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Azimuthal and radial propagation characteristics of perpendicularly propagating fast magnetosonic waves in an axis‐symmetrical medium with the presence of plasmapause is investigated analytically based on Snell's law. We find thatQ = nr sin ψ is conserved during the propagation, where n is wave refractive index, ris geo‐centered distance, andψ is wave azimuthal angle with zero pointing radially outward. The radial range of wave propagation can be determined by comparing Q and the radial profile of nr.Trapped waves, which are bounded in a narrow radial range but migrate azimuthally and even circularly, are identified inside the plasmapause over a broad range of wave azimuthal angles and over a broad range of wave frequencies from the proton gyrofrequency to the lower hybrid resonance frequency. In contrast untrapped waves launched inside and outside the plasmasphere can travel azimuthally 0–4 hrs and 0–7 hrs in local times respectively. The substantial radial and azimuthal propagation may account for the presence of magnetosonic waves away from the source region. Key Points MS waves can be trapped near the plasmapause and trapping condition is given The radial range of MS wave propagation is determined Those untrapped MS waves can propagate azimuthally up to ~ 7 hr local times

Chorus subpackets/subelements are the wave packets occurring at intervals of ∼10–100 msec and are suggested to play a crucial role in the formation of substructures within pulsating aurora. In this study, we investigate the evolution of subpackets from the upstream to downstream regions. Using Van Allen Probe A measurements, we have found that the frequency of the upstream subpackets increases smoothly, but that of the downstream subpackets remains almost unchanged. Through a simulation in the real‐size magnetosphere, we have reproduced the subpackets with characteristics similar to those in observations, and revealed that the frequency chirping is influenced by both resonant current of electrons and wave amplitude due to nonlinear physics. Although the resonant currents in the upstream and downstream regions are comparable, the wave amplitude increases significantly during evolution, resulting in lower sweep rate in the downstream region. Our findings provide a fresh insight into the evolution of chorus subpackets. Plain Language Summary Subpackets within chorus waves are suggested to play a significant role in producing the substructures within pulsating aurora. How does the frequency change inside subpackets is still an open question. In this study, the subpackets are found with Van Allen Probe A observation to be excited upstream of the magnetic equator, and propagate toward downstream. The frequency of subpackets increases with time in the upstream region, while it keeps almost unchanged in the downstream region. Meanwhile, a particle‐in‐cell simulation has been performed to study the characteristics of subpackets, and the simulation results agree well with those in observations. The frequency variation of subpackets is influenced by both resonant electrons and wave amplitude. Our study provides a clue for better understanding the nonlinear wave‐particle interactions in the evolution of chorus subpackets. Key Points The source region of chorus subpackets has been observed by Van Allen Probe A The chorus subpackets have been investigated via the general curvilinear particle‐in‐cell simulation in the real‐size magnetosphere Nonlinear physics is a dominant process in the evolution of chorus subpackets

Here we examine properties of MeV electron microbursts to better understand their generation mechanisms. Using 15 years of data from Solar, Anomalous, Magnetospheric Particles Explorer/Heavy Ion Large Telescope, >1 MeV microburst repetition periods (time spacing between bursts) are examined and clear dependencies on Auroral Electrojet (AE), L shell, and magnetic local time (MLT) are discovered. Microburst repetition periods are shortest around 0–6 hr MLT and 4–5 L shell, and grow longer toward the day and afternoon sectors and larger L shells. Shorter repetition periods (<1 s) are also found to be more common during higher AE, while longer periods (>10 s) more common during quiet times. The microburst repetition period distributions are compared directly to those of rising tone chorus wave elements and found to be similar in the night, dawn and day MLT sectors, suggesting chorus wave repetition periods are likely directly controlling those of microburst precipitation. However, dusk‐side distributions differ, indicating that the dusk‐side microbursts properties may be controlled by other processes. Plain Language Summary Looking at energetic electrons in Earth's magnetosphere from the Heavy Ion Large Telescope instrument on board the Solar, Anomalous, Magnetospheric Particles Explorer satellite helps us better understand the feature called microbursts. Microbursts are very rapid bursts of enhanced high‐energy electrons entering our atmosphere. In this study, we characterize the properties of the microbursts to understand when, and where they happen, what causes them, and what impact they might have. We do so by looking at factors such as their magnetic local time as well as their time separation. This study also compares these microbursts' results to previous chorus wave studies. Chorus waves have been thought to be related to microbursts and could be a cause for some of their properties. We discuss more about this correlation in the result section of this study. Key Points The repetition period of MeV electron microbursts is studied for the first time using 15 years of Solar, Anomalous, Magnetospheric Particles Explorer/Heavy Ion Large Telescope data Microburst repetition periods are most often <1 s, and drop off as a power law moving to longer periods Repetition periods show strong agreement with chorus wave element periodicities in all magnetic local time sectors except for the dusk sector

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

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

Chorus subpackets are the wave packets with modulated amplitudes in chorus waves, commonly observed in the magnetospheres of Earth and other planets. Nonlinear wave‐particle interactions have been suggested to play an important role in subpacket formation, yet the corresponding electron dynamics remain not fully understood. In this study, we have investigated the electron trapping through cyclotron resonance with subpackets, using a self‐consistent general curvilinear plasma simulation code simulation model in dipole fields. The electron trapping period has been quantified separately through electron dynamic analysis and theoretical derivation. Both methods indicate that the electron trapping period is shorter than the subpacket period/duration. We have further established the relation between electron trapping period and subpacket period through statistical analysis using simulation and observational data. Our study demonstrates that the nonlinear electron trapping through cyclotron resonance is the dominant mechanism responsible for subpacket formation. Plain Language Summary The spectrum of chorus waves comprises a series of subpackets, characterized by modulated amplitudes within a timescale of ∼10–100 milliseconds. In this study, we have investigated the self‐consistent wave‐particle interactions with subpackets, using two‐dimensional particle‐in‐cell simulations in dipole fields. Cyclotron resonant electrons are trapped in wave phases, and we have measured their trapping period. Since these electrons move in the opposite direction of subpacket propagation, the corresponding trapping period is smaller than the period of subpackets. We have further established the relation between the two periods and validated it through both simulation and observational data. This relation facilitates evaluating electron trapping period from direct measurement of subpackets in observations. Our study sheds important lights on the key role of nonlinear electron trapping through cyclotron resonance in the formation of subpackets. Key Points Electron trapping dynamics in the formation of quasi‐parallel chorus subpackets have been investigated The linkage between electron trapping period and subpacket period is quantified via a geometric relation, where the trapping period is shorter The proposed relation between electron trapping period and subpacket period is an extension of the classical results of O’Neil (1965)

The dispersion relation of parallel propagating EMIC waves is investigated in a magnetized homogeneous plasma consisting of hot H+ and He+ ions. We demonstrate that the hot plasma effects associated with He+ and H+ significantly modify the cold plasma dispersion relation, especially near ΩHe+. For plasmas with a sufficiently small fraction of warm He+ and a sufficiently dense, hot and anisotropic H+ population, the cold plasma stop band above ΩHe+ may vanish, and waves near ΩHe+ may be unstable. The maximum wavenumber for unstable L‐mode waves due to the hot plasma modification is used to identify the plasma conditions required for EMIC wave scattering of MeV electrons. We conclude that relatively extreme conditions (ωpe/|Ωe| > ∼25, and H+ anisotropy >1) are required for resonance with electrons near 1 MeV, which limits such scattering only to the region just inside the plasmasphere or storm time plumes. Key Points Hot plasma introduces new features on dispersion relation near He+ gyrofrequency Plasma condition for EMIC instability at He+ gyrofrequency is identified Hot plasma condition for producing MeV electron scattering is identified

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

Coupling between the Rice Convection Model and Ring Current–Atmospheric Interactions Model codes is used to simulate the dynamical evolution of ring current ion phase space density and the thermal electron density distribution for the 22 April 2001 storm. The simulation demonstrates that proton ring distributions (df⊥/dv⊥ > 0) develop over a broad spatial region during the storm main phase, leading to the instability of equatorial magnetosonic waves. Calculations of the convective growth rate of magnetosonic waves for multiples of the proton gyrofrequency from 2 to 42 are performed globally. We find that the ratio between the perpendicular ring velocity and the equatorial Alfven speed determines the frequency range of unstable magnetosonic waves. Low harmonic waves (ω < 10 tend to be excited in the high‐density nightside plasmasphere and within the duskside plume, whereas higher‐frequency waves (ω > 20 are excited over a broad spatial region of low density outside the morningside plasmasphere.

We present magnetic local time (MLT)‐dependent simulations of pitch angle scattering of relativistic (approximately MeV) electrons by chorus and electromagnetic ion cyclotron (EMIC) waves. Numerical simulations indicate that in the case of scattering by chorus waves, the pitch angle distribution is relatively independent of MLT. In the case of scattering by EMIC and chorus waves, the modeled pitch angle distribution shows significant variations with MLT. MLT‐averaged simulations tend to overestimate net loss during a storm but can accurately predict equilibrium loss rates and the overall shape of the pitch angle distribution. Numerical simulations show that EMIC waves not only scatter electrons into the loss cone but also create gradients in the pitch angle distribution, assisting chorus waves in scattering relativistic electrons into the loss cone. We also show that changes in the spectral properties of waves can significantly change loss rates. Loss rates reach a maximum level for EMIC waves with amplitudes above approximately 1 nT, present over a few percent of the drift orbit, and then become relatively independent of the amplitudes of EMIC waves.