Chorus Generation Research Articles

Quantifying the role of electron plateau distribution on the chorus gap formation using one-dimension PIC simulations

Although ubiquitous in the Earth’s inner magnetosphere, how chorus waves with a gap in intensity near half the electron cyclotron frequency, 0.5fce, is formed remains to be understood. One hypothesis invokes the often-observed feature in electron phase space density where two anisotropic populations of warm and hot temperatures, respectively, are separated by a relatively isotropic beam-like component, called the parallel plateau distribution. According to linear theory, its mean velocity is such that the plateau population can lead to a sufficient cyclotron damping in a narrow frequency range near 0.5fce. To test this hypothesis more quantitatively, we carry out a series of one-dimensional particle-in-cell simulations in a parabolic magnetic field with observationally constrained plateau density and mean velocity. We find that even though the chorus generation involves nonlinear physics, the gap formation is largely determined by the linear properties of plateau electrons. In addition, given a sufficiently large plateau density with a right combination of warm and/or hot source populations, our simulations were able to generate lower-band-only chorus, upper-band-only chorus, banded chorus with partial damping at the gap, and banded chorus with a strong power gap. When it comes to comparing with observations, however, we find that (1) the minimum plateau density required to generate banded chorus is somewhat larger than that observed; (2) even with the largest plateau density used, the gap formation in the simulations is not consistent; and (3) most importantly, the dependence of the gap frequency on the plateau velocity in our parametric analysis differs quite substantially from that of the recent statistical results. Provided that the simplifying assumptions in our simulations remain valid, these discrepancies would indicate that the electron plateau distribution is not the major contributor to the chorus gap formation.

Possible Global Generation Region of Nonlinear Whistler‐Mode Chorus Emission Waves at Mercury

AbstractChorus waves are a kind of intense electromagnetic emission wave in magnetized planets and can play important roles in the kinetic electron dynamics in planetary magnetospheres. Rapid changes of the ring electron current belt in Mercury’s magnetosphere and the contribution of chorus waves have remained long‐standing scientific issues from the first Mercury flyby observations by Mariner 10 in 1970s because of the small size of the magnetosphere. Based on theoretical analyses and simulations successfully reconstructing Earth’s chorus wave properties, we report on possible generation regions of chorus waves in Mercury’s magnetosphere. The theoretical analysis for low‐temperature‐anisotropy electrons shows a clear asymmetric day–night spatial distribution of the possible chorus generation region because of the difference in the nonlinear convective wave growth along the magnetic field lines. Simulation results show a rapid enhancement of the ring electron current belt by resonant interactions with repetitive chorus waves. Our study suggests that energetic electrons in Mercury’s magnetosphere can be enhanced locally by nonlinear chorus wave–particle interactions.

Whistler-mode chorus waves at Mars

Chorus waves are naturally occurring electromagnetic emissions in space and are known to produce highly energetic electrons in the hazardous radiation belt. The characteristic feature of chorus is its fast frequency chirping, whose mechanism remains a long-standing problem. While many theories agree on its nonlinear nature, they differ on whether or how the background magnetic field inhomogeneity plays a key role. Here, using observations of chorus at Mars and Earth, we report direct evidence showing that the chorus chirping rate is consistently related to the background magnetic field inhomogeneity, despite orders of magnitude difference in a key parameter quantifying the inhomogeneity at the two planets. Our results show an extreme test of a recently proposed chorus generation model and confirm the connection between the chirping rate and magnetic field inhomogeneity, opening the door to controlled plasma wave excitation in the laboratory and space.

Banded chorus generation by an electron shell distribution in an inhomogeneous magnetic field: 1D PIC simulations

Although many theoretical models have been proposed over several decades, the origin of banded chorus with a gap in intensity at Ωe/2 (Ωe being the angular electron cyclotron frequency) is still debated. In one of those models, the chorus gap formation is attributed to two anisotropic electron populations separated by an isotropized population (called the parallel plateau) at energy resonant with waves of frequency ∼Ωe/2. Here, we simplify the plateau population as an electron shell distribution in velocity space and investigate its role in the gap formation using a particle-in-cell code in a non-uniform magnetic field. The base plasma is configured to generate rising chorus elements spanning in frequency from below to above Ωe/2. Then, multiple simulations are run with an additional shell distribution with different density values to investigate the gap formation. The simulation results show that even a relatively small fraction of shell is quite effective in arresting the frequency chirping of lower-band chorus at ∼Ωe/2, resulting in a power gap there. Phase space analysis indicates that the resonant current contributed by the phase-trapped shell electrons (forming a phase space hill) can counteract nonlinear chorus growth driven by the phase space hole of energetic, anisotropic electrons. This process occurs in combination with the linear cyclotron damping suggested in earlier studies, and the resulting nonlinear damping may exceed the latter effect.

Simulation of Chorus Wave Excitation in the Compressed/Stretched Dipole Magnetic Field

AbstractThe properties of chorus waves have been extensively studied, which are important to understand chorus generation and wave‐particle interactions between chorus and energetic electrons. Observations reveal that there exists a distinct day‐night asymmetry for the properties of chorus waves, such as the sweep rate and duration, which is predicted to be relevant to the asymmetric configuration of Earth's background magnetic field. In this paper, using the one‐dimensional (1‐D) particle‐in‐cell (PIC) simulation model with a compressed/stretched dipole magnetic field, we study the dependences of the properties of rising‐tone chorus waves on the background magnetic field. It is demonstrated that the saturated amplitude and the chorus sweep rate increase while the chorus duration decreases with an increase of the compression factor ξ, which represents the compression/stretch degree of the field line. Moreover, the threshold of exciting chorus waves in the compressed dipole field is generally lower than that in the stretched dipole field. These results are useful to understand the chorus excitation and the day‐night asymmetry of chorus properties.

Backward-propagating source as a component of rising tone whistler-mode chorus generation

Whistler-mode chorus waves in the magnetosphere play a crucial role in space weather via wave–particle interactions. The past two decades have observed tremendous advances in theory and simulations of chorus generation; however, several details of the generation mechanism are still actively contended. To simulate chorus generation, a new envelope particle-in-cell code is introduced. The model produces a rising tone chorus element in a parabolic geomagnetic field. The initial chorus element “embryo” frequency is shown to initialize near the equator at the frequency of maximum linear growth. A backward resonant current is then observed to propagate upstream of the equator. The trajectory of the backward current follows that of a freely falling electron that has been de-trapped at the equator superimposed with forward motion at the group velocity. The backward current iteratively radiates a rising tone element where the highest frequency components are generated furthest upstream. The work provides new advancements in modeling chorus and corroborates other recent work that has also demonstrated a backward-moving source during the generation of coherent whistler-mode waves.

Short Chorus Wave Packets: Generation Within Chorus Elements, Statistics, and Consequences on Energetic Electron Precipitation.

Short and intense lower‐band chorus wave packets are ubiquitous in the Earth's outer radiation belt. In this article, we perform various Vlasov hybrid simulations, with one or two triggering waves, to study the generation of short chorus packets/subpackets inside long rising tone elements. We show that the length of the generated short wave packets is consistent with a criterion of resonance non‐overlap for two independent superposed waves, and that these chorus packets have similar characteristics as in Van Allen Probes observations. We find that short wave packets are mainly formed near the middle/end of long rising tones for moderate linear growth rates, and everywhere for stronger linear growth rates. Finally, we analyze an event characterized by Time History of Events and Macroscale Interactions during Substorms spacecraft measurements of chorus rising tones near the equator and simultaneous measurements by low altitude ELFIN CubeSats of precipitating and trapped electron fluxes in the same sector. The measured precipitating electron fluxes are well recovered by test particle simulations performed using measured plasma and wave properties. We show that short chorus wave packets of moderate amplitudes (160–250 pT) essentially lead to a more diffusive‐like transport of 50–200 keV electrons toward the loss cone than long packets. In contrast, long chorus packets are found to produce important nonlinear effects via anomalous trapping, which significantly reduces electron precipitation below 150 keV, especially for higher wave amplitudes.

A Statistical Analysis of Duration and Frequency Chirping Rate of Falling Tone Chorus

AbstractThe duration (τ) and chirping rate (Γ) of whistler mode chorus waves are two of the most important properties to understand chorus generation mechanism and to quantify effects of nonlinear wave particle interactions on radiation belt electron acceleration. In this study, we perform the first statistical analysis of the duration and chirping rate of falling tone chorus elements using Van Allen Probes data. We found that τ increases and Γ decreases with increasing L‐shell, although the dependence is weak. The duration from dawnside and dayside have similar distributions, which is a bit longer than those from duskside and nightside. However, Γ has little dependence on MLT. The relation between τ and Γ shows that τ scales with Γ as , supporting one of the previous theoretical models of rising tone chorus in Teng et al. (2017). Our results should provide important insights to deepen our understanding of falling tone chorus excitation.

Measurability of the Nonlinear Response of Electron Distribution Function to Chorus Emissions in the Earth's Radiation Belt

AbstractWe conduct test particle simulations to study the perturbations in a hot electron velocity distribution caused by a rising chorus element propagating parallel to the ambient magnetic field in the Earth's outer radiation belt. The wavefield is constructed from the nonlinear growth theory of chorus emissions of Omura (2021, https://doi.org/10.1186/s40623-021-01380-w), with additional considerations about saturation and propagation of the transverse resonant current being applied to model the subpacket structure. Using Liouville's theorem, we trace electrons back in time to reconstruct the evolution of electron velocity distribution at the magnetic equator. The electromagnetic hole created by nonlinear trapping and transport effects appears as a depression in the velocity distribution, aligned with the resonance velocity curve. We analyze the decrease of particle flux in this depression and estimate the energy resolution, pitch angle resolution, time resolution and geometric factor of particle analyzers needed to observe the perturbation. We conclude that particle detectors on current or recently operating spacecraft are always lacking in at least one of these parameters, which explains the missing direct observations of sharp phase space density depressions during chorus‐electron nonlinear resonant interaction. However, with a dedicated experiment and appropriate measurement strategy, such observations are within the possibilities of the current technology. Similarity of the simulated density perturbation and a step function mathematical model is used to draw an analogy between the backward wave oscillator regime of chorus generation and the nonlinear growth theory.

Observation of Unusual Chorus Elements by Van Allen Probes

AbstractWhistler mode chorus waves play an important role in the radiation belt dynamics, which usually appear as discrete elements with frequency sweeping. Finer structure analysis shows that a chorus element is composed of several frequency‐sweeping subelements, and such two‐level structures can be successfully reproduced by modeling based on nonlinear theories. Previous observations and models suggest that an element and its subelements should have the same frequency‐sweep direction. However, we here present two unexpected chorus rising tone events within which the subelements exhibit clearly reversed, falling frequency‐sweep. Moreover, the subelements consist of several wave packets that also show falling frequency‐sweep features. The three‐level structured chorus elements are distinctly different from all the reported observations and seem to bring challenges to the existing theories. We propose a possible scenario that the falling tone subelements are formed by nonlinear process with much shorter timescale and the starting frequency of each subelement is controlled by fast varying electron distribution. This study may inspire more studies toward a thorough understanding of the chorus generation process.

Discrete Rising Tone Elements of Whistler‐Mode Waves in the Vicinity of the Moon: ARTEMIS Observations

AbstractWe report on discrete rising‐tone elements of whistler‐mode waves observed by Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) in the vicinity of the Moon. The two‐probe ARTEMIS observations suggest that a free energy source for the wave generation is provided by electron anisotropy resulting from lunar surface absorption and magnetic reflection. High time resolution dynamic spectra reveal that the waves consist of multiple rising tone elements, exhibiting striking similarities to the well‐known whistler‐mode chorus in planetary magnetospheres. The observed frequency sweep rates are generally consistent with those predicted by the nonlinear growth theory of chorus emissions by Omura et al. (2008, https://doi.org/10.1029/2007JA012622). These results imply that whistler‐mode waves can grow nonlinearly into chorus‐like emissions even around airless bodies without magnetospheres and that a well‐defined dipole field is not a prerequisite for the chorus generation.

Controlling the Chirping of Chorus Waves via Magnetic Field Inhomogeneity

AbstractWhistler mode chorus waves are coherent electromagnetic emissions in planetary magnetospheres, characterized by rising‐tone or falling‐tone chirping elements. Understanding the cause of different chirping directions and their properties is an important step in resolving the long‐standing problem of nonlinear chorus generation. We report here, for the first time, particle‐in‐cell simulations of bidirectional chirping of whistler waves in a uniform magnetic field and falling‐tone‐only chirping in an inhomogeneous field. Combined with previous simulations of rising‐tone‐only emissions, we demonstrate that the background magnetic field inhomogeneity is not required for chirping of chorus, but it plays a key role in determining the chirping direction. The findings of the present work also unveil the critical role of the dipole geometry of Earth's magnetic field in causing the statistical predominance of rising‐tone chorus and the oblique propagation of falling‐tone chorus.

Nonlinear Wave Growth Analysis of Whistler‐Mode Chorus Generation Regions Based on Coupled MHD and Advection Simulation of the Inner Magnetosphere

AbstractWe show the regions where nonlinear growth of whistler‐mode chorus waves is preferred to occur in the inner magnetosphere. A global magnetohydrodynamics (MHD) simulation was used to obtain large‐scale electric and magnetic fields under the southward interplanetary magnetic field condition. With the electric and magnetic fields obtained by the MHD simulation, we ran a comprehensive inner magnetosphere‐ionosphere model to solve the evolution of phase space density of electrons. Hot electrons originating from the tail region drift sunward and penetrate deep into the inner region due to a combination of convection and substorm‐associated electric fields. Cold electrons also drift sunward, resulting in a contraction of the plasmasphere. We obtained the following results. (1) The whistler waves can first grow due to the linear mechanism (pitch angle anisotropy) in the premidnight‐prenoon region outside the plasmapause, followed by rapid, nonlinear mechanism accompanied with rising‐tone chorus elements. (2) When the solar wind speed is high, the whistler waves grow more efficiently due to linear and nonlinear mechanisms over a wider area because of deep penetration of hot electrons and the large contraction of the plasmasphere. This is consistent with the observation that the outer belt electrons increase for the fast solar wind. (3) For slow solar wind, the linear growth is mostly suppressed, but the nonlinear growth can still take place when external seed waves are present. This may explain the persistence of dawn chorus and large‐amplitude chorus waves that are often observed in the premidnight‐postdawn region in relatively weak geomagnetic activities.

Magnetospheric chorus wave simulation with the TRISTAN-MP PIC code

We present the results of particle-in-cell simulations of the whistler anisotropy instability that results in magnetospheric chorus wave excitation. The simulations were carried out using, for the first time for this problem, the 2D TRISTAN-massively parallelized code, widely used before in the modeling of astrophysical shocks. The code has been modified to allow for two populations of electrons: cold electrons (which maintain the wave propagation) and hot electrons (which provide the wave growth). For the hot electrons, the anisotropic form of the relativistic Maxwell–Jüttner distribution is implemented. We adopt the standard approximation of a parabolic magnetic field to simulate the Earth's magnetic field close to the equator. Simulations with different background magnetic field inhomogeneity strengths demonstrate that higher inhomogeneity yields lower frequency chirping rates and, eventually, it suppresses chorus generation. The results are in agreement with other numerical simulations and the theoretical predictions for the frequency chirping rates.

On the linear theory of oblique magnetospheric chorus excitation

Some aspects of the theory of generation of magnetospheric chorus are discussed. An original approach to solving the problem of oblique chorus generation near the Gendrin angle is outlined and partially realized within the framework of a beam pulsed amplifier mechanism. Parameters of the resonance electron beam in the chorus excitation region are determined theoretically. A short electromagnetic pulse amplification is calculated by means of a linear approach. Some important properties of the oblique chorus emissions, such as the location of the excitation region, frequency band, wave vector direction, group velocity direction, temporary dynamics, and energy of particles and waves are explained.

Nonlinear Coupling Between Whistler‐Mode Chorus and Electron Cyclotron Harmonic Waves in the Magnetosphere

AbstractElectromagnetic whistler‐mode chorus and electrostatic electron cyclotron harmonic (ECH) waves can contribute significantly to auroral electron precipitation and radiation belt electron acceleration. In the past, linear and nonlinear wave‐particle interactions have been proposed to explain the occurrences of these magnetospheric waves. By analyzing Van Allen Probes data, we present here the first evidence for nonlinear coupling between chorus and ECH waves. The sum‐frequency and difference‐frequency interactions produced the ECH sidebands with discrete frequency sweeping structures exactly corresponding to the chorus rising tones. The newly generated weak sidebands did not satisfy the original electrostatic wave dispersion relation. After the generation of chorus and normal ECH waves by hot electron instabilities, the nonlinear wave‐wave interactions could additionally redistribute energy among the resonant waves, potentially affecting to some extent the magnetospheric electron dynamics.

Spatial Extent and Temporal Correlation of Chorus and Hiss: Statistical Results From Multipoint THEMIS Observations

AbstractThe spatial localization of whistler mode waves, determined by their generation process, propagation, and damping, is important for assessing the efficiency of wave‐particle interactions and the dynamics of the radiation belts. We use 11 years of multipoint wave measurements in 2007–2017 from five Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft covering L = 2–10 at low magnetic latitudes over all magnetic local times (MLTs) to characterize both the instantaneous spatial extent of chorus and hiss active regions and their wave amplitude distribution in the vicinity of their respective generation regions, making use of the time domain correlation technique. The correlation of lower band chorus wave power dynamics from two spacecraft measurements remains significant up to 250–800 km transverse to the background magnetic field, in agreement with the typical scale of a chorus element, with a shorter correlation length for higher peak wave power. Additionally, a coordinated analysis of average chorus amplitudes at separate locations shows that the radial extent of the chorus active region varies from 0.2 RE on the nightside to 1 RE on the dayside, with an azimuthal width of 1 MLT. The wave power correlation scale of hiss has no fine structure and is generally larger (1,500–3,000 km); its correlation remains nonnegligible up to 1.5 RE. Such observations are consistent with chorus generation by localized electron injections and subsequent hiss amplification at lower L shells from seed chorus waves having propagated and spread over a wider region inside the plasmasphere. The connection between hiss and chorus is further explored statistically through the correlation between their respective wave power variations, suggesting a significant link between them.

Dependence of Generation of Whistler Mode Chorus Emissions on the Temperature Anisotropy and Density of Energetic Electrons in the Earth's Inner Magnetosphere

AbstractWe carry out a series of self‐consistent electron hybrid code simulations for the dependence of chorus generation process on the temperature anisotropy and density of energetic electrons in the Earth's inner magnetosphere. We use the same magnetic field gradient in the simulation system and different temperature anisotropy AT for the initial distribution of energetic electrons at the magnetic equator. We conduct 6 sets of simulations for different AT from 4 to 9, changing the initial number density Nh of energetic electrons at the equator in each set of simulations. By analyzing the spectra obtained in the simulation results, we identify chorus elements with rising tones in the results for higher Nh but no distinct chorus in smaller Nh. We compare the simulation results with estimations of the threshold and optimum amplitude proposed by the nonlinear wave growth theory. We find that the chorus generation processes reproduced in the simulation results are consistently explained by the theoretical estimates. We also compare the simulation results with linear growth rates for all simulation runs. We find clear disagreement between the spectral characteristics of reproduced chorus and the predictions by the linear theory. The present study clarifies that the spectra of chorus are essentially different from those predicted by the linear theory and are determined fully by nonlinear processes of wave‐particle interactions in the chorus generation region.

Generation of banded chorus by a two-component energetic electron distribution in an inhomogeneous magnetic field

The generation of banded chorus by a two-component energetic electron distribution in a mirror-like inhomogeneous magnetic field is investigated in this work by a 1D hybrid code DAWN. A previous study by Liu et al. [Geophys. Res. Lett. 38, L14108 (2011)] suggested that banded chorus waves can be independently generated by two energetic electron populations. In this work, we first conduct a series of simulations to confirm that the starting frequency of chorus elements is close to the frequency of maximum linear growth rate. With carefully chosen simulation parameters, we then successfully generate banded chorus with a gap near half the electron gyrofrequency. By expanding the parameter range, however, we demonstrate that the gap can be located at frequencies other than the half electron gyrofrequency. We conclude that though the previous mechanism proposed by Liu et al. [Geophys. Res. Lett. 38, L14108 (2011)] can explain the relative independence of upper band and lower band chorus, further work is needed to explain why the linear properties of energetic electrons in the magnetosphere should produce a gap at 0.5Ωe0.

Unique concurrent observations of whistler mode hiss, chorus, and triggered emissions

AbstractWe present a unique 2 h ground‐based observation of concurrent magnetospheric hiss, chorus, VLF triggered emissions as well as ELF/VLF signals generated locally by the High Frequency Active Auroral Research Program (HAARP) facility. Eccentricity of observed wave polarization is used as a criteria to identify magnetospheric emissions and estimate their ionospheric exit points. The observations of hiss and chorus in the unique background of coherent HAARP ELF/VLF waves and triggered emissions allow for more accurate characterization of hiss and chorus properties than in typical ground‐based observations. Eccentricity and azimuth results suggest a moving ionospheric exit point associated with a single ducted path at L ~ 5. The emissions exhibit dynamics in time suggesting an evolution of a magnetospheric source from hiss generation to chorus generation or a moving plasmapause location. We introduce a frequency band‐limited autocorrelation method to quantify the relative coherency of the emissions. A range of coherency was observed from high order of coherency in local HAARP transmissions and their echoes to lower coherency in natural chorus and hiss emissions.