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Chorus waves are intense electromagnetic emissions critical in modulating electron dynamics. In this study, we perform two‐dimensional particle‐in‐cell simulations to investigate self‐consistent wave‐particle interactions with oblique chorus waves. We first analyze the electron dynamics sampled from cyclotron and Landau resonances with waves, and then quantify the advection and diffusion coefficients through statistical studies. It is found that phase‐trapped cyclotron resonant electrons satisfy the second‐order resonance condition and gain energy from waves. While phase‐bunched cyclotron resonant electrons cannot remain in resonance for long periods. They transfer energy to waves and are scattered to smaller pitch angles. Landau resonant electrons are primarily energized by waves. For both types of resonances, advection coefficients are greater than diffusion coefficients when the wave amplitude is large. Our study highlights the important role of advection in electron dynamics modulation resulting from nonlinear wave‐particle interactions. Plain Language Summary Wave‐particle interactions can modulate electron distributions through advection and diffusion. Previous studies focusing on advection and diffusion primarily relied on test particle simulations, which uses a simplified model of wave evolution. In this study, we perform self‐consistent simulations to investigate the wave‐particle interactions with chorus waves and quantify the advection and diffusion coefficients of resonant electrons. It is found that advection coefficients are greater than diffusion coefficients in both cyclotron and Landau resonances, indicating the significant role of nonlinear wave‐particle interactions. The quantification of advection and diffusion coefficients in a self‐consistent system is important for understanding and predicting the loss and energization processes in radiation belt electrons. This study complements previous diffusion models that regarded the evolution of electron dynamics in wave‐particle interactions as a slow diffusive process. Key Points Electron advection and diffusion in wave‐particle interactions with chorus waves are investigated through self‐consistent simulations The second‐order time derivative of gyrophase angle is nearly zero for phase‐trapped electrons but is negative for phase‐bunched electrons The advection and diffusion coefficients for cyclotron and Landau resonant electrons interacting with chorus waves are quantified

The global distribution of chorus wave amplitudes and their wave normal angles is investigated using high‐resolution wave spectra and waveform data from THEMIS for lower‐band and upper‐band chorus separately. Statistical results show that large amplitude chorus (>300 pT) occurs predominantly from premidnight to postdawn and is preferentially observed at lower L shells (<8) near the magnetic equator. However, strong or moderate chorus extends further into the afternoon sector and to higher L shells. For lower‐band chorus, strong waves (>50 pT) tend to have wave normal angles of <20° and their wave normal angles become even smaller with increasing wave amplitudes. For modest waves, the wave normal angles are distributed over a broad range with a major peak at <20° and a secondary peak at 60°–80°. Wave normal angles of lower‐band chorus are generally smaller on the dayside than on the nightside possibly due to the more uniform and more compressed magnetic field configuration on the dayside. Lower‐band chorus becomes more oblique with increasing latitude on the dayside, whereas on the nightside the probability of observing oblique chorus decreases at higher latitudes. Compared to lower‐band chorus, the properties of upper‐band chorus are somewhat different. Upper‐band chorus is considerably weaker in magnetic wave amplitudes, shows tighter confinement to the magnetic equator (<10°), and occurs at smaller L shells (<8). Furthermore, wave normal angles of upper‐band chorus are generally larger than those of lower‐band chorus, but the occurrence rate still peaks at wave normal angles of <20°, particularly for strong upper‐band chorus. Key Points Large amplitude chorus occurs from premidnight to dawn near the equator Strong lower‐band chorus typically has small wave normal angles (less than 20 deg) Upper‐band chorus is more oblique and much weaker than lower‐band chorus

A 2‐D GCPIC simulation in a dipole field system has been conducted to explore the excitation of oblique whistler mode chorus waves driven by energetic electrons with temperature anisotropy. The rising tone chorus waves are initially generated near the magnetic equator, consisting of a series of subpackets, and become oblique during their propagation. It is found that electron holes in the wave phase space, which are formed due to the nonlinear cyclotron resonance, oscillate in size with time during subpacket formation. The associated inhomogeneity factor varies accordingly, giving rise to various frequency chirping in different phases of subpackets. Distinct nongyrotropic electron distributions are detected in both wave gyrophase and stationary gyrophase. Landau resonance is found to coexist with cyclotron resonance. This study provides multidimensional electron distributions involved in subpacket formation, enabling us to comprehensively understand the nonlinear physics in chorus wave evolution. Plain Language Summary Subpackets are a series of wave packets within chorus waves, characterized by wave amplitude modulation. In this study, we investigate the electron distributions in various phase spaces associated with subpacket formation, by performing a two‐dimensional simulation in a dipole field. It is found that the electrons can be trapped in the wave phase space through both cyclotron and Landau resonances. These two resonance interactions can also produce the “bump” and “plateau” shapes in momentum space, as well as the fine density structures in spatial space. Therefore, both cyclotron and Landau resonances play an important role in subpacket formation. Our study provides new inspiration for the nonlinear theory of chorus subpackets. Key Points Oblique chorus subpackets are generated in the 2‐D GCPIC simulation model Electron hole associated with the inhomogeneity factor oscillates with time during subpacket formation Cyclotron and Landau resonances coexist during subpacket formation

The precipitation of tens to hundreds of keV electrons from Earth's magnetosphere plays a crucial role in magnetosphere‐ionosphere coupling, primarily driven by chorus wave scattering. Most existing simulations of electron precipitation rely on test particle models that neglect particle feedback on waves. However, both theoretical and observational studies indicate that the feedback from energetic electrons significantly influences chorus wave excitation and evolution. In this study, we quantify electron precipitation driven by chorus waves using self‐consistent simulations at L = 6 with typical magnetospheric plasma parameters. Electrons in the ∼10–200 keV range are precipitated, exhibiting energy‐dispersive characteristics. The precipitation intensity reaches ∼108–109 ${10}^{8}\\!\\mathit{\\mbox{--}}\\!{10}^{9}$ keV/s/sr/cm2/MeV $\\mathrm{k}\\mathrm{e}\\mathrm{V}/\\mathrm{s}/\\mathrm{s}\\mathrm{r}/{\\mathrm{c}\\mathrm{m}}^{2}/\\mathrm{M}\\mathrm{e}\\mathrm{V}$, consistent with the typical values in observations. As a comparison, test particle simulations underestimate the precipitation intensity by nearly an order of magnitude. These results highlight the importance of self‐consistent simulations in quantifying electron precipitation and investigating wave‐particle interactions that modulate magnetospheric dynamics.

Whistler‐mode chorus waves play a critical role in the dynamics of energetic electrons in the inner magnetosphere. Extensive theoretical research has been conducted to explain the frequency chirping of chorus waves, with two primary theoretical chirping rates proposed: one associated with magnetic field inhomogeneity and the other linked to wave amplitude. The validity of these chirping rates has been a subject of debate. In this study, we compare these two theoretical chirping rates using a data set of 3,166 lower‐band rising‐tone chorus wave elements from Van Allen Probes observations, evaluating their statistical performance. Our analysis shows that the chirping rate associated with magnetic field inhomogeneity exhibits better agreement with observations, demonstrating higher correlation and smaller standard deviation compared to the nonlinear chirping rate. These findings suggest that both chirping rates should be considered valid expressions for chorus waves, supporting a key prediction of a recently proposed theoretical model of chorus.

The frequency chirping of chorus waves is commonly observed in the Earth’s inner magnetosphere, but its generation remains an open question. Recently, Liu et al. (2021), https://doi.org/10.1029/2021JA029258 reported two unusual rising‐tone (upward chirping) chorus elements. Although the central frequency of constituent subpackets rises, the frequency of a single subpacket is surprisingly downward chirping. With a gcPIC‐δf$\\delta f$simulation in the dipole field, we successfully reproduce this kind of substructure, which contains alternating signs of chirping. Interestingly, both hole and hill structures are formed around the theoretical resonant velocities in the electron phase space, no matter whether the chirping is upward or downward. However, during each chirping interval, only one structure (either a hole or a hill) is associated with wave excitation: the upward chirping is related to the hole, while the hill contributes to the downward chirping. Our study provides a fresh perspective on the theory of frequency chirping in chorus waves. Plain Language Summary The frequency chirping is a typical feature of chorus waves in the Earth’s inner magnetosphere, which generally contain either rising‐tone (upward chirping) elements or falling‐tone (downward chirping) elements. Previous theory has suggested that the chirping is due to the nonlinear wave‐particle interaction, where the hole or hill structure is formed in the electron phase space. Recently, Liu et al. (2021), https://doi.org/10.1029/2021JA029258 have observed the upward chirping elements with their subpackets of downward chirping. What electron structure is associated with these elements becomes a puzzle. With a one‐dimensional (1D) general curvilinear particle‐in‐cell (gcPIC) δf simulation in the dipole magnetic field, we successfully reproduce this kind of chorus element, whose frequency contains alternating upward and downward chirping. Interestingly, both the hole and hill structures are formed during a chirping interval, but only one of the two structures is responsible for wave excitation and frequency chirping. The structure of hole‐hill combination provides an important clue into the theory of the frequency chirping in chorus waves. Key Points With a gcPIC‐δf$\\delta f$simulation in the dipole field, we reproduce the upward chirping chorus element, whose subpackets are downward chirping Both hole and hill structures can be formed in the ζ−v‖$\\zeta -{v}_{\\Vert }$phase space, no matter whether the frequency is upward or downward chirping The time evolution of the hole and hill structures in the phase space leads to the alternating frequency chirping

The power gap of chorus waves at ∼0.5fce has been discovered for decades, but its generation mechanism is still under debate. Previous studies have revealed that electron plateau distributions are vitally important for the gap formation. By analyzing over one‐year Van Allen Probes data, we have studied chorus waves with (banded events) and without a power gap (no‐gap events), and their correlations with the electron plateau distribution. Although there is no significant difference in the morphology of velocity distributions in banded and no‐gap events, banded chorus events are typically accompanied by a plateau component with about one order higher number density than no‐gap events. The plateau components can cause severe damping at ∼0.5fce through cyclotron resonance rather than Landau resonance, and the gap frequency is roughly determined by the bulk velocity of plateau components. Our study provides new observational constraints on the generation mechanisms of power gap. Plain Language Summary The generation mechanism of power gap at ∼0.5fce of chorus waves has been a long‐standing problem for decades. Although its generation mechanism is still under debate, there is a consensus that the electron plateau in the parallel velocity distribution is a key factor to solve this problem. Here, we try to find out what role the electron plateau plays in the gap formation based on a statistical analysis of Van Allen Probes data. First of all, we find banded chorus events indeed have a more pronounced plateau shape (about one order higher number density) than no‐gap events, confirming the importance of electron plateau. We further find that the electron plateau can cause the severe wave damping at ∼0.5fce via cyclotron resonance rather than Landau resonance, and the gap frequency is roughly determined by the bulk velocity of electron plateau based on the cyclotron resonance condition. We also compare the morphology of electron velocity distributions in banded and no‐gap events, but do not find an obvious difference between them. Our study provides new observational constraints on the generation mechanisms of the power gap, which may help scientists finally solve this problem. Key Points Banded chorus events typically have a more pronounced plateau shape than no‐gap events in the parallel electron distribution The electron plateau can cause severe damping at ∼0.5fce via cyclotron resonance, and roughly determine the gap frequency There is no significant difference between the normalized electron velocity distributions in banded and no‐gap events

Wave‐particle interactions are essential for energy transport in the magnetosphere. In this study, we investigated an event during which electrons interact simultaneously with waves in different scales, using data from the Magnetospheric Multiscale mission. At the macroscale (∼105 ${\\sim} 1{0}^{5}$ km), drift resonance between ultra‐low frequency (ULF) waves and 70–300 keV electrons is observed. At the microscale (∼100−101 ${\\sim} 1{0}^{0}-1{0}^{1}$ km), lower‐band chorus waves and electron cyclotron harmonic (ECH) waves are alternately generated, showing signatures of modulation by ULF waves. We found that compressional ULF waves affect the temperature anisotropy of 1–10 keV electrons, thereby periodically exciting chorus waves. Through linear instability analysis, we propose that ULF waves modulate ECH wave emissions by regulating the gradient of electron phase space density at the edge of the loss cone. Our results enhance the understanding of cross‐scale wave‐particle interactions, highlighting their importance in magnetospheric dynamics.

We present statistical distributions of whistler‐mode chorus and hiss waves at frequencies ranging from the local proton gyrofrequency to the equatorial electron gyrofrequency (fce,eq) in Jupiter's magnetosphere based on Juno measurements. The chorus wave power spectral densities usually follow the fce,eq variation with major wave power concentrated in the 0.05fce,eq–fce,eq frequency range. The hiss wave frequencies are less dependent on fce,eq variation than chorus with major power concentrated below 0.05fce,eq, showing a separation from chorus at M < 10. Our survey indicates that chorus waves are mainly observed at 5.5 < M < 13 from the magnetic equator to 20° latitude, consistent with local wave generation near the equator and damping effects. The hiss wave powers extend to 50° latitude, suggesting longer wave propagation paths without attenuation. Our survey also includes the whistler‐mode waves at high latitudes which may originate from the Io footprint, auroral hiss, or propagating hiss waves reflected to high M shells. Plain Language Summary Whistler‐mode chorus and hiss waves in Jupiter's magnetosphere are major plasma wave modes, characterized by perturbations in electric and magnetic fields at frequencies from the proton gyrofrequency to the electron gyrofrequency. Chorus waves are typically observed at 0.05fce,eq–fce,eq frequencies (fce,eq is the electron gyrofrequency at the equator) with coherent wave structures. Chorus waves, generated by hot electrons, could cause electron precipitation into the atmosphere and acceleration in the radiation belt. In contrast, hiss waves are usually incoherent with wave frequencies less dependent on fce,eq than chorus. Hiss waves have mixed sources and mainly drive energetic electron loss. Using Juno satellite measurements, we analyze the statistical distribution of chorus and hiss waves in Jupiter's magnetosphere. Our survey reveals different latitudinal coverages and statistical properties of chorus and hiss waves, suggesting their different sources and damping effects. Additionally, our survey includes whistler‐mode waves at high latitudes, potentially originating from various sources such as the Io footprint at the ionosphere, auroral hiss, or reflection of hiss waves at high M shells. The whistler‐mode wave distributions from our study provide valuable insights for future modeling of whistler‐mode wave sources and energetic electron dynamics in Jupiter's magnetosphere. Key Points Intense chorus waves at 0.05–1 equatorial electron gyrofrequencies (fce,eq) are observed at 5.5 < M < 13 within 20° magnetic latitudes Hiss waves from 50 Hz to 0.05 fce,eq have extended latitudinal coverage up to 50° and exhibit propagation effects High latitude (>50°) whistler‐mode waves at 0.05–1 fce,eq are observed in two groups due to different sources

Simultaneous observations of whistler‐mode chorus and magnetosonic (MS) waves are reported within a magnetic peak in the inner magnetosphere for the first time. During the magnetic peak, Van Allen Probe A observes flux enhancements of both ring current electrons and relativistic electrons, while medium‐energy proton fluxes are reduced but high‐energy proton fluxes are raised. Those flux variations of ring current particles are almost concentrated in the perpendicular direction of the background magnetic field, leading to enhancements of the electron temperature anisotropy and a positive gradient of proton velocity distributions. The calculated linear growth rates show that unstable electrons with temperature anisotropic instabilities and unstable protons with ring distribution during the magnetic peak structure can provide free energy for the excitation of whistler‐mode chorus and MS waves, respectively. Our findings suggest that injected particles encountering the magnetic peak structure may form more complex unstable electron and ion distributions driving multiple instabilities simultaneously. Plain Language Summary Recently, dipolarizing flux bundles have also been observed in the inner magnetosphere. These magnetic field structures are usually accompanied by dispersion of particle energies and pitch angles, resulting in complex and unstable particle distributions during magnetic structures, which may provide free energy for wave excitation. Previous observed waves during magnetic structures belong to single instability (electron type or proton type), rarely taking into account waves driven by both proton and electron instabilities. In this letter, simultaneous observations of chorus and magnetosonic (MS) waves are reported during a magnetic peak in the inner magnetosphere for the first time. Our results show that the complex distribution in the velocity phase space of ring current electrons and protons during the magnetic peak in the inner magnetosphere has the potential to simultaneously trigger chorus and MS waves. Key Points Whistler‐mode chorus and fast magnetosonic (MS) waves are simultaneously observed during the magnetic peak in the inner magnetosphere Enhancements of ring current particle instabilities during the magnetic peak cause the excitation of whistler‐mode chorus and MS waves Our results contribute to understanding the evolution of injected electrons and protons encountering the magnetic peak