave particle interactions. At Saturn, however, we show that the different plasma density environment leads to acceleration of the electrons rather than loss. The ratio of plasma frequency to electron gyrofrequency frequently falls below one creating conditions for hiss to accelerate electrons. The location of hiss at high latitudes (>25°) coincides very well with this region of very low density. The interaction between electrons and hiss only occurs at these higher latitudes, therefore the acceleration is limited to mid to low pitch angles leading to butterfly pitch angle distributions. The hiss is typically an order of magnitude stronger than chorus at Saturn and the resulting acceleration is rapid, approaching steady state in one day at 0.4 MeV at L = 7 and the effect is stronger with increasing L-shell.

Quasilinear theories have been shown to well describe a range of transport phenomena in magnetospheric, space, astrophysical and laboratory plasma “weak turbulence” scenarios. It is well known that the resonant diffusion quasilinear theory for the case of a uniform background field may formally describe particle dynamics when the electromagnetic wave amplitude and growth rates are sufficiently “small”, and the bandwidth is sufficiently “large”. However, it is important to note that for a given wave spectrum that would be expected to give rise to quasilinear transport, the quasilinear theory may indeed apply for given range of resonant pitch-angles and energies, but may not apply for some smaller, or larger, values of resonant pitch-angle and energy. That is to say that the applicability of the quasilinear theory can be pitch-angle dependent, even in the case of a uniform background magnetic field. If indeed the quasilinear theory does apply, the motion of particles with different pitch-angles are still characterised by different timescales. Using a high-performance test-particle code, we present a detailed analysis of the applicability of quasilinear theory to a range of different wave spectra that would otherwise “appear quasilinear” if presented by e.g., satellite survey-mode data. We present these analyses as a function of wave amplitude, wave coherence and resonant particle velocities (energies and pitch-angles), and contextualise the results using theory of resonant overlap and small amplitude criteria. In doing so, we identify and classify five different transport regimes that are a function of particle pitch-angle. The results in our paper demonstrate that there can be a significant variety of particle responses (as a function of pitch-angle) for very similar looking survey-mode electromagnetic wave products, even if they appear to satisfy all appropriate quasilinear criteria. In recent years there have been a sequence of very interesting and important results in this domain, and we argue in favour of continuing efforts on: (i) the development of new transport theories to understand the importance of these, and other, diverse electron responses; (ii) which are informed by statistical analyses of the relationship between burst- and survey-mode spacecraft data.

Abstract Theoretical analysis has revealed a specific resonance that shares the same condition as Landau resonance, but instead involves wave electromagnetic fields rather than traditionally electrostatic fields. While this resonance, referred to as electromagnetic Landau resonance due to its properties, is considered significant for magnetospheric dynamics, rare reports or evaluations based on observations have been made thus far. Here, we present an event detected by the Magnetospheric Multiscale mission near the dayside magnetopause. During this event, ∼748‐eV protons are observed to be in resonance with a wave. Detailed data analysis demonstrates the resonant velocity closely matches the wave's parallel phase speed, which, combined with the significant work done by wave perpendicular electric field, confirms this interaction as electromagnetic Landau resonance. Further investigation indicates these protons are being secularly accelerated within this resonance. Consequently, our observations provide the first empirical evidence supporting the previously suggested theoretical importance of the electromagnetic Landau resonance.

In the inner magnetosphere, fast magnetosonic waves (MS waves) are known to resonantly interact with ring current protons, causing these protons to gain energy preferentially in the direction perpendicular to the background magnetic field. An anisotropic distribution of enhanced ring current protons is a necessary condition to excite electromagnetic ion cyclotron (EMIC) waves which are known to facilitate a rapid depletion of ultra‐relativistic electrons in the outer radiation belt. So, when a simultaneous observation of high‐frequency EMIC (HFEMIC) waves, anisotropic low‐energy protons, and MS waves was first reported, a chain of energy flow from MS waves to HFEMIC waves through proton heating was naturally proposed. In this study, we carry out a statistical analysis using Van Allen Probes data to provide deeper insights into this energy pathway. Our results show that the occurrence of HFEMIC waves exhibits good correlation with the enhanced flux and anisotropy of low‐energy protons, but the correlation between the low‐energy protons and the concurrent MS waves is rather poor. The latter result is given support by quasilinear diffusion analysis, indicating negligible momentum diffusion rates at sub‐keV energies, unless MS wave frequency gets very close to the proton cyclotron frequency (which constitutes only a small number of the cases). The fact that the first chain of the coupling is statistically inconclusive calls for an alternative explanation for the major source of the low‐energy anisotropic proton population in the inner magnetosphere. Key Points: Energy coupling from magnetosonic to high‐frequency electromagnetic ion cyclotron (EMIC) waves through low‐energy proton heating is investigated using correlation analysisHigh‐frequency EMIC wave occurrence correlates well with large anisotropy of 10–100 eV protons, required for the wave generationThe correlation between low‐energy protons and MS waves is rather poor, calling for alternative explanation for the origin of these protons [ABSTRACT FROM AUTHOR]

Plasma escape from the high‐latitude ionosphere (ion outflow) serves as a significant source of heavy plasma to the magnetospheric plasma sheet and ring current regions. Outflows alter mass density and reconnection rates, hence global responses of the magnetosphere. A new fully kinetic and semi‐kinetic model, KAOS (Kinetic model of Auroral ion OutflowS), is constructed from first principles which traces large numbers of individual O+ ion macro‐particles along curved magnetic field lines, using a guiding‐center approximation, in order to facilitate calculation of ion distribution functions and moments. Particle forces include mirror and parallel electric field forces, a self‐consistent ambipolar electric field, and a parameterized source of ion cyclotron resonance wave heating, thought to be central to the transverse energization of ions. The model is initiated with a steady‐state ion density altitude profile and Maxwellian velocity distribution and particle trajectories are advanced via a direct simulation Monte Carlo scheme. This outlines the implementation of the kinetic outflow model, demonstrates the model's ability to achieve near‐hydrostatic equilibrium necessary for simulation spin‐up, and investigates L‐shell dependent wave heating and pressure cookers scenarios. This paper illustrates the model initialization process and numerical investigations of L‐shell dependent outflows and pressure cooker environments and serves to advance our understanding of the drivers and particle dynamics in the auroral ionosphere. Key Points: A new model, KAOS (Kinetic model of Auroral ion OutflowS), is introduced for studying ionospheric outflows from first principlesWe quantify dependence of upflowing/outflowing ion distributions on parameters pertaining to the characterization of pressure cookersMagnetospheric potential structures may transport highly transversely energized ion distributions to ionospheric altitudes [ABSTRACT FROM AUTHOR]

Although both the field line curvature (FLC) and electromagnetic ion cyclotron (EMIC) waves are recognized to contribute importantly to the loss of energetic protons in the Earth's ring current, their quantitative differences in scattering ring current protons are still not fully understood. In this study, using a realistic, nondipolar magnetic field model, we perform a detailed analysis of the scattering effects of ring current protons and the resultant proton lifetimes due to FLC and EMIC waves at different L‐shells under different levels of geomagnetic activity. We find that compared with EMIC wave‐driven scattering, FLC scattering has a stronger dependence on L‐shell and geomagnetic activity. Pitch angle scattering efficiency due to FLC enhances significantly as proton energy increases. In contrast, scattering by H+ band EMIC waves tends to be weaker with increasing proton energy, while the scattering rates by He+ band EMIC waves increase first and then decrease. The results of proton lifetime against pitch angle scattering show that EMIC wave‐driven scattering dominates the loss of ring current protons at lower L‐shells (L < 6), especially during geomagnetically quiet conditions. During geomagnetically active conditions at L ≥ 6, EMIC wave‐driven scattering dominates at lower proton energies, while FLC scattering dominates at higher proton energies. This study improves the current understanding of the relative contributions of scattering by FLC and EMIC waves to the Earth's ring current proton dynamics. Key Points: We make a detailed comparison between field line curvature (FLC) and electromagnetic ion cyclotron (EMIC) waves induced scattering losses of ring current protonsFLC scattering has a stronger dependence on L‐shell and the level of geomagnetic activity than EMIC wave scatteringPronounced discrepancies are found in the dependences on proton energy and pitch angle between FLC and EMIC wave scattering [ABSTRACT FROM AUTHOR]

Electromagnetic ion cyclotron (EMIC) waves can drive radiation belt depletion and Low‐Earth Orbit satellites can detect the resulting electron and proton precipitation. The ELFIN (Electron Losses and Fields InvestigatioN) CubeSats provide an excellent opportunity to study the properties of EMIC‐driven electron precipitation with much higher energy and pitch‐angle resolution than previously allowed. We collect EMIC‐driven electron precipitation events from ELFIN observations and use POES (Polar Orbiting Environmental Satellites) to search for 10s–100s keV proton precipitation nearby as a proxy of EMIC wave activity. Electron precipitation mainly occurs on localized radial scales (∼0.3 L), over 15–24 MLT and 5–8 L shells, stronger at ∼MeV energies and weaker down to ∼100–200 keV. Additionally, the observed loss cone pitch‐angle distribution agrees with quasilinear predictions at ≳250 keV (more filled loss cone with increasing energy), while additional mechanisms are needed to explain the observed low‐energy precipitation. Plain Language Summary: Electromagnetic ion cyclotron (EMIC) emissions are a type of plasma wave that can be excited in the near‐Earth environment and interact with energetic electrons in the Earth's radiation belts. Through these wave‐particle interactions, electrons can be pushed into the loss cone and lost into the Earth's atmosphere (electron precipitation), where they deposit their energy by interacting with neutral atoms and cold charged particles. EMIC‐driven electron precipitation still needs to be fully characterized and understood. In this work, we use data from the Electron Losses and Fields InvestigatioN (ELFIN) CubeSats, which provide electron fluxes at high energy and pitch‐angle (look direction) resolution at ∼450 km of altitude. Our analysis reveals that precipitation is most efficient for ∼MeV electrons and is accompanied by weaker low‐energy precipitation down to ∼100–200 keV. Given the ELFIN CubeSats spin, we can also study the distribution of the precipitating electrons along different look directions (pitch‐angles). We find that the loss cone shape is well‐reproduced by quasilinear predictions of EMIC‐electron interactions at higher energies (≳250 keV), while quasilinear calculations underestimate the observed low‐energy precipitation. Key Points: Energetic electron precipitation is observed by Electron Losses and Fields InvestigatioN nearby proton precipitation (a proxy for Electromagnetic ion cyclotron waves) primarily over 15–24 MLTPrecipitation efficiency increases as a function of energy: weak ∼100s keV precipitation is concurrent with intense ∼MeV precipitationThe observed pitch‐angle distribution shows a loss cone filling up with energy, similar to the pitch‐angle profiles from quasilinear theory [ABSTRACT FROM AUTHOR]

Dissipation processes derived from the kinetic theory of gases (shear viscosity and heat conduction) are employed to examine the solar wind that interacts with planetary ionospheres. The purpose of this study is to estimate the mean free path of wave-particle interactions that produce a continuum response in the plasma behavior. Wave-particle interactions are necessary to support the fluid dynamic interpretation that accounts for the interpretation of various features measured in a solar wind–planet ionosphere region; namely, (i) the transport of solar wind momentum to an upper ionosphere in the presence of a velocity shear, and (ii) plasma heating produced by momentum transport. From measurements conducted in the solar wind interaction with the Venus ionosphere, it is possible to estimate that in general terms, the mean free path of wave-particle interactions reaches λH ≥ 1000 km values that are comparable to the gyration radius of the solar wind particles in their Larmor motion within the local solar wind magnetic field. Similar values are also applicable to conditions measured by the Mars ionosphere and in cometary plasma wakes. Considerations are made in regard to the stochastic trajectories of the plasma particles that have been implied from the measurements made in planetary environments. At the same time, it is as possible that the same phenomenon is applicable to the interaction of stellar winds with the ionosphere of exoplanets, and also in regions where streaming ionized gases reach objects that are subject to rotational motion in other astrophysical problems (galactic flow–plasma interactions, black holes, etc.).

In the present paper, we investigate the effects of latitude-dependent wave power spectrum on the interactions of chorus with electrons. Great errors in evaluating the electron diffusion coefficients and the resultant electron temporal evolutions are introduced by the widely adopted latitudinally constant model, compared with the latitudinally varying model. The latitudinally constant model tends to overestimate (underestimate) the diffusion coefficients for electrons below (above) 200 keV. The overestimation and underestimation are mainly confined in small to intermediate pitch angles, increase with decreasing pitch angles, and can reach up to several orders of magnitude. The large differences in diffusion coefficients significantly alter the net changes of electron phase space densities and the resultant shapes of electron pitch angle distributions. Our simulations demonstrate that the wave power spectrum distribution along the magnetic field line plays an important role in controlling the dynamics of radiation belt electrons.

Abstract Electromagnetic ion cyclotron (EMIC) waves can drive radiation belt depletion and Low‐Earth Orbit satellites can detect the resulting electron and proton precipitation. The ELFIN (Electron Losses and Fields InvestigatioN) CubeSats provide an excellent opportunity to study the properties of EMIC‐driven electron precipitation with much higher energy and pitch‐angle resolution than previously allowed. We collect EMIC‐driven electron precipitation events from ELFIN observations and use POES (Polar Orbiting Environmental Satellites) to search for 10s–100s keV proton precipitation nearby as a proxy of EMIC wave activity. Electron precipitation mainly occurs on localized radial scales (∼0.3 L), over 15–24 MLT and 5–8 L shells, stronger at ∼MeV energies and weaker down to ∼100–200 keV. Additionally, the observed loss cone pitch‐angle distribution agrees with quasilinear predictions at ≳250 keV (more filled loss cone with increasing energy), while additional mechanisms are needed to explain the observed low‐energy precipitation.

The features of electron pitch angle distributions (PADs) often imply different physical mechanisms in planetary magnetospheres. We report a simultaneous equatorial electrostatic electron cyclotron harmonic (ECH) wave event with butterfly PADs of electrons at L ∼ 7.6–9 observed by the Cassini spacecraft. Via calculating the bounce‐averaged electron diffusion rates, we found that Saturnian ECH waves can resonate with ∼10 eV to several keV electrons at <60° pitch angles at time scales from ∼10−8 to 10−4 s−1. Simulations show that the formation of ∼100 eV to ∼1 keV electron butterfly PADs are mainly caused by the pitch angle scattering of electrons at low pitch angles (<30°) and the momentum scattering at intermediate pitch angles of ∼30°–45°, though previous studies suggested the adiabatic transport is the dominated mechanism. Additionally, our results successfully reproduce the variation of peak pitch angles (αp) and phase space density ratios between α90° and αp with L‐shell. Plain Language Summary: Charged particles present different pitch angle distributions (PADs) due to different physical mechanisms in Saturn's magnetosphere. Butterfly PADs have local minimum at ∼90° pitch angle, which are commonly observed in Saturn's magnetosphere for electrons over a wide energy range from ∼100 eV to several MeV. Previous studies proposed that the adiabatic transport dominates the transformation from the electron field‐aligned PADs of ∼100 eV–several keV to the butterfly shapes in Saturn's magnetosphere. In our study, we report a simultaneous electrostatic electron cyclotron harmonic (ECH) wave event with the butterfly PADs of electrons at L ∼ 7.6–9 observed by the Cassini spacecraft. Via calculating the bounce‐averaged electron diffusion rates of ECH waves and simulating the evolution of electron phase space densities (PSDs), we find that the formation of ∼100 eV to ∼1 keV electron butterfly PADs is mainly caused by the scattering of electrons induced by ECH waves. Our simulation results successfully reproduce the variation of peak pitch angle (αp) and PSD ratios between α90° and αp with L‐shell. These results would improve the current understanding of the electron dynamics in Saturn's magnetosphere and shed light on understanding the plasma environment of the outer planets and exoplanets. Key Points: We report a simultaneous equatorial electrostatic electron cyclotron harmonic (ECH) wave event with the butterfly PADs of electronsThe Saturnian ECH waves can resonate with ∼10 eV to several keV electrons at <60° pitch anglesThe formation of ∼100 eV to ∼1 keV electron butterfly PADs is attributed to the scattering of electrons induced by ECH waves [ABSTRACT FROM AUTHOR]

A theory of quasilinear diffusion for obliquely propagating electromagnetic waves was developed in the 1960's and applied in the 1970's to model scattering of relativistic electrons by a prescribed distribution of waves. In the latter work, a transformation of variables, from wavevector space to the temporal frequency and tangent of the wave normal angle, was used so that simple Gaussian functions of frequency and tangent of the wave normal angle could be multiplied together to define the distribution of wave power, although arbitrary distributions of power in these two variables is also permitted. Finally, in 2005, previous work was consolidated and has been widely used in heliophysics studies that require computation of quasilinear diffusion coefficients. Here it is shown that this transformation is inppropriate when the precise wave vector distribution is known. The correct transformation is derived and used to produce diffusion coefficients that can differ by orders of magnitude from those computed using the inappropriate transformation. The differences are largest when the distribution of wave power extends to wave normal angles near the resonance cone. When the ratio of the plasma frequency to the gyrofrequency is large, only low energies (keV) are affected, but as the ratio decreases higher energies (MeV) also show differences. It is also shown that the derivation from the 1960's uses a notation that results in the diffusion coefficients depending on the distribution of wave power with respect to the wave azimuthal angle whereas there should be no such dependence. Plain Language Summary: Electrons can become trapped in the near‐Earth space environment and stay trapped for days to years, damaging sensitive electronics on space assets. The flux of relativistic electrons varies over time due to source and loss processes, some of which are due to interactions with electromagnetic waves. When the wave amplitudes are small, the effect of the waves on electrons can be modeled as a diffusion equation, with the diffusion coefficients proportional to the wave power. The theory currently used to compute diffusion coefficients was developed in the 1960s using a coordinate system based on all three components of the wave propagation direction. The theory was adapted to a coordinate system that uses the wave frequency and wave normal angle, and has been used for 50 years in a variety of heliophysics models. It is shown for the first time here that the transformation of the coordinate system is inappropriate when the precise distribution of wave k‐vectors is available, and the correct transformation is derived. The newly computed diffusion coefficients can be orders of magnitude different than the old coefficients, potentially implying large differences in the predicted time scales over which the source and loss processes will occur for some situations. Key Points: Quasilinear theory from the 1960s unphysically allows diffusion coefficients to depend on wave azimuthal angle due to a notation problemWhen the precise k‐vector distribution is known, the transformation of variables in 1970s theory is incorrect, limiting its applicabilityCorrecting the two problems produces diffusion coefficients that can differ from the old values by orders of magnitude in some cases [ABSTRACT FROM AUTHOR]

Among the most intense emissions in the Earth's magnetosphere, electromagnetic ion cyclotron (EMIC) waves are regarded as a critical candidate contributing to the precipitation losses of ring current protons, which however lacks direct multi-point observations to establish the underlying physical connection. Based upon a robust conjunction between the satellite pair of Van Allen Probe B and NOAA-19, we perform a detailed analysis to capture simultaneous enhancements of EMIC waves and ring current proton precipitation. By assuming that the ring current proton precipitation is mainly caused by EMIC wave scattering, we establish a physical model between the wave-driven proton diffusion and the ratio of precipitated-to-trapped proton count rates, which is subsequently applied to infer the intensity of EMIC waves required to cause the observed proton precipitation. Our simulations indicate that the model results of EMIC wave intensity, obtained using either the observed or empirical Gaussian wave frequency spectrum, are consistent with the wave observations, within a factor of 1.5. Our study therefore strongly supports the dominant contribution of EMIC waves to the ring current proton precipitation, and offers a valuable means to construct the global profile of EMIC wave intensity using low-altitude NOAA POES proton measurements, which generally have a broad L-shell coverage and high time resolution in favor of near-real-time conversion of the global EMIC wave distribution.

The dynamics of the outer zone radiation belt has received a lot of attention mainly due to the correlation between the occurrence of enhancing relativistic electron flux and spacecraft operation anomalies or even failures (e.g., Baker et al. 1994). Relativistic electron events are often observed during great storms associated with ultra low frequency (ULF) waves. For example, a large buildup of relativistic electrons was observed during the great storm of March 24, 1991 (e.g., Li et al. 1993; Hudson et al. 1995; Mann et al. 2013). However, the dominant processes which accelerate magnetospheric radiation belt electrons to MeV energies are not well understood. In this paper, we present observations of Pc5 ULF waves in the recovery phase of the Bastille day storm of July 16, 2000 and electron and proton flux simultaneously oscillating with the same frequencies as the waves. The mechanism for the observed electron and proton flux modulations is examined using groundbased and satellite observations. During this storm time, multiple packets of discrete frequency Pc5 ULF waves appeared associated with energetic particle flux oscillations. We model the drift paths of electrons and protons to determine if the particles drift through the ULF wave to understand why some particle fluxes are modulated by the ULF waves and others are not. We also analyze the flux oscillations of electrons and protons as a function of energy to determine if the particle modulations are caused by a ULF wave drift resonance or advection of a particle density gradient. We suggest that the energetic electron and proton modulations by Pc5 ULF waves provide further evidence in support of the important role that ULF waves play in outer radiation belt dyanamics during storm times.

Abstract The features of electron pitch angle distributions (PADs) often imply different physical mechanisms in planetary magnetospheres. We report a simultaneous equatorial electrostatic electron cyclotron harmonic (ECH) wave event with butterfly PADs of electrons at L ∼ 7.6–9 observed by the Cassini spacecraft. Via calculating the bounce‐averaged electron diffusion rates, we found that Saturnian ECH waves can resonate with ∼10 eV to several keV electrons at

Radial diffusion driven by Ultra Low Frequency (ULF) waves is very important for magnetospheric dynamics, as it contributes to both acceleration and loss of relativistic electrons in the outer Van Allen radiation belt, as well as to other planetary magnetospheres. The dependence of ULF wave power spectral density and radial diffusion coefficients ( D LL ) on solar wind parameters has already been investigated but their dependence on the various solar and interplanetary drivers is poorly studied. In this study, we conduct a statistical analysis of radial diffusion coefficients D LL to look into their dependence on different interplanetary drivers, i.e. Interplanetary Coronal Mass Ejections (ICMEs) and Stream Interaction Regions (SIRs), which originate from different solar drivers: CMEs and coronal holes. We use the "SafeSpace" database (https://synergasia.uoa.gr/modules/document/?course=PHYS120), which includes radial diffusion coefficients D LL and ULF wave power spectral density, created using magnetic and electric field measurements by the THEMIS satellites in the 2011–2019 time period. We study how the properties of these solar wind drivers influence the behavior of radial diffusion coefficients. The results indicate significant differences between drivers of different solar origin at the ratio of the electric over the magnetic D LL component ( D LL E over D LL B ), especially when the solar wind dynamic pressure is maximized due to shock existence. Furthermore, differences are observed between SIRs with shock and SIRs without shock. This feature introduces a significant energy dependence to the radial diffusion coefficients, which is further depending on the radial distance and the different first adiabatic invariant (μ) values. These results emphasize the importance of the energy dependence of the magnetic component of the D LL , especially during the occurrence of interplanetary shocks, which is neglected by most semi-empirical models used in radiation belt simulations. [ABSTRACT FROM AUTHOR]

Ray tracing is a commonly used method for modeling the propagation of electromagnetic waves in Earth's magnetosphere. To apply ray tracing results to global models of wave‐particle interaction such as energetic electron scattering, it is useful to map the discrete rays to a volume filling mesh. However, some methods have inherent losses of energy from the wave source, or do not account for the full range of wave properties within a sample volume. We have developed and tested a 3D magnetospheric ray tracing code "MESHRAY" which resolves these issues. MESHRAY uses the conservation of Poynting flux through ray triplets with finite volume to determine the local field amplitudes. Electromagnetic wave energy density from all ray data points is mapped to a mesh and verified against the wave source power for energy conservation varying time step length, number of rays, and total time steps. We find that the method is self‐consistent and numerically robust. We further investigate whether the neglect of phase information and superposition has a significant impact on the accuracy of mapping wave intensity to a mesh. We find excellent agreement between the analytic solution for waves emitted by a line source in a plane‐stratified medium and an equivalent ray tracing solution. When phase information is excluded, ray tracing reproduces an average amplitude spread over regions of coherent constructive and destructive interference. This may be an important consideration for interpolating ray tracing results of longer wavelength waves such as magnetosonic, electromagnetic ion cyclotron, or ULF waves. Key Points: Ray tracing amplitude calculations using finite‐volume ray triplets and methods using discrete, constant‐power rays are self‐consistentIntegrating electric and magnetic field wave energy density onto a space‐filling mesh is energy conserving for sufficiently small time stepsSpatially averaged amplitudes are consistent with superposed waves for regions larger than the scale of interference pattern structure [ABSTRACT FROM AUTHOR]

Ring current electrons (1-100 keV) have received significant attention in recent decades, but many questions regarding their major transport and loss mechanisms remain open. In this study, we use the four-dimensional Versatile Electron Radiation Belt code to model the enhancement of phase space density that occurred during the 17 March 2013 storm. Our model includes global convection, radial diffusion, and scattering into the Earth's atmosphere driven by whistler-mode hiss and chorus waves. We study the sensitivity of the model to the boundary conditions, global electric field, the electric field associated with subauroral polarization streams, electron loss rates, and radial diffusion coefficients. The results of the code are almost insensitive to the model parameters above 4.5 R E R E, which indicates that the general dynamics of the electrons between 4.5 R E and the geostationary orbit can be explained by global convection. We found that the major discrepancies between the model and data can stem from the inaccurate electric field model and uncertainties in lifetimes. We show that additional mechanisms that are responsible for radial transport are required to explain the dynamics of ≥40-keV electrons, and the inclusion of the radial diffusion rates that are typically assumed in radiation belt studies leads to a better agreement with the data. The overall effect of subauroral polarization streams on the electron phase space density profiles seems to be smaller than the uncertainties in other input parameters. This study is an initial step toward understanding the dynamics of these particles inside the geostationary orbit.

Finite difference time domain (FDTD) simulations are applied to study the amplification and decay of nonlinear whistler waves in pulsar wind nebulae. The considered plasma system comprises of streaming, hot positrons and electrons. The main emphasis is on the feedback process between particle beams and excited nonlinear waves. It is found that accelerated and parallel streaming electrons and positrons led to whistler wave amplification. Contrarily, the counter streaming electrons and positrons resulted in diverse and complex phenomena. Whistler waves at smaller propagation angles led to pitch angle decay for positrons and vice versa. It is noticed that pitch angles increased with increase of both plasma concentration and ambient magnetic field strength. Our results may be important for comprehensive understanding of nonlinear turbulence in pulsar wind nebulae. [ABSTRACT FROM AUTHOR]

By constructing an empirical model of the spectral and latitudinal distribution of ion cyclotron waves on the basis of Cassini datasets, we investigate the resonant interactions between ion cyclotron waves and radiation belt electrons at Saturn. Calculations based on quasi‐linear bounce‐averaged diffusion coefficients show that at Saturn ion cyclotron waves can efficiently pitch angle scatter >∼1 MeV to tens of MeV electrons into the loss cone thereby inducing precipitation loss, while the mixed and momentum scattering effects are typically negligible. The resultant electron loss timescales range from a few to tens of minutes, which in fact decrease significantly with increasing L‐shell at L = 4–6. We also find that the kinetic effects introduced by pick‐up ring particles cause distinct changes in pitch angle scattering efficiency for lower energy electrons (<3 MeV at L = 5). Our results demonstrate that ion cyclotron waves play a significant role in the dynamics of Saturn's radiation belt electrons. Plain Language Summary: Ion cyclotron waves are a common electromagnetic wave mode in the planetary magnetospheres. At Saturn, ion cyclotron waves are usually observed with wave frequencies near the gyro‐frequency of water‐group ions (e.g., O+, OH+, and H2O+). They are known to be excited by a ring distribution of the pick‐up water‐group ions which are extracted from the extended neutral clouds. In this paper, we investigate the resonant interactions between ion cyclotron waves and radiation belt electrons at Saturn. By constructing an empirical model of the spectral and latitudinal distribution of ion cyclotron waves based on Cassini observations, we calculate the bounce‐averaged electron diffusion coefficients and resultant electron loss timescales. Our results suggest that Saturn's ion cyclotron waves can cause efficient precipitation loss of radiation belt electrons by scattering them into the loss cone. The corresponding loss timescales range from a few to tens of minutes, decreasing with increasing radial distance from Saturn. Our results confirm the important role of ion cyclotron waves in the dynamics of Saturnian radiation belt electrons. Key Points: The resonant interactions between ion cyclotron waves and radiation belt electrons at Saturn are investigatedIon cyclotron waves can efficiently pitch angle scatter >∼1 MeV to tens of MeV electrons into the loss cone for precipitation lossThe resultant electron loss timescales range from a few to tens of minutes, which decrease significantly with increasing L‐shell over L = 4–6 [ABSTRACT FROM AUTHOR]

Transport consequences of the wave–particle interactions in the quasilinear plateau (QP) regime are presented. Eulerian approach is adopted to solve the drift kinetic equation that includes the physics of the nonlinear trapping (NT) and QP regimes. The localization of the perturbed distribution simplifies the test particle collision operator. It is shown that a mirror force like term responsible for the flattening of the distribution in the NT regime is subdominant in the QP regime, and controls the transition between these two regimes. Transport fluxes, flux-power relation, and nonlinear damping or growth rate are all calculated. There is no explicit collision frequency dependence in these quantities; however, the width of the resonance does. Formulas that join the asymptotic results of these two regimes to facilitate thermal and energetic particle transport, and nonlinear wave evolution of a single mode are presented.

Abstract By constructing an empirical model of the spectral and latitudinal distribution of ion cyclotron waves on the basis of Cassini datasets, we investigate the resonant interactions between ion cyclotron waves and radiation belt electrons at Saturn. Calculations based on quasi‐linear bounce‐averaged diffusion coefficients show that at Saturn ion cyclotron waves can efficiently pitch angle scatter >∼1 MeV to tens of MeV electrons into the loss cone thereby inducing precipitation loss, while the mixed and momentum scattering effects are typically negligible. The resultant electron loss timescales range from a few to tens of minutes, which in fact decrease significantly with increasing L‐shell at L = 4–6. We also find that the kinetic effects introduced by pick‐up ring particles cause distinct changes in pitch angle scattering efficiency for lower energy electrons (

Interactions between the incident solar wind plasma and lunar crustal magnetic fields can lead to modifications in electron and ion dynamics that can result in the generation of electrostatic and electromagnetic waves. The resulting waves can then interact with the ambient electrons, leading to perpendicular and/or parallel electron heating. We analyze 10 years of data from the Acceleration, Reconnection, Turbulence, and Electrodynamics of Moon's Interaction with the Sun mission, when the spacecraft was within 200 km of the dayside lunar surface and within the solar wind, in order to characterize the near‐Moon plasma environment. We find that as the reflected ion density increases, electrostatic waves associated with plasma conditions favorable for the electron cyclotron drift instability play an increasingly important role in perpendicular electron heating, while electromagnetic interactions display the opposite trend. Additionally, we find that electrostatic waves associated with parallel heating exhibit plasma characteristics that are consistent with both the electron two‐stream instability and the modified two‐stream instability. Key Points: Electron heating near the lunar surface is observed in association with electrostatic and electromagnetic wavesPerpendicular electron heating is associated with electron cyclotron drift instability and correlated with the reflected ion density ratioParallel electron heating is associated with electron two‐stream instabilities and suggestive of modified two‐stream instabilities [ABSTRACT FROM AUTHOR]

Man‐made very low frequency (VLF) transmitter waves play a critical role in energetic electron scattering and precipitation from the inner radiation belt, a type of which is called wisp precipitation. Wisps exhibit dispersive energy‐versus‐L spectra due to the evolution of electron cyclotron resonance conditions with near‐monochromatic VLF transmitter waves. Here, we report on such observations of inner belt wisp precipitation events with full pitch angle resolution in the energy range of 50 to ∼500 keV as measured by Electron Loss and Fields Investigation (ELFIN) at L < ∼2 between March 2021 and April 2022. Statistical observations (82 events) reveal occasional (18 events) wisp precipitation events with local bounce‐loss‐cone electron flux enhancements, which provide new information compared with flux enhancements measured in previous studies only in the drift loss cone. Based on magnetic field and plasmaspheric density models, quasilinear theory, and detailed pitch angle distributions of wisps from ELFIN, we have estimated the wisp electron bounce‐averaged pitch angle diffusion coefficients to be of the order of 10−4 to 10−2 s−1. These are several orders of magnitude larger than the diffusion rates calculated from models using global statistical averages of VLF transmitter wave power. When using our estimated diffusion coefficients to deduce the associated local transmitter wave amplitudes near the equator, based on quasilinear calculations from a transmitter‐induced electron diffusion model, we find these wave amplitudes to be >1 mV/m. Although probable overestimates, such inferred wave amplitudes exceed the theoretical threshold amplitude for nonlinear interactions, strongly suggesting that it is necessary to include nonlinear effects for an accurate evaluation of energetic electron scattering by transmitter waves. Plain Language Summary: Man‐made ground‐based very low frequency (VLF) transmitter waves can scatter and precipitate energetic radiation belt electrons, which pose a threat to telecommunication and human assets in space. Therefore, understanding the controlling parameters and the efficiency of energetic electron scattering by VLF transmitter waves are of both theoretical and practical importance. Our paper reports statistical analyses of inner belt wisp precipitation events due to scattering by VLF transmitter waves as observed by the Electron Loss and Fields Investigation CubeSats. Occasional strong local wisp precipitation events have been found to occur at preferential longitudes east of the South Atlantic Anomaly in the Northern Hemisphere and were primarily observed in the morning magnetic local time. These local wisp precipitation events have been used to infer energetic electron diffusion rates and VLF transmitter wave amplitudes near the equator based on quasilinear diffusion theory. Such inferred wave amplitudes exceed the theoretical threshold amplitude for nonlinear interactions, strongly suggesting that it is necessary to include nonlinear effects for an accurate evaluation of energetic electron scattering by transmitter waves. Key Points: We report statistical observations of inner belt wisps with full pitch angle distributions measured by Electron Loss and Fields InvestigationLocal bounce‐loss‐cone wisp precipitation events allow inference of quasilinear diffusion rates and transmitter wave amplitudesInferred transmitter wave amplitudes exceed nonlinear interaction threshold amplitudes near the equator [ABSTRACT FROM AUTHOR]

Microbursts are impulsive (

The present study addresses two basic questions related to banded chorus waves in the Earth's magnetosphere: 1) are chorus spectral gaps formed near the equatorial source region or during propagation away from the equator? and 2) why are chorus spectral gaps usually located below 0.5 fce (fce: electron gyro‐frequency)? By analyzing Van Allen Probes data, we demonstrate that chorus spectral gaps are observed in the source region where chorus waves propagate both in the parallel and anti‐parallel directions to the magnetic field. Chorus spectral gaps below 0.5 fce are associated with electron parallel acceleration at energies above the equatorial Landau resonant energies. We explain that initially generated chorus waves quickly isotropize the electron distribution through Landau resonant acceleration, and the isotropization occurs for higher energies at higher latitudes. The isotropized population, after returning to the magnetic equator, leads to a chorus gap typically below 0.5 fce by suppressing wave excitation. Plain Language Summary: Chorus waves are naturally occurring electromagnetic waves in the Earth's magnetized space known as the magnetosphere, and they typically have two frequency bands. A previous study proposed that the banded characteristics is produced by two anisotropic electron populations. This study aims to address two basic questions about banded chorus waves: 1) are chorus frequency gaps formed near the equatorial source region or during propagation away from equator? and 2) why are chorus frequency gaps usually located below 0.5 fce (fce: electron gyro‐frequency)? Van Allen Probe spacecraft data reveals that chorus frequency gaps are formed in the equatorial source region where the waves propagate both in the parallel and anti‐parallel directions to the magnetic field. By showing the electron distribution in association with banded chorus waves, we explain that initially generated chorus waves quickly accelerate electrons as they propagate away from equator, and the electrons being accelerated at high latitudes lead to a chorus gap below 0.5 fce when they bounce back to the equatorial source region. Key Points: Chorus spectral gaps are formed near the equatorial source region where parallel and anti‐parallel emissions are interleavedLandau resonance causes electron parallel acceleration and phase space density isotropization around half electron Alfven velocity, which increases with latitudesChorus spectral gaps are usually found below 0.5 fce due to electron anisotropy reduction caused by Landau resonance at high latitudes [ABSTRACT FROM AUTHOR]

Relativistic electron losses in Earth's radiation belts are usually attributed to electron resonant scattering by electromagnetic waves. One of the most important wave modes for such scattering is the electromagnetic ion cyclotron (EMIC) mode. Within the quasi‐linear diffusion framework, the cyclotron resonance of relativistic electrons with EMIC waves results in very fast electron precipitation to the atmosphere. However, wave intensities often exceed the threshold for nonlinear resonant interaction, and such intense EMIC waves have been shown to transport electrons away from the loss cone due to the force bunching effect. In this study we investigate if this transport can block electron precipitation. We combine test particle simulations, low‐altitude observations of EMIC‐driven electron precipitation by the Electron Losses and Fields Investigations mission, and ground‐based EMIC observations. Comparing simulations and observations, we show that, despite the low pitch‐angle electrons being transported away from the loss cone, the scattering at higher pitch angles results in the loss cone filling and electron precipitation. Plain Language Summary: Precipitation of relativistic electrons from the Earth's radiation belts to the atmosphere has long been attributed to electron resonant scattering by electromagnetic ion cyclotron (EMIC) waves. These relativistic electron losses significantly contribute to the radiation belt dynamics, whereas precipitating electron fluxes may alter the atmosphere chemical properties. Thus, electron resonant scattering by EMIC waves has been intensively studied, in both theory and spacecraft observations. Models of two main regimes of wave‐particle interactions, diffusive scattering and nonlinear resonant transport, however, predict contradicting results for electron precipitation: diffusive scattering will lead to electron losses, whereas nonlinear resonant transport may block such losses. This study combines spacecraft observations and numerical simulations to demonstrate that in reality, these two regimes work together to cause strong electron precipitation that mainly come from higher pitch angles. Key Points: The Electron Losses and Fields Investigations observations of electromagnetic ion cyclotron‐driven precipitation of relativistic electronsTest‐particle model reproduce precipitating electron energy rangeElectron precipitation is caused by interplay of nonlinear resonant effects and the diffusive scattering [ABSTRACT FROM AUTHOR]