Propagating Whistler Mode Waves Research Articles

Comparison of quasilinear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations

[1] We present a comparison between the classical quasilinear diffusion coefficients and those calculated using a general test particle code. The trajectories of a large number of electrons are followed as they traverse a numerically‐ constructed, broadband, small‐amplitude wave field, using a general relativistic test particle code. The change in each electron’s pitch angle and energy is shown to be stochastic and the resulting diffusion of the entire population is found to be in excellent agreement with quasilinear theory. We also demonstrate that the diffusion coefficients presented by Summers, derived specifically for parallel propagating waves, are a factor of two larger than the test particle results if the power spectral density is one‐sided (w > 0). Our results demonstrate the general validity of using quasilinear theory to describe the effects of broadband small amplitude waves on radiation belt electrons. Citation: Tao, X., J. Bortnik, J. M. Albert, K. Liu, and R. M. Thorne (2011), Comparison of quasilinear diffusion coefficients for parallel propagating whistler mode waves with test particle simulations, Geophys. Res. Lett., 38, L06105,

The source region and its characteristic of pulsating aurora based on the Reimei observations

[1] Using image and particle data sets obtained from observations by the Reimei satellite, we carried out time-of-flight (TOF) analysis for 29 pulsating aurora events to understand the precise properties of pulsating auroras and the possible generation process. While the sources identified using a standard TOF model were distributed almost continuously from magnetic latitudes 50° to −20°, the sources identified using a different TOF model that takes into account whistler mode wave propagation were confined to the equatorial region up to about 15°. The latter source distribution agrees with previous statistical studies of whistler mode chorus waves. In addition, the cold plasma density of the source region and the wave frequency can be estimated from the latter TOF analysis. The estimated cold plasma densities and wave frequencies normalized by the equatorial cyclotron frequency ranged in 0.20–21.7 cm−3 and 0.22–0.65, respectively. The estimated wave frequency showed clear dependence on the invariant latitudes of the pulsating aurora source region and increased up to the frequency range of the upper band chorus as the distance from the Earth decreased (up to about 5–6 RE). These results suggest that both lower and upper band chorus wave contribute to the electron scattering of pulsating auroras, which depends on the radial distance of the source region.

Time of flight analysis of pulsating aurora electrons, considering wave‐particle interactions with propagating whistler mode waves

We propose a model for the energy dispersion of electron precipitation associated with pulsating auroras, considering the wave‐particle interactions with propagating whistler mode waves from the equator. Since the resonant energy depends on the magnetic latitude, the pitch angle scattering of different energy electrons can occur continuously along the field line. Considering the energy‐dependent path length and the precipitation start time of the precipitating electrons, the transit time of whistler mode waves, and the frequency drift, we calculated the precipitation of electrons observed at the topside ionosphere. Note that higher energy electrons precipitate into the ionosphere of the opposite hemisphere earlier than lower energy electrons. As a result, an energy dispersion of precipitating electrons is observed at the topside ionosphere, even though the modulation of low energy electrons occurs prior to that of high energy electrons. Using the model, we conducted a time‐of‐flight (TOF) analysis of precipitating electrons observed by the REIMEI satellite, assuming an interaction with the whistler mode chorus rising tone. Our TOF analysis suggests that the modulation region of the pitch angle scattering is near the magnetic equator, whereas previous models expected that the modulation region is far from the magnetic equator. The estimated parameters, such as wave‐frequency and latitudinal distribution of the modulation region, are consistent with previous statistical studies of whistler waves at the magnetosphere.

Propagation of whistler mode waves with a modulated frequency in the magnetosphere

This paper presents results from experimental and numerical studies of the propagation of whistler mode waves in the Earth's magnetosphere. An experiment conducted at the High Frequency Active Auroral Research Program (HAARP) on 16 March 2008 demonstrates that ionospherically generated waves with particular frequency‐time formats are amplified on their pass from HAARP to the conjugate location in the South Pacific Ocean more efficiently than waves with a constant frequency. Numerical simulations of a one‐dimensional electron magnetohydrodynamics (MHD) model in the dipole magnetic field geometry reveal that the amplification takes place more efficiently when the frequency of the whistler mode waves (in the frequency range from 0.5 to 1.0 kHz) changes in the equatorial magnetosphere with the rate from 0.25 to 0.47 kHz/s. The maximum amplification occurs when this rate is 0.33 kHz/s and no/very little amplification is observed when this gradient is equal to 0 or when it is larger than 0.78 kHz/s.

Generation of whistler mode emissions in the inner magnetosphere: An event study

On July 24, 2003, when the Cluster 4 satellite crossed the magnetic equator at about 4.5 RE radial distance on the dusk side (∼15 MLT), whistler wave emissions were observed below the local electron gyrofrequency (fce) in two bands, one band above one‐half the gyrofrequency (0.5fce) and the other band below 0.5fce. A careful analysis of the wave emissions for this event has shown that Cluster 4 passed through the wave source region. Simultaneous electron particle data from the PEACE instrument in the generation region indicated the presence of a mid‐energy electron population (∼100 s of eV) that had a highly anisotropic temperature distribution with the perpendicular temperature 10 times the parallel temperature. To understand this somewhat rare event in which the satellite passed directly through the wave generation region and in which a free energy source (i.e., temperature anisotropy) was readily identified, a linear theory and particle in cell simulation study has been carried out to elucidate the physics of the wave generation, wave‐particle interactions, and energy redistribution. The theoretical results show that for this event the anisotropic electron distribution can linearly excite obliquely propagating whistler mode waves in the upper frequency band, i.e., above 0.5fce. Simulation results show that in addition to the upper band emissions, nonlinear wave‐wave coupling excites waves in the lower frequency band, i.e., below 0.5fce. The instability saturates primarily by a decrease in the temperature anisotropy of the mid‐energy electrons, but also by heating of the cold electron population. The resulting wave‐particle interactions lead to the formation of a high‐energy plateau on the parallel component of the warm electron velocity distribution. The theoretical results for the saturation time scale indicate that the observed anisotropic electron distribution must be refreshed in less than 0.1 s allowing the anisotropy to be detected by the electron particle instrument, which takes several seconds to produce a distribution.

Simultaneous ground-based and satellite observations of natural VLF waves in Antarctica: A case study of downward ionospheric penetration of whistler-mode waves

To investigate downward ionospheric-penetration characteristics of VLF (several hundred Hz to 17.8 kHz) whistler-mode waves, we conducted simultaneous observations (in 2006) of natural VLF waves using both ground stations in Antarctica and the Japanese Akebono satellite. The ground-based and satellite observations included an interesting event for which both observed similar VLF waves. In this study, we theoretically calculate down-going whistler-mode wave propagation based on ground-satellite observations using the full-wave analysis. In a case study, the observed wave-normal angles were approximately 140–160 degrees for a dayside chorus event on 15 March 2006. The theoretical calculation showed that the wave-normal angles for ionospheric penetration should be around 155.6 degrees, with its angular width of approximately 2 degrees. Moreover, the wave-energy loss due to ionospheric penetration is estimated at 20.4 dB based on our theoretical calculation, in accordance with the observed 17–19 dB.

Oblique propagation of whistler mode waves in the chorus source region

Whistler mode chorus has been shown to play a role in the process of local acceleration of electrons in the outer Van Allen radiation belt. Most of the quasi‐linear and nonlinear theoretical studies assume that the waves propagate parallel to the terrestrial magnetic field. We show a case where this assumption is invalid. We use data from the Cluster spacecraft to characterize propagation and spectral properties of chorus. The recorded high‐resolution waveforms show that chorus in the source region can be formed by a succession of discrete wave packets with decreasing frequency that sometimes change into shapeless hiss. These changes occur at the same time in the entire source region. Multicomponent measurements show that waves in both these regimes can be found at large angles to the terrestrial magnetic field. The hiss intervals contain waves propagating less than one tenth of a degree from the resonance cone. In the regime of discrete wave packets the peak of the wave energy density is found at a few degrees from the resonance cone in a broad interval of azimuth angles. The wave intensity increases with the distance from the magnetic field minimum along a given field line, indicating a gradual amplification of chorus in the source region.

Effect of frequency modulation on whistler mode waves in the magnetosphere

We present results from numerical studies of whistler mode wave propagation in the Earth's magnetosphere. Numerical simulations, based on the novel algorithm, solving one‐dimensional electron‐MHD equations in the dipole coordinate system, demonstrate that the amplitude (and power) of the whistler mode waves generated by the ground‐based transmitter can be significantly increased in some particular location along the magnetic field line (for example, at the equatorial magnetosphere) by the frequency modulation of the transmitted signal. The location where the amplitude of the signal reaches its maximum is defined by the time delay between different frequency components of the signal. Simulations reveal that a whistler mode wave with a discrete frequency modulation (where the frequency changes by a finite step) in the range from 1 to 3 kHz can be compressed as efficiently as a signal with a continuous frequency modulation when the frequency difference between components of the discrete‐modulated signal is not greater than 100 Hz.

Efficiency of electron acceleration in the Earth’s magnetosphere by whistler mode waves

The efficiency of energetic electron cyclotron acceleration in the Earth’s magnetosphere in different regimes of electron resonant interaction with parallel propagating whistler mode waves of variable frequency, specifically, with chorus ELF-VLF emissions, is considered. The regime of stochastic acceleration, typical of the interaction between particles and noise-like emissions, and particle acceleration in the regime of nonlinear trapping by a quasimonochromatic wave field are discussed. The specific feature of the latter regime consists in its non-diffuse character, i.e., the definite sign of the energy variation depending on the frequency variation in the wave packet. The trapped electron energy becomes higher if frequency increases within an element, which is typical of chorus emissions. For the parameters typical of chorus emissions (the amplitude of a wave magnetic field B ∼ = 102 nT, the initial frequency ω ∼ 0.3ω H , and the frequency variation &Dω ∼ 0.15ω H , where ω H is the electron gyrofrequency), the energy increase during one act of such an interaction at L = 4−5 exceeds the rms variation in the energy of untrapped electron (during stochastic acceleration) by one-two orders of magnitude. The estimates indicate that a considerable fraction (several tens of percent) of the chorus element energy can be absorbed by electrons accelerated in the trapping regime during a single hop.

Storm-Time Evolution of Energetic Electron Pitch Angle Distributions by Wave-Particle Interaction

The quasi-pure pitch-angle scattering of energetic electrons driven by field-aligned propagating whistler mode waves during the 9∼15 October 1990 magnetic storm at L ≈ 3 ∼ 4 is studied, and numerical calculations for energetic electrons in gyroresonance with a band of frequency of whistler mode waves distributed over a standard Gaussian spectrum is performed. It is found that the whistler mode waves can efficiently drive energetic electrons from the larger pitch-angles into the loss cone, and lead to a flat-top distribution during the main phase of geomagnetic storms. This result perhaps presents a feasible interpretation for observation of time evolution of the quasi-isotropic pitch-angle distribution by Combined Release and Radiation Effects Satellite (CRRES) spacecraft at L ≈ 3 ∼ 4.

Effects of Spatial Variation of Thermal Electrons onWhistler-Mode Waves in Magnetosphere

A ray-tracing method is developed to evaluate the wave growth/dampingand specifically propagation trajectories of the magnetosphericallyreflected Whistler-mode waves. The methodology is valid for weak wavegrowth/damping when plasma is comprised of a cold electron populationand a hot electron population, together with background neutralizingions, e.g. protons. The effect of anisotropic thermal electrons on thepropagation of Whistler-mode waves is studied in detail. Numericalresults are obtained for a realistic spatial variation model of plasmapopulation, including the cold electron density distribution, and thethermal electron density and temperature distribution. It is found that,analogous to the case of the typical cold plasma approximation, theoverall ray path of Whistler-mode waves is insensitive to the thermalelectron density and temperature anisotropy, and the ray path reflectswhere wave frequency is below or comparable to the local lower hybridresonance frequency flhr. However, the wave growth is expected tobe influenced by the thermal electron population. The results present afirst detailed verification for the validity of the typical cold plasmaapproximation for the propagation of Whistler-mode waves and may accountfor the observation that the Whistler-mode waves tend to propagate on aparticular magnetic shell L where the wave frequency is comparable toflhr.

Study of whistler mode instability in Saturn's magnetosphere

Abstract. A dispersion relation for parallel propagating whistler mode waves has been applied to the magnetosphere of Saturn and comparisons have been made with the observations made by Voyager and Cassini. The effect of hot (suprathermal) electron-density, temperature, temperature anisotropy, and the spectral index parameter, κ, on the temporal growth rate of the whistler mode emission is studied. A good agreement is found with observations. Electron pitch angle and energy diffusion coefficients have been obtained using the calculated temporal growth rates.

Thermal effects on parallel resonance energy of whistler mode wave

In this short communication, we have evaluated the effect of thermal velocity of the plasma particles on the energy of resonantly interacting energetic electrons with the propagating whistler mode waves as a function of wave frequency and L-value for the normal and disturbed magnetospheric conditions. During the disturbed conditions when the magnetosphere is depleted in electron density, the resonance energy of the electron enhances by an order of magnitude at higher latitudes, whereas the effect is small at low latitudes. An attempt is made to explain the enhanced wave activity observed during magnetic storm periods.

Dispersion properties of ducted whistlers, generated by lightning discharge

Abstract. Whistler-mode wave propagation in magnetospheric ducts of enhanced cold plasma density is studied. The case of the arbitrary ratio of the duct radius to the whistler wavelength is considered, where the ray-tracing method is not applicable. The set of duct eigenmodes and their spatial structure are analysed and dependencies of eigenmode propagation properties on the duct characteristics are studied. Special attention is paid to the analysis of the group delay time of one-hop propagation of the whistler wave packet along the duct. We found that, in contrast to the case of a wide duct, the group delay time in a rather narrow duct decreases as the eigenmode number increases. The results obtained are suggested for an explanation of some types of multi-component whistler signals.

Whistler mode wave coupling effects on electron dynamics in the near Earth magnetosphere

Nonlinear electron whistler mode wave particle interactions in the near earth magnetosphere suggest several candidate mechanisms for phase space diffusion of electrons into the loss cone to provide a source of auroral precipitating electrons. A unidirectional whistler mode wave propagating parallel to the background magnetic field and interacting with an electron can be shown to produce resonance (trapping of electrons) but the process is not stochastic. Chaos can be introduced by resonance between electrons that mirror many times in the earth's field, and a whistler wavefield. Here, we show that an electron interacting with two oppositely directed, parallel propagating whistler mode waves exhibits stochastic behaviour in addition to resonance. The background field is uniform, so that stochasticity arises solely due to the presence of the wavefield without requiring bounce motion of electrons between mirror points. Stochasticity first appears for wave amplitudes not inconsistent with observations at disturbed times in the near earth magnetosphere and therefore may contribute to pitch angle diffusion.

Plasma wave characteristics of the Jovian magnetopause boundary layer: Relationship to the Jovian aurora?

The Jovian magnetopause boundary layer (BL) plasma wave spectra from 10−3 to 102 Hz have been measured for the first time. For one intense event the magnetic (B′) and electric (E′) spectra were 2 × 10−4 ƒ2.4 nT2/Hz and 4 × 10−9 ƒ2.4 V2/m2 Hz, respectively. Although no measurable wave amplitudes were detected above the electron gyrofrequency, ∼140 Hz, this finding may be due to the low signal strength characteristic of this region. The B′/E′ ratio is relatively frequency independent. It is possible that waves are obliquely propagating whistler mode waves. The B′ and E′ spectra are broadband with no obvious spectral peaks. The waves are sufficiently intense to cause cross‐field diffusion of magnetosheath plasma to create the BL itself. A Jovian BL thickness of 10,700 km is predicted, which is consistent with past in situ measurements. The Jovian boundary layer wave properties are quite similar to the BL waves at Earth (however, the Jovian waves are orders of magnitude less intense). It appears that the solar wind/magnetosphere dynamos at the two planets are similar enough to be consistent with a common wave generation mechanism. The predicted ionospheric latitudinal width of the BL of ∼100–200 km is quite similar to the Jovian auroral high‐latitude ring measured by Hubble. The location of the BL at and inside the foot point of the last closed field line may place the boundary layer and the aurora on approximately the same magnetic field lines. The Jovian BL waves are sufficiently intense to cause strong pitch angle diffusion for <5‐keV electrons and 1‐keV to 1‐MeV protons. The estimated energy precipitation rate from this interaction <1 erg cm−2 s−1, sufficient for a weak high‐latitude auroral ring. This intensity is 2 to 3 orders of magnitude too low to cause the main aurora ring, however. If it is found that this main aurora maps into the boundary layer, then other mechanisms such as (ionospheric) double layers must be responsible for the particle energization and precipitation.

Parallel electric field-induced instability in the magnetospheric ion-electron plasma

A complete dispersion relation for a whistler mode wave propagation in an anisotropic warm ion-electron magnetoplasma in the presence of parallel electric field using the dispersion relation for a circularly polarized wave has been derived. The dispersion relation includes the effect of anisotropy for the ion and electron velocity distribution functions. The growth rate of electron-ion cyclotron waves for different plasma parameters observed atL = 6.6REhas been computed and the results have been discussed in detail in the light of the observed features of VLF emissions and whistlers. The role of the combination of ion-cyclotron and whistler mode electromagnetic wave propagation along the magnetic field in an anisotropic Maxwellian weakly-ionized magnetoplasma has been studied.

The propagation of damped or growing whistler-mode waves

The influence of damping or growth on plane plasma wave propagation is studied analytically under the assumption that the corresponding decrement of damping or increment of growth are small. The general equations are applied to whistler-mode waves propagating parallel to the magnetic field. It is pointed out that unless these waves are in an almost marginally stable state both damping and growth of whistler-mode waves result in an increase of their refractive index. This should be taken into account when studying the propagation of whistler-mode waves at frequencies close to the electron gyrofrequency.

Ray-tracing study of the plasmapause effect on non-ducted whistler-mode wave propagation

The effect of the plasmapause on whistler-mode wave propagation and generation is investigated by means of the two-dimensional ray tracings started at the equator over a wide frequency range, 0.1 < Λ o < 1.0 ( Λ 0: wave frequency normalized by the equatorial gyrofrequency) and for a wide range of the initial wave normal angle θ 0. The main important findings are summarized as follows: (1) efficient gradient trapping is recognized at the inner edge of the plasmapause (especially with strong gradient) for lower frequency ( Λ 0 < 0.4) waves with smaller initial θ 0s (−40° ∼ + 40°) generated at the equator; (2) lower frequency waves generated at the equator inside the plasmapause are found to have an access to low-altitude satellites and to ground, and their transmission latitude is slightly smaller than the plasmapause location; and (3) the outer edge of the plasmapause (especially with weak gradient) is also found to act as a guide for higher frequency (Λ > 0.5) waves. These theoretical findings are discussed with their relevance to the experimental facts of different magnetospheric whistler-mode emissions.

On the propagation of half-gyrofrequency whistler-mode waves in the magnetospheric plasma

The propagation of whistler-mode waves at frequencies above one half the electron gyrofrequency has been investigated for a magnetospheric two-component plasma (cold and lower energy hot electrons) by use of the properties of refractive index surfaces. The presence of hot plasma is found to enhance the tendency towards field-aligned focusing of half-gyrofrequency whistler-mode propagation at large wave normal angles close to the oblique resonance angle of the whistler-mode propagation in the corresponding cold plasma.