Propagating Whistler Mode Waves Research Articles

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.

Experimental studies on the propagation of whistler-mode waves in a magnetized plasma structure with a non-uniform density

Propagation of whistler-mode waves in a magnetized plasma structure is investigated in the Keda linear magnetized plasma device. The magnetized plasma structure has its density peak in the center, and the background magnetic field is homogeneous along the axial direction. A whistler-mode wave with a frequency of 0.3 times of electron cyclotron frequency (f ce) is launched into the plasma structure. The wave normal angle (WNA) is about 25°, and the wavefront exhibits a wedge structure. During propagation of the whistler wave, both the propagating angle and WNA slowly approach zero, and then the wave is converged toward the center of the structure. Therefore, the wave tends to be trapped in the plasma structure. The results present observational evidence of the propagation of a whistler-mode wave trapped in the enhanced-density structure in a laboratory plasma. This trapping effect is consistent with satellite observations in the inner magnetosphere.

Ray-tracing simulations of whistler-mode wave propagation in different rescaled dipole magnetic fields

Ray-tracing simulations of whistler-mode wave propagation in different rescaled dipole magnetic fields

Ray-tracing simulations of whistler-mode wave propagation in different rescaled dipole magnetic fields

Kinetic simulation is a powerful tool to study the excitation and propagation of whistler-mode waves in the Earth’s inner magnetosphere. This method typically applies a scaled-down dipole magnetic field to save computational time. However, it remains unknown whether whistler wave propagation in the scaled-down dipole field is consistent with that in the realistic dipole field. In this work, we develop a ray-tracing code with a scalable dipole magnetic field to address this concern. The simulation results show that parallel whistler waves at different frequencies gradually become oblique after leaving the equator and propagate in different raypaths in a dipole magnetic field. During their propagation, the higher frequency waves tend to have larger wave normal angles at the same latitude. Compared with the wave propagation in a realistic dipole field, the wave raypath and wave normal remain the same, whereas the wave amplification or attenuation is smaller because of the shorter propagation time in a scaled-down dipole field. Our study provides significant guidance for kinetic simulations of whistler-mode waves.

Two‐Dimensional Full‐Wave Simulation of Whistler Mode Wave Propagation Near the Local Lower Hybrid Resonance Frequency in a Dipole Field

AbstractWe investigate the propagation of whistler mode waves near the local lower hybrid resonance (LHR) frequency in a dipole field with a two‐dimensional full‐wave model. First, we run a simulation in which a parallel whistler with frequency above the local LHR frequency is launched at the equatorial region in electron plasma. We find that whistler emission propagates along the dipole field line to a high latitude, turns quasi‐electrostatic where the wave frequency is close to the local LHR frequency, and continues to propagate until being absorbed. Then, the proton response is considered. We find that (1) a quasi‐electrostatic whistler reflects where the wave frequency is below the local LHR frequency and propagates to a larger L‐shell and lower latitude, (2) a strong standing‐wave pattern is formed in the LHR reflection region, and (3) the whistler emission turns from right‐hand circularly polarized to linearly polarized near the reflection region. Finally, we run a simulation in which a quasi‐electrostatic whistler is launched at a high latitude with a small‐scale density irregularity added as a depletion to the background plasma. We find that a small portion of quasi‐electrostatic whistler energy can be coupled to a parallel whistler, which can propagate to a much lower altitude while most of the wave energy experiences LHR reflection. Moreover, the mode coupling depends on the transverse and longitudinal sizes of the density irregularity. This makes a possible explanation of ground observations of nonducted whistler emission, which could have been reflected in the high‐latitude ionosphere and magnetosphere.

Two Dimensional Full-wave Simulation of Whistler-mode Wave Propagation Near the Local Lower Hybrid Resonance Frequency in a Dipole Field

Two Dimensional Full-wave Simulation of Whistler-mode Wave Propagation Near the Local Lower Hybrid Resonance Frequency in a Dipole Field

Generation of oblique electromagnetic wave by hot injection electron beam with parallel AC electric field in the magnetosphere of Saturn

The Cassini radio and plasma wave investigation is designed to study radio emissions, plasma waves, thermal plasma, and dust in the vicinity of Saturn. Plasma particles, waves and fields are the major factors on which present knowledge about Saturn’s magnetosphere is based from the three flyby missions. For the present work, our examination is focused to study those waves who have frequency lower than electron cyclotron frequency in Saturnian magnetosphere. In this paper, we investigate the growth rate of whistler mode waves in magneto-plasma of Saturn. A dispersion relation for parallel propagating whistler mode waves has been applied to the magnetosphere of Saturn. The effect of electron density, temperature anisotropy, number density and A.C frequency on the temporal growth rate of the whistler mode emission is studied. For the given magnetic field and external electric field configuration, the general dispersion relation has been derived.

Analytical study of Whistler mode waves for relativistic plasma with AC electric field in inner magnetosphere of Saturn

The population of plasma present in the rotationally dominated inner magnetosphere of Saturn is identified by the observed plasma waves in the magnetosphere. Whistler mode emissions along with electrostatic cyclotron emissions often with harmonics are a common feature of Saturnian inner magnetosphere. We present the outcomes of a study of very large amplitude Whistler mode waves characteristics inside the magnetosphere of radial distance of less than 15 $$\hbox {R}_{\mathrm{s}}$$ . Whistler mode waves with temperature anisotropy in the magnetosphere of Saturn have been studied in the present work. Observations of Whistler mode emissions from Cassini Radio and Plasma Wave Science instruments have been obtained. Whistler mode waves were investigated using the method of characteristic solution by kinetic approach, in the presence of AC field. The observations made by space probes Voyager 1 and 2 and Cassini, launched by NASA, showed that charged particles are trapped in planet’s magnetic field lines. In 2004, the Cassini encounter with Saturn revealed that magnetosphere of Saturn exhibits Maxwellian distribution. So, the dispersion relation, real frequency and growth rate were evaluated using ring distribution function. Effect of AC frequency, temperature anisotropy, energy and number density of particles was found. Temperature anisotropies greater than one ( $$\hbox {T}_\bot {/}\hbox {T}_{\Vert } >1$$ ) and pancake-like distribution can generate Whistler mode emissions of the warmer plasma population. The study also extended to oblique propagation of Whistler mode waves in presence of AC electric field. However, when relativistic factor $${{\upbeta } }=\sqrt{\hbox {1}-\frac{\hbox {v}^{\mathrm {2}}}{\hbox {c}^{\mathrm {2}}}}$$ increases, growth rate decreases. Through comprehensive mathematical analysis, it was found that when Whistler mode waves propagate parallel to the intrinsic magnetic field of Saturn, its growth is enhanced more than in the case of oblique propagation. Results are also discussed while computing the rate with which the wave grows for a particular wavenumber.

The Acceleration of Electrons to High Energies Over the Jovian Polar Cap via Whistler Mode Wave‐Particle Interactions

AbstractUpward traveling electrons with energies from tens of kiloelectron volts to several megaelectron volts have been observed over the Jovian polar regions in association with intense upward propagating whistler mode waves. The electrons have a power law‐like energy distribution, indicative of a stochastic acceleration process. The energy flux of the upward propagating whistler mode waves is comparable to and strongly correlated with the energy flux of the upward traveling energetic electrons, suggesting that the whistler mode waves may be accelerating the electrons. We propose that a downward field‐aligned current over the polar cap generates strong downward parallel electric fields and associated upward electron beams in the low‐density regions of Jupiter's upper ionosphere, a mechanism similar to the formation of inverted‐Vs in Earth's auroral regions. At Jupiter, the upward‐traveling electron beams produce intense upward propagating whistler mode emissions over a broad frequency range, similar to upward propagating auroral hiss at Earth. As the whistler mode waves propagate upward out of the inverted‐V source region, the waves are absorbed by the plasma, thereby accelerating the electrons. We attribute the stochastic power law‐like energy spectrum of the accelerated electrons to the development of Hamiltonian chaos (velocity space diffusion), the signature of which is indicated by the occurrence of spiky soliton‐like variations in the whistler mode electric fields. Acceleration to high energies may be facilitated by the rapid increase in the phase velocity of the whistler mode waves with increasing altitude, which could accelerate some of the electrons trapped in the wavefield to very high relativistic energies.

Nonlinear Evolution of Counter‐Propagating Whistler Mode Waves Excited by Anisotropic Electrons Within the Equatorial Source Region: 1‐D PIC Simulations

AbstractNonlinear physical processes related to whistler mode waves are attracting more and more attention for their significant role in reshaping whistler mode spectra in the Earth's magnetosphere. Using a 1‐D particle‐in‐cell simulation model, we have investigated the nonlinear evolution of parallel counter‐propagating whistler mode waves excited by anisotropic electrons within the equatorial source region. In our simulations, after the linear phase of whistler mode instability, the strong electrostatic standing structures along the background magnetic field will be formed, resulting from the coupling between excited counter‐propagating whistler mode waves. The wave numbers of electrostatic standing structures are about twice those of whistler mode waves generated by anisotropic hot electrons. Moreover, these electrostatic standing structures can further be coupled with either parallel or antiparallel propagating whistler mode waves to excite high‐k modes in this plasma system. Compared with excited whistler mode waves, these high‐k modes typically have 3 times wave number, same frequency, and about 2 orders of magnitude smaller amplitude. Our study may provide a fresh view on the evolution of whistler mode waves within their equatorial source regions in the Earth's magnetosphere.

Numerical Simulation of Whistler Waves in Magnetized Plasma with Small-Scale Irregularities

Propagation of whistler-mode waves in magnetized plasma in the presence of small-scale field-aligned irregularities with enhanced or depressed plasma density is simulated numerically. The numerical experiments have demonstrated the effect of guided propagation of whistler-mode waves in plasma regions occupied by irregularities with transverse dimensions smaller than the whistler wavelength in uniform plasma. It is shown that not only individual irregularities but also the entire modified region, which serves as a specific guiding structure, exhibit waveguide properties.

Study of Oblique Propagating Whistler Mode Waves in Presence of Parallel DC Electric Field in Magnetosphere of Saturn

In this paper whistler mode waves have been investigated in magnetosphere of Saturn. The derivation for perturbed distribution function, dispersion relation and growth rate have been determined by using the method of characteristic and kinetic approach. Analytical expressions for growth rate and real frequency of whistlers propagating oblique to magnetic field direction are attained. Calculations have been performed at 6 radial distances in plasma sheet region of Saturn’s magnetosphere as per data provided by Cassini. Work has been extended for bi-Maxwellian as well as Loss-cone distribution function. Parametric analysis show that temperature anisotropy, increase in number density, energy density and angle of propagation increases the growth rate of whistler waves along with significant shift in wave number. In case of Loss-cone distribution, increase in growth rate of whistlers is significantly more than for bi-Maxwellian distribution function. Generation of second harmonics can also be seen in the graphs plotted. It is concluded that parallel DC field stabilizes the wave and temperature anisotropy, angle of propagation, number density and energy density of electrons enhances the growth rate. Thus the results are of importance in analyzing observed VLF emissions over wide spectrum of frequency range in Saturnian magnetosphere. The analytical model developed can also be used to study various types of instabilities in planetary magnetospheres.

Polarization of obliquely propagating whistler mode waves based on linear dispersion theory

We discuss the variation of whistler mode wave electric and magnetic field polarizations as a function of propagation angle θkB0 with respect to the background magnetic field B0 using linear kinetic dispersion theory. The circular polarization of the whistler mode wave magnetic field at all propagation angles [Verkhoglyadova et al. J. Geophys. Res. 115, A00F19 (2010); P. M. Bellan, Phys. Plasmas 20, 082113 (2013)] is found to be valid only for cold plasma or low plasma beta conditions. The wave magnetic fields, on a plane orthogonal to the wave vector k, tend to become elliptically polarized with an increase in propagation angles for high beta plasma background conditions (βe≥0.1). The electric field polarization plane may not be orthogonal to wave vector k, especially for oblique propagations, and is found to be circularly polarized only at parallel propagation direction as reported by Verkhoglyadova et al. [J. Geophys. Res. 115, A00F19 (2010)] and Bellan [Phys. Plasmas 20, 082113 (2013)]. They become elliptically polarized with an increase in propagation angles. This is valid for arbitrary plasma beta conditions. The results are also analysed and compared for an inner magnetospheric plasma model with three electron species. The two major angles, Gendrin and resonance cone angles, are also discussed.

Quasiperiodic VLF emissions with short‐period modulation and their relationship to whistlers: A case study

AbstractWe study properties of quasiperiodic (QP) VLF emissions recorded on 24 December 2011 during the VLF campaign in northern Finland. The main attention is paid to interrelationships between different characteristic periods in the QP spectra. In particular, we analyze regular variations in the QP repetition intervals (1–10 min) during the event from 15:30 to 22 UT, their changes during substorms, and short periodic (several second) modulation observed within separate QP elements. We explained the variations of periods of QP emissions in terms of the model of auto‐oscillation regime of the cyclotron instability in the magnetosphere. During the considered event lasting about 7 h we observed a regular increase in the time intervals between the QP elements. We relate this increase with weakening of the magnetospheric source of energetic electrons. Significant variations in the QP period occurred during substorms. These variations can be due to a substorm‐related increase in the energetic‐electron flux and/or due to the precipitation of these electrons into the ionosphere which changes the reflection coefficient of VLF waves. We analyze the fine structure of QP element spectra and reveal the periods related to the time scales of guided propagation of whistler mode waves along the magnetic field line, which suggests that ducted propagation regime took place for the QP emissions. The periods were about 6–9 s for frequencies 1.2–4 kHz, respectively, which was similar to the period of almost simultaneously observed two‐hop whistlers. In the low‐frequency part of QP spectra periodic emissions with shorter periods of about 3 s were observed. Analysis of fine structure of QP elements shows that their formation is affected by both linear effects (i.e., group‐velocity dispersion) and quasi‐linear effects related to the modification of the energetic electron distribution function. It allows us to observe the transition from purely linear to quasi‐linear regime of wave‐particle interactions in the spectra of these short periodic emissions. The nonlinear regime can be understood in terms of passive mode locking in magnetospheric cyclotron maser.

Narrowband frequency-drift structures in solar type IV bursts

We have established the Zao Solar Radiospectrograph (ZSR), a new solar radio observation system, at the Zao observatory of Tohoku University, Japan. We observed narrowband fine structures with type IV bursts with ZSR on 2 and 3 November 2008. The observed fine structures are similar to fiber bursts in terms of the drift rates and the existence of emission and absorption stripes. Statistical analysis of the drift rates, however, shows that the observed fine structures are different from the ordinary fiber bursts as regards the sense and the magnitude of their drift rates. First, the observed drift rates include both positive and negative rates, whereas ordinary fiber bursts are usually characterized by negative drift rates. Second, the absolute values of the observed drift rates are tens of MHz s−1, whereas the typical drift rate of fiber bursts at 325 MHz is approximately −9 MHz s−1. In addition, all fine structures analyzed have narrow emission bands of less than 17 MHz. We also show that the observed narrowband emission features with drift rates of approximately 40 MHz s−1 can be interpreted as the propagation of whistler-mode waves, which is the same process as that underlying fiber bursts.

Relativistic electron microbursts associated with whistler chorus rising tone elements: GEMSIS‐RBW simulations

Relativistic electron microbursts, which are bursty enhancements of the precipitation of relativistic electrons, are often observed by low‐altitude satellite measurements. These microbursts are likely to play an important role in high‐energy electron flux loss in the outer radiation belt. Some observations suggest that whistler chorus waves are a cause of relativistic electron microbursts. First, we derived the relativistic time of flight model considering the propagation of whistler mode waves, and then investigated characteristics of the precipitations. We found that relativistic electron precipitation has a positive energy dispersion at low altitude. The duration of electron precipitation by one whistler chorus element decreases when the energy of the precipitated electrons is increased. We then performed three‐dimensional test particle simulation with a newly developed wave‐particle interaction model using realistic plasma parameters in the inner magnetosphere. The test particle simulation showed for the first time that the resonant interactions with whistler chorus elements at high‐latitudes produce bursty enhancements of relativistic electron precipitation, thus confirming the results of the TOF analysis. A few Hz modulations are embedded in the precipitating electron flux variations, which is associated with the repetition period of the whistler chorus elements. The simulation results indicate that microbursts of relativistic electrons of the outer belt are caused by chorus wave‐particle interactions at high latitudes and a series of rising tone elements of chorus waves produce a few Hz modulation of microbursts observed by the SAMPEX satellite.

Comparison of bounce‐averaged quasi‐linear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations

Quasi‐linear bounce‐averaged diffusion coefficients for interactions between electrons and parallel propagating whistler waves in a dipole field are compared with test particle simulations. We solve equations of motion for a large number of electrons interacting with waves with a Gaussian distribution of wave power. For broadband and small amplitude waves, which are assumed by the quasi‐linear analysis, our test particle simulation results agree well with quasi‐linear theory predictions. We then demonstrate the effect of the wave amplitude on diffusion coefficients. We show that as the amplitude increases, the bounce‐averaged quasi‐linear diffusion coefficients become invalid. Critical wave amplitudes for the breakdown of the bounce‐averaged diffusion coefficients for a range of energies and pitch angles are calculated for the set of wave parameters we used. Finally, we investigate the effect of wave bandwidth on bounce‐averaged diffusion coefficients. Consistent with a previous theoretical prediction, bounce‐averaged quasi‐linear diffusion coefficients are still valid for narrowband waves, as long as the wave amplitude is small. When the amplitude of the narrowband wavefield increases, nonlinear effects such as phase‐bunching and trapping become dominant and correspondingly quasi‐linear theory becomes invalid. Our results demonstrate the validity of applying quasi‐linear theory to interactions between electrons and small amplitude plasma waves in the radiation belt.

Propagation of whistler mode waves through the ionosphere

We present results from numerical studies of whistler mode wave propagation in the Earth's ionosphere when artificially created plasma ducts are present. Using realistic density profiles from the SAMI2 ionospheric code, we solve the two‐dimensional electron magnetohydrodynamics equations to study the trans‐ionospheric propagation of artificially generated whistler waves at HAARP latitudes (L = 4.9). Both ducted and non‐ducted propagation is considered, but only ducted whistlers are able to propagate without a significant reduction in wave amplitude. The conditions necessary for the trapping of waves in both high‐ and low‐density ducts are discussed with particular attention paid to the practical accessibility of these parameter regimes.

Modeling the propagation of whistler-mode waves in the presence of field-aligned density irregularities

We present a numerical study of propagation of VLF whistler-mode waves in a laboratory plasma. Our goal is to understand whistler propagation in magnetic field-aligned irregularities (also called channels or ducts). Two cases are examined, that of a high-frequency (ω>Ωce/2) whistler in a density depletion duct and that of a low-frequency (ω<Ωce/2) whistler in a density enhancement. Results from a numerical simulation of whistler wave propagation are compared to data from the UCLA Los Angeles Physics Teachers Alliance Group plasma device and whistler propagation in pre-existing density depletion and density enhancement ducts is demonstrated.

The relations between magnetospheric chorus and hiss inside and outside the plasmasphere boundary layer: Cluster observation

[1] Magnetospheric whistler mode emissions (chorus and hiss) can play an important role in acceleration and loss of energetic electrons by wave-particle interaction. Here we present a first report of two events in the simultaneous observations of chorus and hiss by the Cluster constellation. During the event of 30 August 2001, one spacecraft observed chorus in the plasmasphere boundary layer (PBL), and three spacecraft observed hiss in the plasmasphere. In the event of 18 November 2002, one Cluster spacecraft observed hiss inside the plasmasphere, and the other three spacecraft observed chorus outside the plasmasphere. The correlation between chorus and hiss waves in both events are analyzed via intensity comparison and cross-correlation analysis. It is found that chorus and hiss waves have significant correlation in the first event but have no correlation in the second event. Furthermore, we perform a ray-tracing study to investigate the correlation by adopting two typical density models: the MTotal density model associated with the PBL structure and the global core density model. Simulation results demonstrate that chorus waves outside the plasmapause can propagate into the plasmasphere and possibly evolve into hiss waves under the MTotal density model, supporting the previous finding that the plasmaspheric hiss may originate from discrete chorus emission. However, chorus cannot travel into the plasmasphere under the global core density model. This paper presents a first result that chorus has more opportunity to propagate into the plasmasphere through the PBL than through the plasmapause. The results suggest that the gradual density variation of the PBL appears to favor the inward propagation of whistler mode waves.