Whistler-mode Chorus Emissions Research Articles

Experimental study on chorus emission in an artificial magnetosphere

Wave particle interaction plays an important role in geospace and space weather phenomena. Whistler mode chorus emissions, characterized by non-linear growth and frequency chirping, are common in planetary magnetospheres. They are regarded as the origin of relativistic acceleration of particles in the radiation belts and pulsating aurora. Intensive theoretical investigations and spacecraft observations have revealed several important features of chorus emissions. However, there is a need to conduct high-resolution and reproducible controlled laboratory experiments to deepen the understanding of space weather. Here, we present the spontaneous excitation of chirping whistler waves in hot-electron high-β plasma (β is the ratio of the plasma pressure to the magnetic pressure) in an “artificial magnetosphere”, a levitated dipole experiment. These experiments suggest that the generation and nonlinear growth of coherent chorus emissions are ubiquitous in dipole magnetic configuration. We anticipate that these experiments will accelerate the laboratory investigation of space weather phenomena.

Precipitation Rates of Electrons Interacting With Lower‐Band Chorus Emissions in the Inner Magnetosphere

AbstractElectrons trapped in the Earth's magnetic field can be scattered by whistler mode chorus emissions and precipitate into the Earth's upper atmosphere. Whistler mode chorus waves propagating in the Earth's inner magnetic field are usually observed with oblique wave normal angles (WNAs). In this study, we apply 12 chorus wave models with four various WNA sets (the maximum WNA are 0°, 20°, 60°, and 90% of resonance cone angles) and three wave amplitude sets (the maximum wave magnetic fields are 2.1 nT, 307 pT, and 49.4 pT) at L = 4.5. We use test‐particle simulations to trace electrons interacting with the waves and create Green's function sets for electrons initially at kinetic energies (K) 10–6,000 keV and equatorial pitch angles (α) 5°–89°. The simulation results show that in the 2.1 nT cases, the very oblique chorus waves contribute to more electron precipitation than the other three chorus wave models, especially at energies 50–100 keV. Checking the highest initial equatorial pitch angle of the precipitated electrons, we find that the very oblique chorus waves can precipitate electrons with α > 45°. In contrast, the other chorus waves can only precipitate electrons with α < 30°. Furthermore, the precipitation rates reveal that the anomalous trapping effect, which moves low equatorial pitch angle electrons away from the loss cone, in the oblique cases is much weaker than in the parallel case, resulting in higher precipitation rates. Finally, we derive the pitch angle scattering rates and verify the precipitation by nth cyclotron resonances with oblique chorus.

Prompt Enhancements of Radiation Belt Electrons over a Wide Energy Range Based on Phase Space Density Variations: A Detailed Case Study

Based on Van Allen Probes observations, we report a prompt enhancement event of radiation belt electrons over a wide energy range from tens of keV to multiple meV spanning 2013 January 13–15. During this period, we also observe prolonged moderate substorm activities and intense whistler-mode chorus emissions. To differentiate the underlying mechanisms responsible for this prompt electron enhancement process, we investigate in detail the evolution of electron phase space densities (PSDs) for various values of the first and second adiabatic invariants (μ and K). The results show that tens to hundreds of keV electrons rapidly penetrated to L* < 4 during the substorm period, with the corresponding PSDs increasing by more than 3 orders of magnitude within about 1 day. Comparatively, the PSD enhancements of higher energy electrons are less significant and shift to higher L*. We find that the fast acceleration of hundreds of keV seed electrons to multi-meV electrons may be reasonably attributed to interactions with the concurrent chorus waves. Specifically, the electron PSD increases for μ≥ 300 MeV G−1 become less pronounced as K increases, consistent with the pitch angle dependence of chorus-induced electron energy diffusion at high energies. Our results therefore provide clear observational evidence for the combined effect of substorm-induced injection and chorus wave scattering on the prompt enhancements of radiation belt electrons over a wide energy range within a couple of days.

Energetic Electron Precipitation Induced by Oblique Whistler Mode Chorus Emissions

AbstractEnergetic electron acceleration and precipitation in the Earth's outer radiation belt are highly associated with wave‐particle interactions between whistler mode chorus waves and electrons. We perform test particle simulations to investigate electrons interacting with parallel and oblique chorus emissions with maximum amplitude 2.1 nT and 370 pT at L = 4.5. We build up a database of Green's functions, which are treated as results of the input electrons interacting with one chorus emission. The loss process of electrons caused by consecutive chorus emissions in the outer radiation belt are traced by applying the convolution integrals of distribution functions and the Green's functions. Oblique chorus emissions lead to more electron precipitation than parallel chorus emissions in the range 370 pT–2.1 nT. By checking the resonance condition and resonant energies, we find that electrons are difficult to be scattered into the loss cone directly by Landau resonance. We propose a two‐step precipitation process for oblique chorus emissions that contributes to more electron loss: (a) Through Landau resonance interaction with a chorus emission, electrons at high pitch angles are effectively accelerated in the parallel direction, and their pitch angles become lower. (b) The electrons bounce back toward the equator, and they are pushed into loss cone through nonlinear scattering due to cyclotron resonance with another chorus emission. The combination of Landau resonance and cyclotron resonance by oblique chorus emissions results in a higher precipitation rate than the single cyclotron resonance by purely parallel chorus emissions.

Quasilinear Model of Jovian Whistler Mode Emission

AbstractThe whistler mode chorus emissions are pervasively detected by the Juno satellite in Jupiter’s magnetospheric environment. This article pays particular attention to a sample observation made by the Juno on 3 November 2019, where typical whistler mode chorus waves are measured. The emission is characterized by a broad range of wave frequencies from below fce/2, where fce denotes the local electron cyclotron frequency, down to the lower‐hybrid frequency, with a gradually downshifting frequency over time. The excitation appears to coincide with the detection of a “butterfly” pitch‐angle distribution and the expected loss‐cone feature associated with the energetic electrons. These anisotropic features, especially the butterfly pitch‐angle distribution, gradually disappear as the waves are excited and the electron phase space distribution becomes isotropic. The aim of this article is to model the characteristics by means of quasilinear kinetic theory of the whistler instability driven by a loss‐cone electron distribution function with a narrow loss‐cone angle, which is to be expected from low‐latitude regions of the Jovian magnetosphere. It is shown that the theoretically constructed dynamic wave spectrum is consistent with the observation made on 3 November 2019. The present finding demonstrates that the quasilinear theory can be a powerful theoretical tool for interpreting various Jovian plasma wave emissions, which includes the whistler waves, but also other wave modes.

Frequency Dependence of Very Low Frequency Chorus Poynting Flux in the Source Region: THEMIS Observations and a Model

AbstractUsing Poynting vector measurements of whistler mode chorus emissions detected by the THEMIS spacecraft within the source region, that is, close to the magnetic field minimum, we found both in individual events and statistically that chorus elements propagating equatorward had systematically higher frequencies and smaller amplitudes compared with simultaneously observed elements propagating away from the equator. We demonstrate similar features in the results of numerical simulations based on backward wave oscillator equations. It can be qualitatively explained by the nonlinear evolution of the energetic electron distribution function during wave generation. The motion of electrons from the equator is accompanied by a decrease in their velocity component along the magnetic field line due to both the adiabatic mirror force and nonlinear wave‐particle interactions. Thus, the frequency of the chorus elements generated by such electrons and propagating equatorward is higher compared with the elements propagating away from the equator.

The beam pulse amplifier in space and laboratory plasmas

We discuss the physical background of the a new mechanism in which short electromagnetic pulses can be strongly amplified by interaction with suprathermal electrons in a near-equilibrium near-uniform magnetised plasma layer. This occurs under the special condition that the wave phase and group speeds along the field lines are equal, a condition met by extraordinary mode electromagnetic waves propagating in the medium. In this case the pulse interacts strongly via the Čerenkov resonance with suprathermal electrons moving along the field lines at the same speed as the pulse, leading to rapid wave growth, the instability within the pulse being shown to be equivalent to that of a monoenergetic electron beam moving along the field lines in an infinite uniform plasma. This effect accounts for basic features of powerful pulsed electromagnetic emissions in planetary magnetospheres, specifically whistler-mode chorus emissions in space plasmas, the remarkable radio emissions observed from brown dwarf objects, as well as in laboratory plasma.

Nonlinear Evolution of Radiation Belt Electron Fluxes Interacting With Oblique Whistler Mode Chorus Emissions

AbstractNonlinear whistler mode wave‐particle interaction is one of the processes to generate relativistic electrons in the Earth's outer radiation belt. Applying test particle simulations with a pair of whistler mode chorus emissions, we traced a large number of electrons in various initial conditions along an magnetic field line to build a set of Green's functions for analyzing evolution of the electron distribution under the chorus emissions. Employing convolution integral for the Green's functions, we tracked the formation of relativistic electron fluxes from an injected energetic electron through interaction with consecutive chorus emissions. We compared the simulation results among a purely parallel wave model and two oblique wave models with wave normal angles gradually increased from 0° to 20° and 60°. Multiple resonances result in a higher probability of nonlinear trapping. Hence, the trapped electrons for the oblique cases are scattered to a wider range of pitch angles than those for the parallel case. Oblique chorus can accelerate 10–30 keV electrons to MeV level rapidly in several wave emission cycles (about 10 s), which is much faster than that of the parallel wave model. The study shows comprehensive evolutions of electron fluxes interacting with oblique chorus emissions through cyclotron and Landau resonances in the outer radiation belt.

Nonlinear Dynamics of Radiation Belt Electrons Interacting With Chorus Emissions Localized in Longitude

AbstractUsing results of test particle simulations of electrons interacting with whistler mode chorus emissions, we numerically obtain Green's functions to model evolution of the electron distribution function after all of the possible interactions with the waves. In both wave models with and without subpackets, electrons undergoing the cyclotron resonance with the waves are efficiently accelerated by nonlinear wave trapping. Since the strong modulation of the wave amplitude (in the case of the waves with subpackets) affects dynamics of resonant electrons, the electrons are detrapped from the wave potential or entrapped into it more frequently than those interacting with the waves without subpackets. As a result of interaction with the waves with subpackets, the number of electrons undergoing the acceleration is increased, while the acceleration efficiency in energy is decreased because of shorter interaction time. Modifying the numerical Green's function method with the simplified model of chorus waves uniform in longitude (Omura et al., 2015, https://doi.org/10.1002/2015JA021563), we compute the formation process of the outer radiation belt electron fluxes induced by the interaction with the chorus waves localized in longitude occurring for a time scale of 1 hr. The formation of MeV electron fluxes is characterized by large acceleration rates and butterfly pitch angle distributions, which are found in satellite observation results.

Data processing in Software-type Wave\u2013Particle Interaction Analyzer onboard the Arase satellite

The software-type wave–particle interaction analyzer (S-WPIA) is an instrument package onboard the Arase satellite, which studies the magnetosphere. The S-WPIA represents a new method for directly observing wave–particle interactions onboard a spacecraft in a space plasma environment. The main objective of the S-WPIA is to quantitatively detect wave–particle interactions associated with whistler-mode chorus emissions and electrons over a wide energy range (from several keV to several MeV). The quantity of energy exchanges between waves and particles can be represented as the inner product of the wave electric-field vector and the particle velocity vector. The S-WPIA requires accurate measurement of the phase difference between wave and particle gyration. The leading edge of the S-WPIA system allows us to collect comprehensive information, including the detection time, energy, and incoming direction of individual particles and instantaneous-wave electric and magnetic fields, at a high sampling rate. All the collected particle and waveform data are stored in the onboard large-volume data storage. The S-WPIA executes calculations asynchronously using the collected electric and magnetic wave data, data acquired from multiple particle instruments, and ambient magnetic-field data. The S-WPIA has the role of handling large amounts of raw data that are dedicated to calculations of the S-WPIA. Then, the results are transferred to the ground station. This paper describes the design of the S-WPIA and its calculations in detail, as implemented onboard Arase.

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.

Software-type Wave\u2013Particle Interaction Analyzer on board the Arase satellite

We describe the principles of the Wave–Particle Interaction Analyzer (WPIA) and the implementation of the Software-type WPIA (S-WPIA) on the Arase satellite. The WPIA is a new type of instrument for the direct and quantitative measurement of wave–particle interactions. The S-WPIA is installed on the Arase satellite as a software function running on the mission data processor. The S-WPIA on board the Arase satellite uses an electromagnetic field waveform that is measured by the waveform capture receiver of the plasma wave experiment (PWE), and the velocity vectors of electrons detected by the medium-energy particle experiment–electron analyzer (MEP-e), the high-energy electron experiment (HEP), and the extremely high-energy electron experiment (XEP). The prime objective of the S-WPIA is to measure the energy exchange between whistler-mode chorus emissions and energetic electrons in the inner magnetosphere. It is essential for the S-WPIA to synchronize instruments to a relative time accuracy better than the time period of the plasma wave oscillations. Since the typical frequency of chorus emissions in the inner magnetosphere is a few kHz, a relative time accuracy of better than 10 μs is required in order to measure the relative phase angle between the wave and velocity vectors. In the Arase satellite, a dedicated system has been developed to realize the time resolution required for inter-instrument communication. Here, both the time index distributed over all instruments through the satellite system and an S-WPIA clock signal are used, that are distributed from the PWE to the MEP-e, HEP, and XEP through a direct line, for the synchronization of instruments within a relative time accuracy of a few μs. We also estimate the number of particles required to obtain statistically significant results with the S-WPIA and the expected accumulation time by referring to the specifications of the MEP-e and assuming a count rate for each detector.

Chorus Wave Modulation of Langmuir Waves in the Radiation Belts

AbstractUsing high‐resolution waveforms measured by the Van Allen Probes, we report a novel observation in the radiation belts. Namely, we show that multiband, discrete, rising‐tone whistler mode chorus emissions exhibit a one‐to‐one correlation with Langmuir wave bursts. Moreover, the periodic Langmuir wave bursts are generally observed at the phase location where the chorus wave E|| component is oriented opposite to its propagation direction. The electron measurements show a beam in phase space density at the particle velocity that matches the parallel phase velocity of the chorus waves. Based on this evidence, we conclude that the chorus waves accelerate the suprathermal electrons via Landau resonance and generate a localized electron beam in phase space density. Consequently, the Langmuir waves are excited locally and are modulated by the chorus wave phase. This microscale interaction between chorus waves and high‐frequency electrostatic waves provides a new insight into the nonlinear wave‐particle interaction process.

Laboratory simulation of magnetospheric chorus wave generation

Whistler mode chorus emissions with a characteristic frequency chirp are important magnetospheric waves, responsible for the acceleration of outer radiation belt electrons to relativistic energies and also for the scattering loss of these electrons into the atmosphere. A laboratory experiment (Van Compernolle et al 2015 Phys. Rev. Lett. 114 245002, An et al 2016 Geophys. Res. Lett.) in the large plasma device at UCLA was designed to closely mimic the scaled plasma parameters observed in the inner magnetosphere, and shed light on the excitation of discrete frequency whistler waves. It was observed that a rich variety of whistler wave emissions is excited by a gyrating electron beam. The properties of the whistler emissions depend strongly on plasma density, beam density and magnetic field profiles.

Method for direct detection of pitch angle scattering of energetic electrons caused by whistler mode chorus emissions

AbstractThe Wave‐Particle Interaction Analyzer (WPIA), a new instrument proposed by Fukuhara et al. (2009), measures the relative phase angle between the wave magnetic field vector and the velocity vector of each particle and calculates the energy exchange from waves to particles. In this study, we expand its applicability by proposing a method of using the WPIA to directly detect pitch angle scattering of resonant particles by plasma waves by calculating the g values. The g value is defined as the accumulation value of the Lorentz force acting on each particle and indicates the lost momentum of waves. We apply the proposed method to the results of a one‐dimensional electron hybrid simulation reproducing the generation of whistler mode chorus emissions around the magnetic equator. Using the wave and particle data obtained at fixed observation points assumed in the simulation system, we conduct a pseudo‐observation of the simulation result using the WPIA and analyze the g values. Our analysis yielded significant values indicating the strong pitch angle scattering for electrons in the kinetic energy and pitch angle ranges satisfying the cyclotron resonance condition with the reproduced chorus emissions. The results of this study demonstrate that the proposed method enables us to directly and quantitatively identify the location at which pitch angle scattering occurs in the simulation system and that the method can be applied to the results of space‐based observations by the forthcoming Exploration of energization and Radiation in Geospace (ERG) satellite.

Formation process of relativistic electron flux through interaction with chorus emissions in the Earth's inner magnetosphere

AbstractWe perform test particle simulations of energetic electrons interacting with whistler mode chorus emissions. We compute trajectories of a large number of electrons forming a delta function with the same energy and equatorial pitch angle. The electrons are launched at different locations along the magnetic field line and different timings with respect to a pair of chorus emissions generated at the magnetic equator. We follow the evolution of the delta function and obtain a distribution function in energy and equatorial pitch angle, which is a numerical Green's function for one cycle of chorus wave‐particle interaction. We obtain the Green's functions for the energy range 10 keV–6 MeV and all pitch angles greater than the loss cone angle. By taking the convolution integral of the Green's functions with the distribution function of the injected electrons repeatedly, we follow a long‐time evolution of the distribution function. We find that the energetic electrons are accelerated effectively by relativistic turning acceleration and ultrarelativistic acceleration through nonlinear trapping by chorus emissions. Further, these processes result in the rapid formation of a dumbbell distribution of highly relativistic electrons within a few minutes after the onset of the continuous injection of 10–30 keV electrons.

Nonlinear wave growth theory of coherent hiss emissions in the plasmasphere

AbstractRecent observations of plasmaspheric hiss emissions by the Van Allen Probes show that broadband hiss emissions in the plasmasphere comprise short‐time coherent elements with rising and falling tone frequencies. Based on nonlinear wave growth theory of whistler mode chorus emissions, we have examined the applicability of the nonlinear theory to the coherent hiss emissions. We have generalized the derivation of the optimum wave amplitude for triggering rising tone chorus emissions to the cases of both rising and falling tone hiss elements. The amplitude profiles of the hiss emissions are well approximated by the optimum wave amplitudes for triggering rising or falling tones. Through the formation of electron holes for rising tones and electron hills for falling tones, the coherent waves evolve to attain the optimum amplitudes. An electromagnetic particle simulation confirms the nonlinear wave growth mechanism as the initial phase of the hiss generation process. We find very good agreement between the theoretical optimum amplitudes and the observed amplitudes as a function of instantaneous frequency. We calculate nonlinear growth rates at the equator and find that nonlinear growth rates for rising tone emissions are much larger than the linear growth rates. The time scales of observed hiss emissions also agree with those predicted by the nonlinear theory. Based on the theory, we can infer properties of energetic electrons generating hiss emissions in the equatorial region of the plasmasphere.

Excitation of Chirping Whistler Waves in a Laboratory Plasma.

Whistler mode chorus emissions with a characteristic frequency chirp are important magnetospheric waves, responsible for the acceleration of outer radiation belt electrons to relativistic energies and also for the scattering loss of these electrons into the atmosphere. Here, we report on the first laboratory experiment where whistler waves exhibiting fast frequency chirping have been artificially produced using a beam of energetic electrons launched into a cold plasma. Frequency chirps are only observed for a narrow range of plasma and beam parameters, and show a strong dependence on beam density, plasma density, and magnetic field gradient. Broadband whistler waves similar to magnetospheric hiss are also observed, and the parameter ranges for each emission are quantified.

Can One Hear Whistler Waves?

The aim of this article is to propose a mathematical framework giving access to a better understanding of whistler-mode chorus emissions in space plasmas. There is presently a general agreement that the emissions of whistler waves involve a mechanism of wave-particle interaction which can be described in the framework of the relativistic Vlasov-Maxwell equations. In dimensionless variables, these equationsinvolve a penalized skew-symmetric term where the inhomogeneity of the strong exterior magnetic field plays an essential part. The description of the related phenomena is achieved in two stages. The first is based on a new approach allowing to extend in longer times the classical insights on fast rotating fluids; it justifies the existence and the validity of long time gyro-kinetic equations; it furnishes criterions to impose on a magnetic field in order to obtain the long time dynamical confinement of plasmas. The second stage is based on a study of oscillatory integrals implying special phases; it deals with the problem of the creation of light inside plasmas.

Wave normal angles of whistler mode chorus rising and falling tones

AbstractWe present a study of wave normal angles (θk) of whistler mode chorus emission as observed by Time History of Events and Macroscale Interactions during Substorms (THEMIS) during the year 2008. The three inner THEMIS satellites THA, THD, and THE usually orbit Earth close to the dipole magnetic equator (±20°), covering a large range of L shells from the plasmasphere out to the magnetopause. Waveform measurements of electric and magnetic fields enable a detailed polarization analysis of chorus below 4 kHz. When displayed in a frequency‐θk histogram, four characteristic regions of occurrence are evident. They are separated by gaps at f/fc,e≈0.5 (f is the chorus frequency, fc,e is the local electron cyclotron frequency) and at θk∼40°. Below θk∼40°, the average value for θk is predominantly field aligned, but slightly increasing with frequency toward half of fc,e (θk up to 20°). Above half of fc,e, the average θk is again decreasing with frequency. Above θk∼40°, wave normal angles are usually close to the resonance cone angle. Furthermore, we present a detailed comparison of electric and magnetic fields of chorus rising and falling tones. Falling tones exhibit peaks in occurrence solely for θk&gt;40° and are propagating close to the resonance cone angle. Nevertheless, when comparing rising tones to falling tones at θk&gt;40°, the ratio of magnetic to electric field shows no significant differences. Thus, we conclude that falling tones are generated under similar conditions as rising tones, with common source regions close to the magnetic equatorial plane.