Whistler Mode Chorus Research Articles

Electron hybrid code simulation of whistler-mode chorus generation with real parameters in the Earth’s inner magnetosphere

We carry out a self-consistent simulation of the generation process of whistler-mode chorus by a spatially one-dimensional electron hybrid code, by assuming the magnetic field inhomogeneity corresponding to L = 4 of the dipole field. Chorus emissions with rising tones are reproduced in the simulation result, while the frequency range, sweep rate, and the amplitude profiles in the spectra of the reproduced elements are consistently explained by the nonlinear wave growth theory. We compare the simulation results with the observation by the Cluster spacecraft (Santolik et al. in J Geophys Res 108:1278, 2003, doi: 10.1029/2002JA009791 ; Santolik in Nonlinear Process Geophys 15:621–630, 2008) and reveal similarities of the spectral fine structure of reproduced chorus elements with the observation. On the other hand, there is no gap at half the gyrofrequency in the spectra of the reproduced chorus elements, which is evident in the observation. This difference implies that the mechanism of a gap at half the gyrofrequency is governed by the process that is not described by the spatially one-dimensional simulation treating purely parallel propagating electromagnetic waves.

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.

Survey of whistler mode chorus intensity at Jupiter

AbstractWhistler mode chorus emission is important in the acceleration of electrons and filling of the radiation belts at Jupiter. In this work chorus magnetic intensity levels (frequency‐integrated spectral density, PB) at Jupiter are comprehensively binned and parameterized. The frequency range of chorus under study extends from the lower hybrid frequency, flh, to fceq/2 and fceq/2 < f < 0.8 fceq, where fceq is the cyclotron frequency mapped to the magnetic equator. The goal is to obtain a quantized distribution of magnetic intensity for use in stochastic modeling efforts. Parametric fits of magnetic plasma wave intensity are obtained, including PB versus frequency, latitude, and L shell. The results indicate that Jupiter chorus occurrence probability and intensity are higher than those at Saturn, reaching values observed at Earth. Jovian chorus is observed over most local times, confined primarily to the range 8 < L < 15, outside the high densities of the Io torus. The largest intensity levels are seen on the dayside; however, the sampling of chorus on the nightside is much less than on the dayside. Peak intensities occur near the equator with a weak dependence on magnetic latitude, λ. We conclude that Jovian chorus average intensity levels are approximately an order of magnitude lower than those at Earth. In more isolated regions the intensities are comparable to those observed at Earth. The spatial range of the chorus emissions extends beyond that assumed in previous Jovian global diffusive models of wave‐particle electron acceleration.

Rapid flattening of butterfly pitch angle distributions of radiation belt electrons by whistler‐mode chorus

AbstractVan Allen radiation belt electrons exhibit complex dynamics during geomagnetically active periods. Investigation of electron pitch angle distributions (PADs) can provide important information on the dominant physical mechanisms controlling radiation belt behaviors. Here we report a storm time radiation belt event where energetic electron PADs changed from butterfly distributions to normal or flattop distributions within several hours. Van Allen Probes observations showed that the flattening of butterfly PADs was closely related to the occurrence of whistler‐mode chorus waves. Two‐dimensional quasi‐linear STEERB simulations demonstrate that the observed chorus can resonantly accelerate the near‐equatorially trapped electrons and rapidly flatten the corresponding electron butterfly PADs. These results provide a new insight on how chorus waves affect the dynamic evolution of radiation belt electrons.

The relationship between the macroscopic state of electrons and the properties of chorus waves observed by the Van Allen Probes

AbstractPlasma kinetic theory predicts that a sufficiently anisotropic electron distribution will excite whistler mode waves, which in turn relax the electron distribution in such a way as to create an upper bound on the relaxed electron anisotropy. Here using whistler mode chorus wave and plasma measurements by Van Allen Probes, we confirm that the electron distributions are well constrained by this instability to a marginally stable state in the whistler mode chorus waves generation region. Lower band chorus waves are organized by the electron β∥e into two distinct groups: (i) relatively large‐amplitude, quasi‐parallel waves with and (ii) relatively small‐amplitude, oblique waves with . The upper band chorus waves also have enhanced amplitudes close to the instability threshold, with large‐amplitude waves being quasi‐parallel whereas small‐amplitude waves being oblique. These results provide important insight for studying the excitation of whistler mode chorus waves.

Observation of chorus waves by the Van Allen Probes: Dependence on solar wind parameters and scale size

AbstractHighly energetic electrons in the Earth's Van Allen radiation belts can cause serious damage to spacecraft electronic systems and affect the atmospheric composition if they precipitate into the upper atmosphere. Whistler mode chorus waves have attracted significant attention in recent decades for their crucial role in the acceleration and loss of energetic electrons that ultimately change the dynamics of the radiation belts. The distribution of these waves in the inner magnetosphere is commonly presented as a function of geomagnetic activity. However, geomagnetic indices are nonspecific parameters that are compiled from imperfectly covered ground based measurements. The present study uses wave data from the two Van Allen Probes to present the distribution of lower band chorus waves not only as functions of single geomagnetic index and solar wind parameters but also as functions of combined parameters. Also the current study takes advantage of the unique equatorial orbit of the Van Allen Probes to estimate the average scale size of chorus wave packets, during close separations between the two spacecraft, as a function of radial distance, magnetic latitude, and geomagnetic activity, respectively. Results show that the average scale size of chorus wave packets is approximately 1300–2300 km. The results also show that the inclusion of combined parameters can provide better representation of the chorus wave distributions in the inner magnetosphere and therefore can further improve our knowledge of the acceleration and loss of radiation belt electrons.

Ionosphere‐magnetosphere energy interplay in the regions of diffuse aurora

AbstractBoth electron cyclotron harmonic (ECH) waves and whistler mode chorus waves resonate with electrons of the Earth's plasma sheet in the energy range from tens of eV to several keV and produce the electron diffuse aurora at ionospheric altitudes. Interaction of these superthermal electrons with the neutral atmosphere leads to the production of secondary electrons (E < 500–600 eV) and, as a result, leads to the activation of lower energy superthermal electron spectra that can escape back to the magnetosphere and contribute to the thermal electron energy deposition processes in the magnetospheric plasma. The ECH and whistler mode chorus waves, however, can also interact with the secondary electrons that are coming from both of the magnetically conjugated ionospheres after they have been produced by initially precipitated high‐energy electrons that came from the plasma sheet. After their degradation and subsequent reflection in magnetically conjugate atmospheric regions, both the secondary electrons and the precipitating electrons with high (E > 600 eV) initial energies will travel back through the loss cone, become trapped in the magnetosphere, and redistribute the energy content of the magnetosphere‐ionosphere system. Thus, scattering of the secondary electrons by ECH and whistler mode chorus waves leads to an increase of the fraction of superthermal electron energy deposited into the core magnetospheric plasma.

Explaining the dynamics of the ultra-relativistic third Van Allen radiation belt

Since the discovery of the Van Allen radiation belts over 50 years ago, an explanation for their complete dynamics has remained elusive. Especially challenging is understanding the recently discovered ultra-relativistic third electron radiation belt. Current theory asserts that loss in the heart of the outer belt, essential to the formation of the third belt, must be controlled by high-frequency plasma wave–particle scattering into the atmosphere, via whistler mode chorus, plasmaspheric hiss, or electromagnetic ion cyclotron waves. However, this has failed to accurately reproduce the third belt. Using a data-driven, time-dependent specification of ultra-low-frequency (ULF) waves we show for the first time how the third radiation belt is established as a simple, elegant consequence of storm-time extremely fast outward ULF wave transport. High-frequency wave–particle scattering loss into the atmosphere is not needed in this case. When rapid ULF wave transport coupled to a dynamic boundary is accurately specified, the sensitive dynamics controlling the enigmatic ultra-relativistic third radiation belt are naturally explained. The appearance of a third radiation belt in the Earth’s Van Allen belts is difficult to explain using existing models for two belts. However, a model based on ultra-low-frequency waves agrees quantitatively with measurements of the third belt.

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.

Relativistic electron microbursts and variations in trapped MeV electron fluxes during the 8–9 October 2012 storm: SAMPEX and Van Allen Probes observations

AbstractIt has been suggested that whistler mode chorus is responsible for both acceleration of MeV electrons and relativistic electron microbursts through resonant wave‐particle interactions. Relativistic electron microbursts have been considered as an important loss mechanism of radiation belt electrons. Here we report on the observations of relativistic electron microbursts and flux variations of trapped MeV electrons during the 8–9 October 2012 storm, using the SAMPEX and Van Allen Probes satellites. Observations by the satellites show that relativistic electron microbursts correlate well with the rapid enhancement of trapped MeV electron fluxes by chorus wave‐particle interactions, indicating that acceleration by chorus is much more efficient than losses by microbursts during the storm. It is also revealed that the strong chorus wave activity without relativistic electron microbursts does not lead to significant flux variations of relativistic electrons. Thus, effective acceleration of relativistic electrons is caused by chorus that can cause relativistic electron microbursts.

Banded structures in electron pitch angle diffusion coefficients from resonant wave-particle interactions

Electron pitch angle (Dαα) and momentum (Dpp) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies ≤10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = ±1, ±2, … ±5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (α) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in Dαα and Dpp coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The Dpp diffusion coefficient for ECH waves is one to two orders smaller than Dαα coefficients. For chorus waves, Dpp coefficients are about an order of magnitude smaller than Dαα coefficients for the case n ≠ 0. In case of Landau resonance, the values of Dpp coefficient are generally larger than the values of Dαα coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89° and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10° and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies ≥1 keV, and for whistler mode chorus waves, structures appear for energies >2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.

Oblique Whistler-Mode Waves in the Earth’s Inner Magnetosphere: Energy Distribution, Origins, and Role in Radiation Belt Dynamics

In this paper we review recent spacecraft observations of oblique whistler-mode waves in the Earth’s inner magnetosphere as well as the various consequences of the presence of such waves for electron scattering and acceleration. In particular, we survey the statistics of occurrences and intensity of oblique chorus waves in the region of the outer radiation belt, comprised between the plasmapause and geostationary orbit, and discuss how their actual distribution may be explained by a combination of linear and non-linear generation, propagation, and damping processes. We further examine how such oblique wave populations can be included into both quasi-linear diffusion models and fully nonlinear models of wave-particle interaction. On this basis, we demonstrate that varying amounts of oblique waves can significantly change the rates of particle scattering, acceleration, and precipitation into the atmosphere during quiet times as well as in the course of a storm. Finally, we discuss possible generation mechanisms for such oblique waves in the radiation belts. We demonstrate that oblique whistler-mode chorus waves can be considered as an important ingredient of the radiation belt system and can play a key role in many aspects of wave-particle resonant interactions.

Generation of multiband chorus by lower band cascade in the Earth's magnetosphere

AbstractChorus waves are intense electromagnetic whistler mode emissions in the magnetosphere, typically falling into two distinct frequency bands: a lower band (0.1–0.5fce) and an upper band (0.5–0.8fce) with a power gap at about 0.5fce. In this letter, with the Time History of Events and Macroscale Interactions during Substorms satellite, we observed two special chorus events, which are called as multiband chorus because upper band chorus is located at harmonics of lower band chorus. We propose a new potential generation mechanism for multiband chorus, which is called as lower band cascade. In this scenario, a density mode with a frequency equal to that of lower band chorus is generated by the ponderomotive effect (inhomogeneity of the electric amplitude) along the wave vector, and then upper band chorus with the frequency twice that of lower band chorus is generated through wave‐wave couplings between lower band chorus and the density mode. The mechanism provides a new insight into the evolution of whistler mode chorus in the Earth's magnetosphere.

Substructures with luminosity modulation and horizontal oscillation in pulsating patch: Principal component analysis application to pulsating aurora

AbstractWe observed a mesoscale aurora (100 km × 100 km) with patchy structure and equatorward propagation at Poker Flat Research Range on 1 December 2011. Fast Fourier transform (FFT) analysis revealed that this pulsating patch clearly exhibited temporal variations that can be categorized into two types: on‐off pulsation (7.8–10 s) with large amplitudes and luminosity modulations excited during on phase with a frequency of about 3.0 Hz. In addition, we applied principal component analysis (PCA) to time series image data of the pulsating aurora for the first time. Time coefficients were estimated by PCA for the whole patch and the substructures were consistent with those obtained from the FFT analysis, and therefore, we concluded that PCA is capable of decomposing several structures that have different coherent spatiotemporal characteristics. Another new insight in this study is that the rapid variations were highly localized; they were excited in only the substructures embedded in the whole structure. Moreover, the whole patch propagated equatorward because of E × B drift of cold plasma, while the substructures did not show such systematic propagation but rather forward‐backward oscillations. The horizontal scale of the substructures was estimated to be no smaller than 410 km at the magnetic equator, which is comparable to that of the wave packet structure of a whistler mode chorus perpendicular to the field line. We suggest that the apparent horizontal oscillation of the substructures is associated with field‐aligned propagations of the whistler mode chorus in a duct.

Intense low‐frequency chorus waves observed by Van Allen Probes: Fine structures and potential effect on radiation belt electrons

AbstractFrequency distribution is a vital factor in determining the contribution of whistler mode chorus to radiation belt electron dynamics. Chorus is usually considered to occur in the frequency range 0.1–0.8fce_eq (with the equatorial electron gyrofrequency fce_eq). We here report an event of intense low‐frequency chorus with nearly half of wave power distributed below 0.1fce_eq observed by Van Allen Probe A on 27 August 2014. This emission propagated quasi‐parallel to the magnetic field and exhibited hiss‐like signatures most of the time. The low‐frequency chorus can produce the rapid loss of low‐energy (∼0.1 MeV) electrons, different from the normal chorus. For high‐energy (≥0.5 MeV) electrons, the low‐frequency chorus can yield comparable momentum diffusion to that of the normal chorus but much stronger (up to 2 orders of magnitude) pitch angle diffusion near the loss cone.

Nature's Grand Experiment: Linkage between magnetospheric convection and the radiation belts

AbstractThe solar minimum of 2007–2010 was unusually deep and long lived. In the later stages of this period the electron fluxes in the radiation belts dropped to extremely low levels. The flux of relativistic electrons (>1 MeV) was significantly diminished and at times was below instrument thresholds both for spacecraft located in geostationary orbits and also those in low‐Earth orbit. This period has been described as a natural “Grand Experiment” allowing us to test our understanding of basic radiation belt physics and in particular the acceleration mechanisms which lead to enhancements in outer belt relativistic electron fluxes. Here we test the hypothesis that processes which initiate repetitive substorm onsets drive magnetospheric convection, which in turn triggers enhancement in whistler mode chorus that accelerates radiation belt electrons to relativistic energies. Conversely, individual substorms would not be associated with radiation belt acceleration. Contrasting observations from multiple satellites of energetic and relativistic electrons with substorm event lists, as well as chorus measurements, show that the data are consistent with the hypothesis. We show that repetitive substorms are associated with enhancements in the flux of energetic and relativistic electrons and enhanced whistler mode wave intensities. The enhancement in chorus wave power starts slightly before the repetitive substorm epoch onset. During the 2009/2010 period the only relativistic electron flux enhancements that occurred were preceded by repeated substorm onsets, consistent with enhanced magnetospheric convection as a trigger.

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.

Electron distribution function formation in regions of diffuse aurora

AbstractThe precipitation of high‐energy magnetospheric electrons (E ∼ 600 eV–10 KeV) in the diffuse aurora contributes significant energy flux into the Earth's ionosphere. To fully understand the formation of this flux at the upper ionospheric boundary, ∼700–800 km, it is important to consider the coupled ionosphere‐magnetosphere system. In the diffuse aurora, precipitating electrons initially injected from the plasma sheet via wave‐particle interaction processes degrade in the atmosphere toward lower energies and produce secondary electrons via impact ionization of the neutral atmosphere. These precipitating electrons can be additionally reflected upward from the two conjugate ionospheres, leading to a series of multiple reflections through the magnetosphere. These reflections greatly influence the initially precipitating flux at the upper ionospheric boundary (700–800 km) and the resultant population of secondary electrons and electrons cascading toward lower energies. In this paper, we present the solution of the Boltzman‐Landau kinetic equation that uniformly describes the entire electron distribution function in the diffuse aurora, including the affiliated production of secondary electrons (E < 600 eV) and its energy interplay in the magnetosphere and two conjugated ionospheres. This solution takes into account, for the first time, the formation of the electron distribution function in the diffuse auroral region, beginning with the primary injection of plasma sheet electrons via both electrostatic electron cyclotron harmonic waves and whistler mode chorus waves to the loss cone, and including their subsequent multiple atmospheric reflections in the two magnetically conjugated ionospheres. It is demonstrated that magnetosphere‐ionosphere coupling is key in forming the electron distribution function in the diffuse auroral region.

Local time distributions of repetition periods for rising tone lower band chorus waves in the magnetosphere

Whistler mode chorus waves generally occur outside the plasmapause in the magnetosphere. The most striking feature of the waves is their occurrence in discrete elements. One of the parameters that describe the discrete elements is the repetition period (Trp), the time between consecutive elements. The Trp has not been studied statistically before. We use high-resolution waveform data to derive distributions of Trp for different local times. We find that the average Trp for the nightside (0.56 s) and dawnside (0.53 s) are smaller than those for the dayside (0.81 s) and duskside (0.97 s). Through a comparison with the background plasma and magnetic fields, we also find that the total magnetic field and temperature are the main controlling factors that affect the variability of Trp. These results are important for understanding the generation mechanism of chorus and choosing parameters in simulations that model the acceleration and loss of electrons by wave-particle interactions.

Different types of whistler mode chorus in the equatorial source region

The Time History of Events and Macroscale Interactions during Substorms-D spacecraft crossed an active equatorial source region of whistler mode chorus rising tones on 23 October 2008. Rising tones are analyzed in terms of spectral and polarization characteristics, with special emphasis on wave normal angles. The latter exhibit large variations from quasi-parallel to oblique, even within single bursts, but seem to follow a definite pattern, which enables an unambiguous classification into five different groups. Furthermore, we discuss the frequently observed splitting of chorus bursts into a lower and an upper band around one half of the local electron cyclotron frequency. At chorus frequencies close to the gap, we find significantly lowered wave planarities and a tendency of wave normal angles to approach the Gendrin angle.