Whistler Mode Waves Research Articles

Modulation instability of whistler wave with electron loss cone distribution in magnetized plasma

Abstract The modulation instability of whistler mode waves caused by thermal electron anisotropy is studied. Based on MHD equations, the nonlinear schrödinger equation (NLSE) that describes the nonlinear modulation of whistler waves is derived by Using the Krylov-Bogoliubov-Mitropolsky (KBM) method. The condition for wave modulation instability is obtained from the loss cone distribution function of thermal electron anisotropy, revealing that the nonlinear growth of the waves tends towards electron perpendicular temperature anisotropy. By setting up continuous background waves and introducing small ion low frequency perturbations, we find that the change in the amplitude of the modulated wave is related with wave number. This finding has been validated through simulations that align with our analytical results. Additionally, we also calculate the maximum amplitude of the wave with loss cone angle and times, which revealed that the electron vertical temperature anisotropy will lead to the modulation instability of the whistler wave. This further confirms the occurrence of the modulation instability of the whistler wave in laboratory plasmas and strengthens their credibility.

A hybrid Eulerian-Lagrangian Vlasov method for nonlinear wave-particle interaction in weakly inhomogeneous magnetic field

We present a hybrid Eulerian-Lagrangian (HEL) Vlasov method for nonlinear resonant wave-particle interactions in weakly inhomogeneous magnetic field. The governing Vlasov equation is derived from a recently proposed resonance tracking Hamiltonian theory. It gives the evolution of the distribution function with a scale-separated Hamiltonian that contains the fast-varying coherent wave-particle interaction and slowly-varying motion about the resonance frame of reference. The hybrid scheme solves the fast-varying phase space evolution on Eulerian grid with an adaptive time step and then advances the slowly-varying dynamics by Lagrangian method along the resonance trajectory. We apply the HEL method to study the frequency chirping of whistler-mode chorus wave in the magnetosphere and the self-consistent simulations reproduce the chirping chorus wave and give high-resolution phase space dynamics of energetic particles at low computational cost. The scale-separated HEL approach could provide additional insights of the wave instabilities and wave-particle nonlinear coherence compared to the conventional Vlasov and particle-in-cell methods.

A multi-satellite survey scheme for addressing open questions on the Earth’s outer radiation belt dynamics

The Earth’s outer radiation belt is highly dynamic, containing relativistic electron fluxes that can increase by several orders of magnitude during magnetospheric disturbances. This greatly increases the likelihood of spacecraft malfunction or failure and significantly influences the solar-terrestrial system’s energy and mass coupling, highlighting the importance of fully understanding the mechanisms governing these dynamics from both theoretical and practical perspectives. Although many theories have been proposed, further research is essential to quantify the specific contributions of different dynamic mechanisms for improving space weather forecasting. To address this, observations of the outer radiation belt with high spatial–temporal resolution to distinguish the spatial and temporal variations are essential. We introduce a 10-CubeSat constellation survey scheme in the geosynchronous transfer orbit (GTO) to achieve this required observation. Three baseline instruments are proposed to be employed: the high energy electron detector (HEED), the search coil wave detector (SCWD), and the magnetometer (MAG). Two groups of physical processes will be investigated: wave-particle interactions involving charged particles interacting with whistler-mode waves, electromagnetic ion cyclotron (EMIC) waves, and ultra-low frequency (ULF) waves; and radial transport encompassing shock-induced injections, substorm injections, storm convection and magnetopause shadowing. The performance parameters of instruments and platform of the constellation are presented. Additionally, aligned with the concept of constellation survey, we outline the COSPAR-coordinated space program, COnstellation of Radiation BElt Survey (CORBES), which will provide a crucial scientific contribution in the absence of the Van Allen Probes. The program’s excellent observational capability enables a comprehensive understanding of the underlying physical mechanisms governing the outer radiation belt dynamics and improved space weather forecasting.

Whistler-mode waves in the tail of Mercury’s magnetosphere: A numerical study

Context. Mercury presents a highly dynamic, small magnetosphere in which magnetic reconnection plays a fundamental role. Aim. We aim to model the global characteristics of magnetic reconnection in the Hermean environment. In particular, we focus on waves observed during the third BepiColombo flyby. Method. In this work, we used two fully kinetic three-dimensional (3D) simulations carried out with the iPIC3D code, which models the interaction of the solar wind with the Hermean magnetosphere. For the simulations, we used southward solar wind conditions that allow for a maximum magnetic coupling between the solar wind and the planet. Results. Our simulations show that a significant wave activity, triggered by magnetic reconnection, develops near the diffusion region in the magnetotail and propagates at large scales in the night-side magnetosphere. We see an increase in electron temperature close to the diffusion region and we specifically observe narrowband whistler waves developing near the reconnection region. These waves propagate nearly parallel to the magnetic field at frequency f ∼ 0.5fce. In addition to the electromagnetic component, these waves also exhibit an electrostatic one. Furthermore, we observe a strong electron temperature anisotropy, suggesting it plays a role as the source of these waves.

Electromagnetic ion cyclotron emission from ion-scale magnetic holes

Ion-scale magnetic holes are nonlinear plasma structures commonly observed in the solar wind and Earth's magnetosphere. These holes are characterized by the magnetic field depletion filled by hot, transversely anisotropic ions and electrons and are likely formed during the nonlinear stage of ion mirror instability. Due to the plasma thermal anisotropy within magnetic holes, they serve as a host of electromagnetic ion cyclotron waves, whistler-mode waves, and electron cyclotron harmonic waves. This makes magnetic holes an important element of the Earth's inner magnetosphere, where electromagnetic waves generated within may strongly contribute to energetic ion and electron scattering. Such scattering, however, will modify the hot-ion distribution that is trapped within magnetic holes and responsible for the magnetic field stress balance. Therefore, hot ion scattering within magnetic holes likely determines the hole lifetime. In this study, we investigate how ion scattering by electromagnetic waves affects the stress balance and lifetime of magnetic holes. For illustration, we used typical characteristics of magnetic holes, ion populations, and ion cyclotron waves observed in the Earth's magnetosphere. We have demonstrated that ion distribution isotropization via scattering by waves does not change significantly magnetic hole magnitude, but ion losses due to scattering into the atmosphere may limit the hole life-times to 10–30 min in the Earth's inner magnetosphere.

Statistical Properties of Whistler-mode Waves in the Dayside Terrestrial Space: MMS Observations

Whistler-mode waves have been extensively observed and investigated in terrestrial space. In this study, we present the dynamic response of whistler-mode waves to different solar wind conditions in the dayside terrestrial space based on Magnetospheric Multiscale (MMS) data. Statistical results show that the occurrence rate, amplitudes, and corresponding electron temperature anisotropy of whistler-mode waves increase with P sw in the dayside terrestrial space, which is attributed to the compression of magnetic fields in these magnetosheath and outer magnetosphere. Furthermore, whistler-mode waves under the southward interplanetary magnetic fields (IMFs) show a higher occurrence rate than that under the northward IMFs, mostly corresponding to T e⊥/T e∥ > 1, and have a higher occurrence rate during quasi-radial IMFs. These results present that whistler-mode waves in these magnetosheath and outer magnetosphere are also modulated by the solar wind as clearly as the inner magnetosphere. This work advanced our understanding in the solar–terrestrial interaction.

Microscopic structure of electromagnetic whistler wave damping by kinetic mechanisms in hot magnetized Vlasov plasmas

Electromagnetic transverse perturbations propagating parallel to the external magnetic field in a warm electron plasma, specifically the warm electron whistler-mode waves, are simulated in Maxwellian as well as κ distributed (with energetic tail) electrons. The Vlasov-Maxwell phase-space continuum simulations are applied to the stable and unstable (i.e. isotropic and anisotropic) VDFs. The variation of real frequency from both numerical solution of dispersion relation and simulations show limited sensitivity to electron temperature in low wave-number regime as compared to high wave number regime, however the opposite holds for the imaginary frequency or the decay rate. The analytically predicted reduction in the decay rate of the whistler-mode with increasing electron temperature is recovered by the Vlasov-Maxwell simulations. The phase-space portraits of the these cases show that after the linear damping phase of the evolution, the particles are trapped in the wave magnetic field leading to the wave amplitudes oscillating about a mean value which follow the theoretical analysis. Palmadesso and Schmidt (1971) Physics of Fluids 14, 1411.

Radiation of twisted waves from a phased array of loop antennas in a resonant magnetoplasma

A study is made of the radiation from a phased array of circular loop antennas in a resonant magnetoplasma. The loops are assumed to have a finite radius and be located on a circumference in such a manner that their axes are aligned with a static magnetic field superimposed on the plasma. The emphasis is placed on determining the total radiated power of such an array and the partial powers going to different azimuthal field harmonics. For these quantities, rigorous integral representations are obtained using an expansion of the excited field in terms of cylindrical vector eigenfunctions of a magnetized plasma medium. Numerical results are reported for the radiation characteristics of the phased array in the whistler frequency range under conditions of the Earth's ionosphere. It is shown that an appropriately phased array is capable of selectively exciting waves with the desired helicity of the phase front and can be useful as a source of twisted whistler-mode waves in a magnetoplasma.

Unusually Low-frequency Whistler-mode Waves and Their Association with High-energy Protons Observed Upstream of Martian Bow Shock

Whistler-mode waves upstream of planetary bow shock are often referred to as “1-Hz waves” due to the center of their observed frequency range being at ∼1 Hz. A series of whistler-mode waves were observed upstream of the Martian bow shock by MAVEN on 2015 August 14, with unusually low frequencies centered at ∼0.4 Hz. These waves were accompanied (though not synchronized) by the significant flux enhancement of high-energy protons up to ∼10 keV. By analyzing the wave dispersion property and the wave–particle interaction condition, we find that the observed whistler-mode waves have the potential of resonating with protons of ∼1 keV with large pitch angles up to nearly perpendicular to the background magnetic field, thereby providing a feasible means of accounting for proton acceleration. Our results indicate the possible origin of energized protons in the Martian environment through the interaction with whistler-mode waves, and their potential relationship with the unique upstream conditions.

Statistical Distribution of Whistler Mode Waves in the Martian Induced Magnetosphere Based on MAVEN Observations

AbstractWhistler mode waves are a common type of electromagnetic waves in the Martian induced magnetosphere. Using high‐resolution magnetic field data from the Magnetometer (MAG) instrument onboard Mars Atmosphere and Volatile Evolution (MAVEN) from October 2014 to November 2022, we perform a detailed analysis of the statistical distribution of the occurrence rate, averaged amplitude, peak frequency, wave normal angle and ellipticity of left‐hand and right‐hand polarized whistler mode waves in the Martian induced magnetosphere. Our results show that whistler mode waves are mainly observed in the subsolar and magnetic pileup region, with the occurrence rate of right‐hand mode waves higher than that of left‐hand mode waves. The averaged wave amplitude ranges from 0.02 to 0.13 nT and peak wave frequency ranges from 2 to 9 Hz. We also find that the wave normal angles for both left‐hand and right‐hand polarized whistler waves are relatively larger in the subsolar region and magnetic pileup region where the corresponding wave ellipticity is closer to the linear polarization. Our results are valuable to in‐depth understanding of the generation mechanism of whistler mode waves as well as their contributions to the electron dynamics in the Martian induced magnetosphere.

Cross‐Scale Modeling of Storm‐Time Radiation Belt Variability

AbstractDuring geomagnetic storms relativistic outer radiation belt electron flux exhibits large variations on rapid time scales of minutes to days. Many competing acceleration and loss processes contribute to the dynamic variability of the radiation belts; however, distinguishing the relative contribution of each mechanism remains a major challenge as they often occur simultaneously and over a wide range of spatiotemporal scales. In this study, we develop a new comprehensive model for storm‐time radiation belt dynamics by incorporating electron wave‐particle interactions with parallel propagating whistler mode waves into our global test‐particle model of the outer belt. Electron trajectories are evolved through the electromagnetic fields generated from the Multiscale Atmosphere‐Geospace Environment (MAGE) global geospace model. Pitch angle scattering and energization of the test particles are derived from analytical expressions for quasi‐linear diffusion coefficients that depend directly on the magnetic field and density from the magnetosphere simulation. Using a study of the 17 March 2013 geomagnetic storm, we demonstrate that resonance with lower band chorus waves can produce rapid relativistic flux enhancements during the main phase of the storm. While electron loss from the outer radiation belt is dominated by loss through the magnetopause, wave‐particle interactions drive significant atmospheric precipitation. We also show that the storm‐time magnetic field and cold plasma density evolution produces strong, local variations of the magnitude and energy of the wave‐particle interactions and is critical to fully capturing the dynamic variability of the radiation belts caused by wave‐particle interactions.

Electron Heating by Magnetic Pumping and Whistler-mode Waves

The investigation of mechanisms responsible for the heating of cold solar wind electrons around the Earth’s bow shock is an important problem in heliospheric plasma physics because such heating is vitally required to run the shock drift acceleration at the bow shock. The prospective mechanism for electron heating is magnetic pumping, which considers electron adiabatic (compressional) heating by ultralow-frequency waves and simultaneous scattering by high-frequency fluctuations. Existing models of magnetic pumping have operated with external sources of such fluctuations. In this study, we generalize these models by introducing the self-consistent electron scattering by whistler-mode waves generated due to the anisotropic electron heating process. We consider an electron population captured within a magnetic trap created by ultralow-frequency waves. Periodical adiabatic heating and cooling of this population drives the generation of whistler-mode waves scattering electrons in the pitch-angle space. The combination of adiabatic heating and whistler-driven scattering provides electron acceleration and the formation of a suprathermal electron population that can further participate in the shock drift acceleration.

Large-scale magnetic field oscillations and their effects on modulating energetic electron precipitation

In this study, we present simultaneous multi-point observations of magnetospheric oscillations on a time scale of tens of minutes (forced-breathing mode) and modulated whistler-mode chorus waves, associated with concurrent energetic electron precipitation observed through enhanced BARREL X-rays. Similar fluctuations are observed in X-ray signatures and the compressional component of magnetic oscillations, spanning from ∼9 to 12 h in MLT and 5 to 11 in L shell. Such magnetospheric oscillations covering an extensive region in the pre-noon sector have been suggested to play a potential role in precipitating energetic electrons by either wave scattering or loss cone modulation, showing a high correlation with the enhancement in X-rays. In this event, the correlation coefficients between chorus waves (smoothed over 8 min), ambient magnetic field oscillations and X-rays are high. We perform an in-depth quasi-linear modeling analysis to evaluate the role of magnetic field oscillations in modulating energetic electron precipitation in the Earth’s magnetosphere through modulating whistler-mode chorus wave amplitude, resonance condition between chorus waves and electrons, as well as loss cone size. Model results further show that the modulation of chorus wave amplitude plays a dominant role in modulating the electron precipitation. However, the effect of the modulation in the resonant energy between chorus waves and energetic electrons due to the background magnetic field oscillations cannot be neglected. The bounce loss cone modulation, affected by the magnetic oscillations, has little influence on the electron precipitation modulation. Our results show that the low frequency magnetospheric oscillations could play a significant role in modulating the electron precipitation through modulating chorus wave intensity and the resonant energy between chorus waves and electron.

Nonlinear Landau resonant interaction between whistler waves and electrons: Excitation of electron-acoustic waves

Electron-acoustic waves (EAWs) as well as electron-acoustic solitary structures play a crucial role in thermalization and acceleration of electron populations in Earth's magnetosphere. These waves are often observed in association with whistler-mode waves, but the detailed mechanism of EAW and whistler wave coupling is not yet revealed. We investigate the excitation mechanism of EAWs and their potential relation to whistler waves using particle-in-cell simulations. Whistler waves are first excited by electrons with a temperature anisotropy perpendicular to the background magnetic field. Electrons trapped by these whistler waves through nonlinear Landau resonance form localized field-aligned beams, which subsequently excite EAWs. By comparing the growth rate of EAWs and the phase mixing rate of trapped electron beams, we obtain the critical condition for EAW excitation, which is consistent with our simulation results across a wide region in parameter space. These results are expected to be useful in the interpretation of concurrent observations of whistler-mode waves and nonlinear solitary structures and may also have important implications for investigation of cross-scale energy transfer in the near-Earth space environment.

Electron precipitation caused by intense whistler-mode waves: combined effects of anomalous scattering and phase bunching

Resonant interactions with whistler-mode waves are a crucial mechanism that drives the precipitation of energetic electrons. Using test particle simulations, we investigated the impact of nonlinear interactions of whistler-mode waves on electron precipitation across a broad energy range (10 keV- 1 MeV). Specifically, we focused on the combined effects of conventional phase bunching and anomalous scattering, which includes anomalous trapping and positive bunching. It is shown that anomalous scattering transports electrons away from the loss cone and the only process directly causing precipitation in the nonlinear regime is the phase bunching. We further show that their combined effects result in a precipitation-to-trapped flux ratio lower than the quasilinear expectations in a quasi-equilibrium state. Additionally, we calculated the diffusion and advection coefficients associated with the nonlinear trapping and bunching processes, which are vital for understanding the underlying mechanisms of the precipitation. Based on these coefficients, we characterized the phase bunching boundary, representing the innermost pitch angle boundary where phase bunching can occur. A further analysis revealed that electrons just outside this boundary, rather than near the loss cone, are directly precipitated, while electrons within the boundary are prevented from precipitation due to anomalous scattering. Moreover, we demonstrated that the regime of dominant nonlinear precipitation is determined by the combination of the phase bunching boundary and the inhomogeneity ratio. This comprehensive analysis provides insights into the nonlinear effects of whistler-mode waves on electron precipitation, which are essential for understanding physical processes related to precipitation, such as microbursts, characterized by intense and bursty electron precipitation.

Observational Evidence of the Four‐Wave Interaction Between Magnetospheric Whistler Mode Waves

AbstractWhistler mode wave is a crucial emission which can significantly affect the electron dynamics in the magnetosphere. The nonlinear three‐wave interaction between whistler mode waves has been frequently observed, while the four‐wave interaction between these waves is seldom reported. Here, we present two multiband whistler mode wave events by Van Allen Probes, in which the relatively weak wave bands occur exactly corresponding to the strong wave bands. We find that the frequencies of the weak and strong bands satisfy the frequency matching conditions of the four‐wave interaction, and the wave normal angles of the weak bands are almost within the possible ranges calculated from the wave vector matching conditions. Additionally, the cross‐correlation coefficients between the amplitudes of the weak bands and that of strong bands approach 0.80. These results indicate that the weak bands are very likely to be produced by the four‐wave interaction between whistler mode waves. Similar to the three‐wave interaction, the four‐wave interaction can extend the frequency of whistler mode waves from close to 0.5fce to a wider range in both the lower (0.26fce) and upper (0.78fce) bands, and thus potentially play an important role in the electron dynamics.

Electron resonant interaction with whistler-mode waves around the Earth's bow shock. II: The mapping technique

Electron resonant scattering by high-frequency electromagnetic whistler-mode waves has been proposed as a mechanism for solar wind electron scattering and pre-acceleration to energies that enable them to participate in shock drift acceleration around the Earth's bow shock. However, observed whistler-mode waves are often sufficiently intense to resonate with electrons nonlinearly, which prohibits the application of quasi-linear diffusion theory. This is the second of two accompanying papers devoted to developing a new theoretical approach for quantifying the electron distribution evolution subject to multiple resonant interactions with intense whistler-mode wave-packets. In the first paper, we described a probabilistic approach, applicable to systems with short wave-packets. For such systems, nonlinear resonant effects can be treated by diffusion theory, but with diffusion rates different from those of quasi-linear diffusion. In this paper, we generalize this approach by merging it with a mapping technique. This technique can be used to model the electron distribution evolution in the presence of significantly non-diffusive resonant scattering by intense long wave-packets. We verify our technique by comparing its predictions with results from a numerical integration approach.

Electron resonant interaction with whistler-mode waves around the Earth's bow shock I: The probabilistic approach

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.

Energy Transfer Between Various Electron Populations Via Resonant Interaction With Whistler Mode Wave

AbstractElectron energization in the Earth's radiation belts caused by resonant interaction with whistler mode waves is currently under intense investigation. When the waves are excited due to cyclotron instability in collisionless plasma, that is, when the energy source for the waves is the free energy of unstable electron distribution, particle energization by excited waves is nothing but energy transfer from one group of electrons to another mediated by the waves. An example of such a process is considered in which a quasi‐monochromatic whistler mode wave packet with the frequency and the wave normal angle corresponding to the maximum growth rate is excited at the equator. Since the maximum growth rate corresponds to parallel propagating wave, only the first cyclotron resonance particles play a part in this excitation. While propagating from the equator toward the Earth, the wave normal vector becomes more and more oblique, and all cyclotron resonances, in particular, Landau resonance come into play. Wave‐particle interaction at Landau resonance leads to the wave damping and the corresponding particle energization on the average. Moreover, we show that the mean square variation of resonant particle energy greatly exceeds the average value, thus, the energy increase of some particles is much larger than the Landau resonance particles get from the wave on the average. This means that the exchange of energy between different groups of particles through a wave is a more efficient process than the amplification or damping of a wave due to its resonant interaction with particles.

Particle-in-Cell Simulations of Sunward and Anti-sunward Whistler Waves in the Solar Wind

We present particle-in-cell simulations of a combined whistler heat flux and temperature anisotropy instability that is potentially operating in the solar wind. The simulations are performed in a uniform plasma and initialized with core and halo electron populations typical of the solar wind beyond about 0.3 au. We demonstrate that the instability produces whistler-mode waves propagating both along (anti-sunward) and opposite (sunward) to the electron heat flux. The saturated amplitudes of both sunward and anti-sunward whistler waves are strongly correlated with their initial linear growth rates, , where for typical electron betas we have 0.6 ≲ ν ≲ 0.9. We show that because of the relatively large spectral width of the whistler waves, the instability saturates through the formation of quasi-linear plateaus around the resonant velocities. The revealed correlations of whistler wave amplitudes and spectral widths with electron beta and temperature anisotropy are consistent with solar wind observations. We show that anti-sunward whistler waves result in an electron heat flux decrease, while sunward whistler waves actually lead to an electron heat flux increase. The net effect is the electron heat flux suppression, whose efficiency is larger for larger electron betas and temperature anisotropies. The electron heat flux suppression can be up to 10%–60% provided that the saturated whistler wave amplitudes exceed about 1% of the background magnetic field. The experimental applications of the presented results are discussed.