Nonlinear spatiotemporal signatures of whistler-mode wave activity around Mercury during six flybys of BepiColombo mission

Both linear and nonlinear interactions between oblique whistler, electrostatic, quasi‐upper hybrid mode waves and an electron beam are studied by linear analyses and electromagnetic particle simulations. In addition to a background cold plasma, we assumed a hot electron beam drifting along a static magnetic field (Bo). Growth rates of the oblique whistler, oblique electrostatic, and quasi‐upper hybrid instabilities were first calculated. We found that there are four kinds of unstable mode waves for parallel and oblique propagations. They are the electromagnetic whistler mode wave (WW1), the electrostatic whistler mode wave (WW2), the electrostatic mode wave (ESW), and the quasi‐upper hybrid mode wave (UHW). When the angle θ between the wave vector k and Bo is small enough (≤10°), the electrostatic instability is dominant compared with the whistler mode instability. When θ is around 30°, the growth rates of whistler (both electrostatic and electromagnetic) mode waves and electrostatic mode waves are of the same order. When θ increases to 60°, the WW2 mode will be the most unstable mode wave. For a very large θ, (∼ 80°), the WW2 instability still has positive growth rates, and the UHW instability begins to have positive growth rates. Electromagnetic particle simulations were performed for parallel and three oblique cases, θ = 0°, 30°, 60° and 80°. When θ = 0°, whistler mode waves can hardly grow from the thermal fluctuation level because the electron beam which is supposed to provide free energy to the whistler mode waves is quickly diffused in the velocity space by much faster growing ESW. The ESW can lead to a secondary electrostatic instability. With θ = 30°, both electrostatic and whistler mode waves grow simultaneously. Also, the electrons diffused by the whistler mode instability to higher υ∥ velocity regions can lead to a secondary electrostatic instability. When θ is 60°, diffusion of the electron beam is controlled mainly by the WW2 instability. For θ = 80°, both WW2 and UHW grow despite their small growth rates. The simulations agree with linear analyses on the ESW growth rate for θ = 0°, but from our simulation data, growth rates of oblique whistler mode, electrostatic mode and quasi‐upper hybrid mode waves are usually smaller than those predicted by linear analyses. The electrostatic and whistler mode instabilities affect each other through their interactions with the electron beam. While the most intense ESW is generated for parallel propagation, the most intense whistler mode wave is observed at an oblique direction. Modulations between different electrostatic waves are found for θ = 0° after the electric field reaches its saturation level. Modulations between whistler waves (θ = 60°,80°) are also found while their magnetic fields increase nonlinearly and reach their saturation levels. A possible mechanism is proposed to explain the satellite observations of whistler mode chorus and accompanied electrostatic waves, whose amplitudes are sometimes modulated at the chorus frequency.

<p>Precipitations of energetic electrons into the Earth's atmosphere are important factor of radiation belt dynamics and the magnetosphere-ionosphere coupling. Microbursts, which are the most intense of such precipitations, are short-living bursts of precipitating fluxes detected by low-altitude spacecraft. Due to wide energy ranges of observed microbursts and their transient nature, they are generally associated with energetic electron scattering into the loss-cone via cyclotron resonance with field-aligned intense whistler-mode chorus waves. In this study, we show that intense sub-relativistic precipitations may be generated via the nonlinear Landau resonance of electrons with very oblique whistler-mode waves. Such precipitations are not associated with electron flux decrease in the radiation belts, but rather indicate the rapid electron acceleration up to 100-200 keV around the equator. We combine theoretical model of the nonlinear Landau resonances and equatorial observations of very oblique intense whistler-mode waves. The proposed scenario of intense sub-relativistic precipitations demonstrate the importance of very oblique whistler-mode waves for the radiation belt dynamics.</p>

Whistler mode waves are among the most intense electromagnetic emissions and play an important role in the energy redistribution between electron populations in the Earth inner magnetosphere through wave‐particle resonant interactions. Usually generated by transversely anisotropic plasma sheet electron populations ( 10–30 keV) through cyclotron resonance, whistler mode waves can effectively accelerate a small fraction of the seed population of energetic electrons ( 100 keV) up to relativistic energies. However, these waves can be efficiently damped through simultaneous interactions with much more numerous suprathermal electrons ( 0.1–1 keV) via Landau resonance. Recent observations indeed show that electron distributions accompanied by intense whistler mode emissions often contain a plateau‐like electron population at energies close to the energy of Landau resonance with the waves. However, simultaneous observations of these waves and of the related plateau population does not prove a causal relationship. Here, we test the hypothesis that such a plateau population may have been formed by whistler mode waves generated earlier, or by other types of waves. Combining analytical estimates and spacecraft observations, we show that this plateau population is often unlikely to be formed by whistler mode waves alone. We suggest three alternative scenarios that can lead to the formation of plateau populations and test these scenarios based on spacecraft observations. We show that a plateau population can be formed by ultralow frequency electric fields (carried by kinetic Alfven waves or time domain structures) often accompanying injections of plasma sheet electrons—the energy source for whistler mode waves. We also discuss the possible role of ionospheric secondary electrons.

Whistler mode waves are commonly observed inside mirror mode structures (MM‐Ss) in the magnetosheath. Although MM‐Ss have also been detected in the magnetosphere, there is no statistical study investigating the properties of whistler mode waves inside MM‐Ss. Using Magnetospheric Multiscale (MMS) satellites, our present study identifies and statistically analyzes whistler mode waves detected inside MM‐Ss in the Earth's magnetosphere. Both the observational evidence (bidirectional propagation) and theoretical analyses suggest that whistler mode waves are excited in the low‐magnetic‐field regions of MM‐Ss. Statistical results indicate that whistler mode waves are frequently observed inside the MM‐Ss in the dusk sector. Most of these waves (>70%) are in the frequency range of 0.1–0.4 fce and have amplitudes less than ∼50 pT. Moreover, most of them are observed to propagate in the direction both parallel and antiparallel to the background magnetic field, and their wave normal angles are typically less than ∼40°. Our study analyzes the properties and generation of whistler mode waves inside MM‐Ss and reveals that MM‐Ss are a possible source region in the Earth's magnetosphere. Therefore, our study provides new insight into the properties of whistler mode waves inside MM‐Ss which are pervasive in space plasmas.

Generation mechanism of the whistler-mode waves in the plasma sheet prior to magnetic reconnection

Whistler mode waves in the magnetotail, especially the plasma sheet and the plasma sheet boundary layer, are frequently detected by a waveform capture on board Geotail satellite. The whistler mode waves with frequencies above 10 Hz are often narrowband and short‐lived. Statistical study shows that these whistler mode waves propagate in a direction quasi‐parallel to the ambient magnetic field with an average wave normal angle of 23°. This suggests that the electron cyclotron resonance is dominant for excitation of the whistler mode waves. Their frequencies range mainly from 0.05 to ∼ 0.5Ωe, where Ωe is the electron cyclotron frequency. Their average frequency is 0.21Ωe. Amplitudes of the whistler mode waves cover a range from a few picoteslas to ∼100 pT. Their mean amplitude is 44 pT or 10−2 B0, where B0 is the magnitude of the ambient magnetic field. One interesting feature is that the whistler mode waves propagate mostly in a direction either parallel or antiparallel to B0. The whistler mode waves are very likely excited by energetic electron beams, which arise from reconnections in the near/deep magnetotail. Another significant feature of the whistler mode waves is that the correlation between their amplitudes and phase speeds. A higher phase speed usually associates with a lower amplitude. Whistler mode waves in the near magnetotail (−100 RE < x <−10 RE) and the deep magnetotail (−210 RE < x < −100 RE) are very much the same in many respects. However, one significant difference is that the average electron resonant energy is higher in the near magnetotail (11 keV) than that in the deep magnetotail (1.6 keV). Observations of whistler mode waves may provide a way to monitor energetic electrons and processes of reconnection in the magnetotail.

Adiabatic heating of solar wind electrons at the Earth's bow shock and its foreshock region produces transversely anisotropic hot electrons that, in turn, generate intense high-frequency whistler-mode waves. These waves are often detected by spacecraft as narrow-band, electromagnetic emissions in the frequency range of [0.1, 0.5] of the local electron gyrofrequency. Resonant interactions between these waves and electrons may cause electron acceleration and pitch-angle scattering, which can be important for creating the electron population that seeds shock drift acceleration. The high intensity and coherence of the observed whistler-mode waves prohibit the use of quasi-linear theory to describe their interaction with electrons. In this paper, we aim to develop a new theoretical approach to describe this interaction, which incorporates nonlinear resonant interactions, gradients of the background density and magnetic field, and the fine structure of the waveforms that usually consist of short, intense wave-packet trains. This is the first of two accompanying papers. It outlines a probabilistic approach to describe the wave–particle interaction. We demonstrate how the wave-packet size affects electron nonlinear resonance at the bow shock and foreshock regions, and how to evaluate electron distribution dynamics in such a system that is frequented by short, intense whistler-mode wave-packets. In the Paper II, this probabilistic approach is merged with a mapping technique, which allows us to model systems containing short and long wave-packets.

Recent observations by Starks et al. (2008) from multiple spacecraft suggest that the actual nighttime intensity of VLF transmitter signals in the radiation belts is approximately 20 dB below the level that is assumed in the model developed by Abel and Thorne (1998) and approximately 10 dB below model values during the day. In the present work, we discuss one experimentally established mechanism which might be responsible for some of this intensity discrepancy, linear mode coupling as electromagnetic whistler mode waves propagate through regions containing small‐scale (2–100 m) magnetic field‐aligned plasma density irregularities. The scattering process excites quasi‐electrostatic whistler mode waves, which represents a power loss for the input waves. Although the distribution and amplitude of the irregularities is not well known at present, we construct plausible models in order to use numerical simulations to determine the characteristics of the mode coupling mechanism and the conditions under which the input VLF waves can lose significant power to the excited quasi‐electrostatic whistler mode waves. For short propagation paths of approximately 15 km, the full‐wave model predicts power losses ranging from −3 dB (25% probability) to −7 dB (2% probability). For longer propagation paths of approximately 150 km, the full‐wave model predicts power losses ranging from −4 dB (25% probability) to over −10 dB (2% probability). We conclude that for the irregularity models investigated, the mode coupling mechanism can result in significant power loss for VLF electromagnetic whistler mode waves.

We report on narrowband electromagnetic waves at frequencies between the local electron cyclotron and lower hybrid frequencies observed by the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft in the Martian induced magnetosphere. The peaked electric field wave spectra below the electron cyclotron frequency were first observed by Phobos‐2 in the Martian magnetosphere, but the lack of magnetic field wave data prevented definitive identification of the wave mode and their generation mechanisms remain unclear. Analysis of electric and magnetic field wave spectra obtained by MAVEN demonstrates that the observed narrowband waves have properties consistent with the whistler mode. Linear growth rates computed from the measured electron velocity distributions suggest that these whistler mode waves can be generated by cyclotron resonance with anisotropic electrons. Large electron anisotropy in the Martian magnetosphere is caused by absorption of parallel electrons by the collisional atmosphere. The narrowband whistler mode waves and anisotropic electrons are observed on both open and closed field lines and have similar spatial distributions in MSO and planetary coordinates. Some of the waves on closed field lines exhibit complex frequency‐time structures such as discrete elements of rising tones and two bands above and below half the electron cyclotron frequency. These MAVEN observations indicate that whistler mode waves driven by anisotropic electrons, which are commonly observed in intrinsic magnetospheres and at unmagnetized airless bodies, are also present at Mars. The wave‐induced electron precipitation into the Martian atmosphere should be evaluated in future studies.

The magnetic field configuration around a magnetic null pair and its associated electron behavior during 3D magnetic reconnection have recently been reported from in situ observations. Electrons are suggested to be temporarily trapped in the central reconnection region as indicated by an electron density peak observed near the magnetic null (He J-S et al 2008 Geophys. Res. Lett. 35 L14104). It is highly interesting that energetic electron beams of a few kiloelectronvolts are found to be related to the magnetic null structure. However, the acceleration mechanism is still not fully understood. In this paper, we show that strong whistler-mode electromagnetic waves are indeed found around the magnetic null. Further we propose a new electron acceleration scenario of trapped electrons near the magnetic null points driven by the whistler-mode waves, which is confirmed by numerical results. It is demonstrated that whistler waves can enhance the phase space density (PSD) of electrons for energies of ∼2 keV by a factor of 100 at lower pitch angles very rapidly, typically within 2 s. The accelerated electrons may escape from the loss cone of the magnetic cusp mirrors around the magnetic null, leading to the observed energetic beams.

The whistler-mode wave is an electromagnetic wave that commonly occurs in space plasma and has been extensively studied, especially within the Earth's magnetosphere. They have also been reported in the near-Mars space, such as Martian upstream solar wind, crustal magnetic field, ionopause, and the magnetic reconnection ion diffusion region. However, the generation of whistler-mode waves in the Martian magnetotail current sheet is still unclear. Based on observations made by Mars Atmosphere and Volatile Evolution spacecraft, we report whistler-mode waves observed within a train of proton-scale magnetic dips during a Martian magnetotail current sheet crossing. The linear growth rate analyses demonstrate that the whistler-mode waves are locally generated within the magnetic dips. Unlike in Earth's plasma environment, the train of magnetic dips in the Martian plasma sheet is attributed to electron mirror-mode instability. Our finding suggests that the mirror-mode structure in the Martian magnetotail can be an important source region for generating whistler-mode waves. This provides a new insight into how whistler-mode waves are generated in unmagnetized planets.

Summary form only given. We first study the generation mechanism of whistler mode chorus emissions. The essential mechanism of the frequency change is due to the inhomogeneity of the geomagnetic field in the equatorial region. A whistler mode wave can trap electrons near the cyclotron resonant velocity. The trapping is only possible near the equator where the Lorentz force due to the magnetic field component of the whistler mode wave is larger than the magnetic mirror force due to the inhomogeneity of the geomagnetic field. The electrons approaching the equator get into resonance with the wave when the parallel velocity increases to the resonance velocity of the wave due to the adiabatic motion. Most of the resonant electrons, however, do not enter the trapping region, because the separatrix of the trapping region is closed. Only a fraction of the resonant electrons near the separatrix get into the trapping region because of the enlargement of the separatrix as the particles approaches to the equator. Consequently, there arises a deficit of trapped particles in the velocity phase space, giving rise to a resonant current causing wave growth and frequency increase. Since the resonant current changes its polarization to cause wave damping on the other side of the equator, the rising tone emissions with increasing amplitudes are only possible when the coherent wave propagates away from the equator interacting with counter-streaming resonant electrons. The relativistic electrons with relatively high pitch angles can readily get into resonance with such a coherent whistler wave, if their parallel velocities satisfy the relativistic cyclotron resonance condition. We performed test particle simulations where we solved relativistic equations of motion for high energy electrons under the electromagnetic fields of a coherent whistler mode wave and the dipole geomagnetic field. We find that resonant trapping of relativistic electrons by a whistler mode wave with a rising tone results in efficient acceleration of resonant particles to relativistic energy.

The acceleration of ionospheric ions transverse to the geomagnetic field by factors of 10³ is believed to be caused by plasma waves. We have made simultaneous measurements of electric fields (0‐16kHz) and energetic ions (50eV to 20keV) within regions of perpendicular ion acceleration from the sounding rocket MARIE. Perpendicular ion acceleration was correlated with plasma waves near and above the lower hybrid frequency. Ions were detected up to energies of 300 eV and the broadband lower hybrid waves reached an amplitude of 10‐30 mV/m (RMS) over the frequency band 4‐16 kHz. Although electric field amplitudes near the O+ cyclotron frequency reached a maximum value of 10 mV/m (RMS), there was no spectral evidence of electrostatic ion cyclotron waves associated with ion acceleration. There was spectral evidence of H+ Bernstein modes near the lower hybrid frequency. If we assume that whistler mode waves near and above the lower hybrid frequency were responsible for the ion acceleration then the conversion efficiency of wave energy to ion energy was .01 to .1.

The nonlinear resonant interaction of intense whistler-mode waves and energetic electrons in the Earth's radiation belts is traditionally described by theoretical models based on the consideration of slow–fast resonant systems. Such models reduce the electron dynamics around the resonance to the single pendulum equation that provides solutions for the electron nonlinear scattering (phase bunching) and phase trapping. Applicability of this approach is limited to not-too-small electron pitch-angles (i.e., sufficiently large electron magnetic moments), whereas model predictions contradict to the test particle results for small pitch-angle electrons. This study is focused on such field-aligned (small pitch-angle) electron resonances. We show that the nonlinear resonant interaction can be described by the slow–fast Hamiltonian system with the separatrix crossing. For the first cyclotron resonance, this interaction results in the electron pitch-angle increase for all resonant electrons, contrast to the pitch-angle decrease predicted by the pendulum equation for scattered electrons. We derive the threshold value of the magnetic moment of the transition to a new regime of the nonlinear resonant interaction. For field-aligned electrons, the proposed model provides the magnitude of magnetic moment changes in the nonlinear resonance. This model supplements existing models for not-too-small pitch-angles and contributes to the theory of the nonlinear resonant electron interaction with intense whistler-mode waves.

Bursts of narrowband and short‐lived electromagnetic waves are frequently observed in the upstream (the electron foreshock and the pure solar wind) by the waveform capture instrument on board Geotail satellite. The electromagnetic waves with frequencies above 10 Hz are all right‐hand circularly polarized and identified as whistler mode waves. We call the waves narrowband and short‐lived whistlers (NSW). Nearly all the NSW in the electron foreshock propagate in a downstream direction parallel to the ambient magnetic field (Bo) with an average θkB of 16°, where θkB is an angle between NSW wave vector and the Bo. Their frequencies cover a range from 0.05 to 1.0Ωe with an average of 0.35Ωe, where Ωe is a local electron cyclotron frequency. Their amplitudes range from a few picoteslas to 100 pT with an average of 23 pT. Because of their parallel propagation, the NSW must be excited by electron cyclotron resonance. These features of the NSW suggest existence of electron beams which travel in an upstream direction parallel to the Bo and which have a temperature anisotropy. Kinetic energies of the beams range from a few eV to about 200 eV (28 eV on average). All these characteristics of the electron beams revealed from the NSW are consistent with ISEE and WIND particle observations. The competition between electrostatic and whistler instabilities and the finite size of the beams are very likely the reasons why the NSW are short‐lived. These NSW can be well explained by a modeled electron beam with a losscone distribution in the electron foreshock. The NSW in solar wind are very similar to those in the electron foreshock. However, they have larger amplitudes (34 pT on average), lower frequencies (0.24Ωe on average), and higher cyclotron resonant energy (100 eV on average). They are very likely excited by halo electrons or nonlocal sources in the solar wind.