Equatorial Electron Gyrofrequency Research Articles

Survey of Whistler‐Mode Wave Amplitudes and Frequency Spectra in Jupiter's Magnetosphere

AbstractWe present statistical distributions of whistler‐mode chorus and hiss waves at frequencies ranging from the local proton gyrofrequency to the equatorial electron gyrofrequency (fce,eq) in Jupiter's magnetosphere based on Juno measurements. The chorus wave power spectral densities usually follow the fce,eq variation with major wave power concentrated in the 0.05fce,eq–fce,eq frequency range. The hiss wave frequencies are less dependent on fce,eq variation than chorus with major power concentrated below 0.05fce,eq, showing a separation from chorus at M < 10. Our survey indicates that chorus waves are mainly observed at 5.5 < M < 13 from the magnetic equator to 20° latitude, consistent with local wave generation near the equator and damping effects. The hiss wave powers extend to 50° latitude, suggesting longer wave propagation paths without attenuation. Our survey also includes the whistler‐mode waves at high latitudes which may originate from the Io footprint, auroral hiss, or propagating hiss waves reflected to high M shells.

Observation of an Electron Microburst With an Inverse Time‐Of‐Flight Energy Dispersion

AbstractInteractions between whistler mode chorus waves and electrons are a dominant mechanism for particle acceleration and loss in the outer radiation belt. One form of this loss is electron microburst precipitation: a sub‐second intense burst of electrons. Despite previous investigations, details regarding the microburst‐chorus scattering mechanism—such as dominant resonance harmonic—are largely unconstrained. One way to observationally probe this is via the time‐of‐flight energy dispersion. If a single cyclotron resonance is dominant, then higher energy electrons will resonate at higher magnetic latitudes: sometimes resulting in an inverse time‐of‐flight dispersion with lower‐energy electrons leading. Here we present a clear example of this phenomena, observed by a FIREBIRD‐II CubeSat on 27 August 2015, that shows good agreement with the Miyoshi‐Saito time‐of‐flight model. When constrained by this observation, the Miyoshi‐Saito model predicts that a relatively narrowband chorus wave with a ∼0.2 of the equatorial electron gyrofrequency scattered the microburst.

Gap Formation Around 0.5Ωe in the Whistler‐Mode Waves Due To the Plateau‐Like Shape in the Parallel Electron Distribution: 2D PIC Simulations

AbstractThe power gap around 0.5Ωe (where Ωe is the equatorial electron gyrofrequency) of whistler‐mode waves is commonly observed in the Earth's inner magnetosphere, but its generation mechanism is still under debate. By performing two‐dimensional particle‐in‐cell simulations in a uniform background magnetic field, we investigate the spectral properties of whistler‐mode waves excited by temperature anisotropic electrons. The waves have positive growth rates in a wide range of normal angles (θ ≈ 0°–35°), resulting in the generation of both parallel and nonparallel waves. Although the nonparallel wave modes are weaker than the parallel ones, they can cause the plateau‐like shape around 0.5 VAe (where VAe represent the electron Alfven speed) in the parallel direction of electron velocity distribution. The plateau‐like electron component can then lead to severe damping in the waves around 0.5Ωe via the cyclotron resonance, and the power gap is formed. This mechanism is called as “spectrum bite”. Our study sheds fresh light on the well‐known gap formation at ∼0.5Ωe in the whistler‐mode waves, which is ubiquitously detected near the equator in the inner magnetosphere.

Quasiperiodic Emissions and Related Particle Precipitation Bursts Observed by the DEMETER Spacecraft

AbstractElectromagnetic waves observed in the inner magnetosphere at frequencies between about 0.5 and 4 kHz sometimes exhibit a quasiperiodic (QP) time modulation of the wave intensity with modulation periods from tens of seconds up to a few minutes. Such waves are typically termed “QP emissions” and their origin is still not fully understood. We use a large set of more than 2,000 of these events identified in the low‐altitude DEMETER spacecraft data to check for energetic electron flux variations matching the individual QP wave elements. Altogether, seven such events are identified and their detailed analysis is performed. Energetic electron fluxes are found to be modulated primarily at energies lower than about 250 keV. While the waves may propagate unducted across L‐shells, the energetic particles follow magnetic field lines from the interaction region down to the observation point. This is used to estimate the locations of anticipated generation regions to L‐shells between about 4 and 6, and the respective source radial dimensions to about 0.6–1.2 Earth radii. The frequencies of the events are confined below half of the equatorial electron gyrofrequency in the determined source regions. Finally, it is shown that individual QP elements exhibit a fine inner structure corresponding to the wave bouncing between the hemispheres.

New Type of Short High‐Frequency VLF Patches (“VLF Birds”) Above 4–5 kHz

AbstractThe new type of daytime natural very low frequency (VLF) whistler mode emissions of the magnetospheric origin was found in the VLF observations at Kannuslehto station (L ∼ 5.5) in Northern Finland. The events occurred at the frequencies above 4–5 kHz even up to 15 kHz. These emissions have never been observed earlier in the spectrograms because they were hidden by strong impulsive atmospherics (sferics) in the same frequency range originating in lightning discharges. After filtering out the sferics, we surprisingly discovered completely new types of high frequency right‐hand polarized peculiar VLF emissions with various unusual dynamic spectra. These new VLF emissions typically occur as a sequence of a number of short (∼1–3 min) burst‐like structures or single short patches with the total duration up to a few hours. The spectral peculiarities of several long‐lasting VLF events as well as individual short VLF patches are discussed. The dynamic spectra of these new VLF patches raise the question of the temporal and spatial details of the wave‐particle interactions in the magnetospheric plasma. These emissions are observed only under quiet or weakly disturbed space weather conditions, but during small negative values of the Dst index, indicating the presence of a certain excess of the radiation belt electrons. Note, these high frequency VLF patches are observed at the frequencies much higher than the half of the equatorial electron gyrofrequency which is equal to ∼2.7 kHz at L ∼ 5.5. It seems that these emissions are generated deep in the magnetosphere, but the detailed nature, generation region, and propagation behavior of these newly discovered VLF emissions remain unknown. An appearance of high frequency VLF patches could be an indirect indicator of a local enhancement of electron fluxes in the radiation belt that are not directly measured and may occur even in the absence of visible ground‐based geomagnetic disturbances. Further researches may shed new light on wave‐particle interactions occurring in the Earth's radiation belts.

Unusual Loss of Van Allen Belt Relativistic Electrons by Extremely Low‐Frequency Chorus

AbstractChorus waves with the frequency usually between 0.1 and 0.8 equatorial electron gyrofrequency fce can accelerate energetic electrons to relativistic energies (several mega‐electron volts, MeV). Here, we report a unique event that both regular chorus and unusual chorus with extremely low frequency (ELF) below 0.1 fce occurred during the 22 December 2014 geomagnetic storm. Relativistic electron fluxes decreased with decreasing wave frequency and had minima exactly corresponding to the presence of ELF chorus. Performing a two‐dimensional simulation, we find that ELF chorus can result in unusual loss of relativistic electrons while regular chorus contributes to the acceleration, leading to the frequency‐modulated fluxes of such high‐energy electrons. The current results provide a new scenario that ELF chorus waves can potentially mitigate space weather by inhibiting relativistic electron flux enhancements.

Analytical Chorus Wave Model Derived from Van Allen Probe Observations

AbstractChorus waves play an important role in the dynamic evolution of energetic electrons in the Earth's radiation belts and ring current. Using more than 5 years of Van Allen Probe data, we developed a new analytical model for upper‐band chorus (UBC; 0.5fce < f < fce) and lower‐band chorus (LBC; 0.05fce < f < 0.5fce) waves, where fce is the equatorial electron gyrofrequency. By applying polynomial fits to chorus wave root mean square amplitudes, we developed regression models for LBC and UBC as a function of geomagnetic activity (Kp), L, magnetic latitude (λ), and magnetic local time (MLT). Dependence on Kp is separated from the dependence on λ, L, and MLT as Kp‐scaling law to simplify the calculation of diffusion coefficients and inclusion into particle tracing codes. Frequency models for UBC and LBC are also developed, which depends on MLT and magnetic latitude. This empirical model is valid in all MLTs, magnetic latitude up to 20°, Kp ≤ 6, L‐shell range from 3.5 to 6 for LBC and from 4 to 6 for UBC. The dependence of root mean square amplitudes on L are different for different bands, which implies different energy sources for different wave bands. This analytical chorus wave model is convenient for inclusion in quasi‐linear diffusion calculations of electron scattering rates and particle simulations in the inner magnetosphere, especially for the newly developed four‐dimensional codes, which require significantly improved wave parameterizations.

Quasiperiodic Whistler Mode Emissions Observed by the Van Allen Probes Spacecraft

AbstractQuasiperiodic (QP) emissions are whistler mode electromagnetic waves observed in the inner magnetosphere that exhibit a QP time modulation of the wave intensity. We analyze 768 QP events observed during the first 5 years of the operation of the Van Allen Probes spacecraft (September 2012 to October 2017). Multicomponent wave measurements performed in the equatorial region, where the emissions are likely generated, are used to reveal new experimental information about their properties. We show that the events are observed nearly exclusively inside the plasmasphere. Wave frequencies are mostly between about 0.5 and 4 kHz. The events observed at larger radial distances and on the duskside tend to have slightly lower frequencies than the emissions observed elsewhere. The maximum event frequencies are limited by half of the equatorial electron gyrofrequency, suggesting the importance of wave ducting. Modulation periods are typically between about 0.5 and 5 min, and they increase with the in situ measured plasma number density. This increase is consistent with the main mechanisms suggested to explain the origin of the QP modulation. Two‐point measurements performed by the Van Allen Probes are used to estimate a typical spatial extent of the emissions to about 1 RE in radial distance and 1.5 hr in magnetic local time. Detailed wave analysis shows that the emissions are right‐hand circularly polarized, and they usually come from several different directions simultaneously. They, however, predominantly propagate at rather low wave normal angles and away from the geomagnetic equator.

New high-frequency (7–12 kHz) quasi-periodic VLF emissions observed on the ground at L ∼ 5.5

Abstract. We reveal previously unknown quasi-periodic (QP) very low frequency (VLF) emissions at the unusually high-frequency band of ∼ 7–12 kHz by applying the digital filtering of strong atmospherics to the ground-based VLF data recorded at Kannuslehto station (KAN). It is located in northern Finland at L ∼ 5.5. The frequencies of QP emissions are much higher than the equatorial electron gyrofrequency at L ∼ 5.5. Thus, these emissions must have been generated at much lower L shells than KAN. Two high-frequency QP emission events have been studied in detail. The emissions were right-hand polarized waves indicating an overhead location of the exit area of waves in the ionosphere. In one event, the spectral–temporal forms of the emissions looked like a series of giant “bullets” due to the very abrupt cessation. Unfortunately, we could not explain such a strange dynamic spectral shape of the waves. In the second event, the modulation period was about 3 min under the absence of simultaneous geomagnetic pulsations. The studied emissions lasted about 4 h and were observed under the very quiet geomagnetic activity. The adequate mechanisms of the generation and propagation of the revealed high-frequency QP emissions have not yet been established. We speculate that studied QP emissions can be attributed to the auto-oscillations of the cyclotron instability in the magnetospheric plasma maser.

Generation of extremely low frequency chorus in Van Allen radiation belts

AbstractRecent studies have shown that chorus can efficiently accelerate the outer radiation belt electrons to relativistic energies. Chorus, previously often observed above 0.1 equatorial electron gyrofrequency fce, was generated by energetic electrons originating from Earth's plasma sheet. Chorus below 0.1 fce has seldom been reported until the recent data from Van Allen Probes, but its origin has not been revealed so far. Because electron resonant energy can approach the relativistic level at extremely low frequency, relativistic effects should be considered in the formula for whistler mode wave growth rate. Here we report high‐resolution observations during the 14 October 2014 small storm and firstly demonstrate, using a fully relativistic simulation, that electrons with the high‐energy tail population and relativistic pitch angle anisotropy can provide free energy sufficient for generating chorus below 0.1 fce. The simulated wave growth displays a very similar pattern to the observations. The current results can be applied to Jupiter, Saturn, and other magnetized planets.

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

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

Electron lifetimes from narrowband wave‐particle interactions within the plasmasphere

AbstractThis paper is devoted to the systematic study of electron lifetimes from narrowband wave‐particle interactions within the plasmasphere. It relies on a new formulation of the bounce‐averaged quasi‐linear pitch angle diffusion coefficients parameterized by a single frequency, ω, and wave normal angle, θ. We first show that the diffusion coefficients scale with ω/Ωce, where Ωce is the equatorial electron gyrofrequency, and that maximal pitch angle diffusion occurs along the line α0 = π/2–θ, where α0 is the equatorial pitch angle. Lifetimes are computed for L shell values in the range [1.5, 3.5] and energies, E, in the range [0.1, 6] MeV as a function of frequency and wave normal angle. The maximal pitch angle associated with a given lifetime is also given, revealing the frequencies that are able to scatter nearly equatorial pitch angle particles. The lifetimes are relatively independent of frequency and wave normal angle after taking into consideration the scaling law, with a weak dependence on wave normal angle up to 60–70°, increasing to infinity as the wave normal angle approaches the resonance cone. We identify regions in the (L, E) plane in which a single wave type (hiss, VLF transmitters, or lightning‐generated waves) is dominant relative to the others. We find that VLF waves dominate the lifetime for 0.2–0.4 MeV at L ~ 2 and for 0.5–0.8 MeV at L ~ 1.5, while hiss dominates the lifetime for 2–3 MeV at L = 3–3.5. The influence of lightning‐generated waves is always mixed with the other two and cannot be easily differentiated. Limitations of the method for addressing effects due to restricted latitude or pitch angle domains are also discussed. Finally, for each (L, E) we search for the minimum lifetime and find that the optimal frequency that produces this lifetime increases as L diminishes. Restricting the search to very oblique waves, which could be emitted during the Demonstration and Science Experiments satellite mission, we find that the optimal frequency is always close to 0.16Ωce.

Characteristics of hiss‐like and discrete whistler‐mode emissions

The characteristics of hiss‐like and discrete (rising and falling tones) whistler‐mode waves in the lower‐band wave frequency range (0.1–0.5 of equatorial electron gyrofrequency) are investigated using waveform data from near‐equatorially orbiting multiple THEMIS spacecraft outside the plasmasphere. Statistical results show that wave polarization properties of hiss‐like emissions are similar to rising tones, but are significantly different from falling tones. The magnetic wave amplitudes of hiss‐like bands and rising tones are generally larger than those of falling tones. Wave normal angles of broadband hiss‐like emissions and rising tones tend to be quasi field‐aligned, whereas falling tones are very oblique. Importantly, discrete emissions including rising and falling tones are predominantly observed in the region of lowfpe/fce(the ratio of plasma frequency to electron gyrofrequency), whereas hiss‐like bands alone preferentially occur in the region of highfpe/fce. These important features of hiss‐like and discrete whistler‐mode emissions should be considered when evaluating their interactions with energetic electrons.

Nonlinear mechanisms of lower‐band and upper‐band VLF chorus emissions in the magnetosphere

We develop a nonlinear wave growth theory of magnetospheric chorus emissions, taking into account the spatial inhomogeneity of the static magnetic field and the plasma density variation along the magnetic field line. We derive theoretical expressions for the nonlinear growth rate and the amplitude threshold for the generation of self‐sustaining chorus emissions. We assume that nonlinear growth of a whistler mode wave is initiated at the magnetic equator where the linear growth rate maximizes. Self‐sustaining emissions become possible when the wave propagates away from the equator during which process the increasing gradients of the static magnetic field and electron density provide the conditions for nonlinear growth. The amplitude threshold is tested against both observational data and self‐consistent particle simulations of the chorus emissions. The self‐sustaining mechanism can result in a rising tone emission covering the frequency range of 0.1–0.7 Ωe0, where Ωe0 is the equatorial electron gyrofrequency. During propagation, higher frequencies are subject to stronger dispersion effects that can destroy the self‐sustaining mechanism. We obtain a pair of coupled differential equations for the wave amplitude and frequency. Solving the equations numerically, we reproduce a rising tone of VLF whistler mode emissions that is continuous in frequency. Chorus emissions, however, characteristically occur in two distinct frequency ranges, a lower band and an upper band, separated at half the electron gyrofrequency. We explain the gap by means of the nonlinear damping of the longitudinal component of a slightly oblique whistler mode wave packet propagating along the inhomogeneous static magnetic field.

Landau damping and resultant unidirectional propagation of chorus waves

Using a numerical ray tracing code and a model of the suprathermal electron distribution in the inner magnetosphere, we calculate the Landau damping of chorus waves under realistic conditions. The chorus emissions are assumed to originate at the magnetic equatorial plane with a wave normal angle set at the generalized Gendrin angle, and a wave frequency which is varied from 0.1 to 0.9 of the equatorial electron gyrofrequency. Each ray is propagated until its wave power is diminished by a factor of 10, at which point we record the propagation time, latitude, and the distance along the ray path from the equator. Results indicate that chorus waves are expected to propagate to latitudes of 10°–20° and are typically Landau damped before experiencing magnetospheric reflections, in agreement with satellite observations. In addition, we find longer propagation distances and lifetimes at those frequencies immediately above the half equatorial gyrofrequency and consider the possibility that this effect may contribute to the formation of the two‐banded structure of chorus emissions.

Magion 5 observations of chorus-like emissions and their propagation features as inferred from ray-tracing simulation

Abstract. After reviewing briefly the present state of knowledge about chorus-like emissions, we present an overview of Magion 5 satellite observations of these emissions in the inner magnetosphere of the Earth. From the extensive VLF data recorded on board the Magion 5 satellite, we show examples of different types of discrete elements, representing rising and falling tones, and discuss their spectral properties, such as the bandwidth and the characteristic frequency as compared to the equatorial electron gyrofrequency. We analyse the possibility of satellite observation of discrete elements, assuming nonducted wave propagation from the source. As for the characteristic dimension of the generation region, we apply the figures obtained from the recently published correlation analysis of chorus emission recorded by four satellites in the Cluster experiment. We conclude that different frequencies in the chorus element should be emitted in a certain span of wave normal angles, so that the whole element could be observed far from the generation region.Key words. Magnetospheric physics (plasmasphere; plasma waves and instabilities) – Space plasma physics (wave-particle interactions) – Ionosphere (wave propagation)

On the similarity features of normalized frequency spectrograms of magnetospherically reflected whistlers

A modified electron whistler dispersion law is derived to be used for analytical and numerical investigation of magnetospherically reflected (MR) whistlers' propagation for finite ratio ωc/ωp of electron gyrofrequencies to plasma frequencies if the wave frequency is much less than ωp. The contribution of ions is included in the value of the lower hybrid resonance frequency only. Ray‐tracing simulations are carried out in order to reproduce MR whistler spectrograms typical of those observed on high‐altitude equatorial and low‐altitude satellites. It is found that spectrograms of MR whistlers with frequencies normalized to the equatorial electron gyrofrequency at the L shell of wave observation are close to each other when satellites are located on the equator at different altitudes (or at low altitude and different latitudes). Moreover, normalized frequencies corresponding to flattening of traces on spectrograms at large group delay times can be obtained by following me path of a single extreme quasi‐resonant whistler ray starting downward at the equator with a group velocity direction corresponding to the resonance cone. On the basis of obtained results, a possible interpretation of the origin and spectral characteristics of discrete plasmaspheric emissions is discussed.

Whistler absorption and electron heating near the plasmapause

Using the HOTRAY code, we demonstrate that lightning‐generated whistlers which enter the magnetosphere over a broad range of latitudes (Δλ ≈ 5°) just inside the plasmapause are strongly focused by the steep plasma density gradient into a narrow range of L shells near the equatorial region. The wave normal angle also remains closely aligned (±20°) with the magnetic field direction along the entire ray path. Under such conditions, Landau resonance is relatively unimportant, and the wave amplitude is controlled by cyclotron resonant interactions with energetic electrons. All waves with frequencies comparable to or larger than one third of the equatorial electron gyrofrequency can be strongly absorbed by resonant electrons, leading to electron heating perpendicular to the ambient magnetic field at energies above 100 eV. Consequently, in the presence of this strongly focused source of wave energy, the electron distribution should evolve toward a marginally stable anisotropic equilibrium distribution with T⊥>T‖. In order to simulate this perpendicular heating, we allow the anisotropy of the electron distribution to evolve so that damping is minimized at a frequency of 5 kHz, corresponding to the peak in the power spectrum of spherics above the ionosphere. When the plasmapause is located at Lp = 4.5, whistlers above 4 kHz experience more than 20 dB attenuation owing mainly to cyclotron resonance with 0.1 to 1 keV electrons near the equator. It is unlikely that these waves would be detectable on the ground. This attenuation will produce an upper cutoff in the whistler frequency considerably below one half the equatorial electron gyrofrequency for waves that are guided along the plasmapause. In contrast, lower‐frequency whistlers (ƒ ≈ 1–3 kHz) should be amplified by the anisotropic electron population; such waves are able to propagate to the conjugate ionosphere and thus be detected on the ground. This energy transfer between whistlers and cyclotron resonant electrons is relatively unimportant when Lp ≤ 3.0, but it should become significant for Lp ≥ 4.5.

Diffusion of radiation belt protons by whistler waves

Whistler waves propagating near the quasi‐electrostatic limit can interact with energetic protons (∼80 ‐ 500 keV) that are transported into the radiation belts. The waves may be launched from either the ground or generated in the magnetosphere as a result of the resonant interactions with trapped electrons. The wave frequencies are significant fractions of the equatorial electron gyrofrequency, and they propagate obliquely to the geomagnetic field. A finite spectrum of waves compensates for the inhomogeneity of the geomagnetic field allowing the protons to stay in gyroresonance with the waves over long distances along magnetic field lines. The Fokker‐Planck equation is integrated along the flux tube considering the contributions of multiple‐resonance crossings. The quasi‐linear diffusion coefficients in energy, cross energy/ pitch angle, and pitch angle are obtained for second‐order resonant interactions. They are shown to be proportional to the electric fields amplitudes. Numerical calculations for the second‐order interactions show that diffusion dominates near the edge of the loss cone. For small pitch angles the largest diffusion coefficient is in energy, although the cross energy/ pitch angle term is also important. This may explain the induced proton precipitation observed in active space experiments.

Proton whistler interactions near the equator in the radiation belts

The interactions of energetic protons with whistlers propagating near the quasi‐electrostatic limit, are investigated using a test particle, Hamiltonian formalism. We assume that wave packets exist with finite bandwidths of frequencies, which are close to the equatorial electron gyrofrequency and propagate obliquely with respect to the geomagnetic field. Near the equator the protons interact with the waves which appear Doppler shifted to some harmonic of their cyclotron frequency. In an inhomogeneous geomagnetic field the spacing between cyclotron harmonic resonances is very small. The Hamiltonian equations of motion are solved including multiple, independent harmonics for each resonance. The wave frequency varies as a function of the distance along the field line, with only one frequency being resonant at a given point. Thus the inhomogeneity of the magnetic field is compensated by the frequency variation. The proton whistler interactions satisfy the conditions for second‐order resonances for all the harmonics. The resonances may also overlap in phase space, leading to significant changes in the protons energies and pitch angles. The combined contributions of positive and negative harmonics allow protons to diffuse toward smaller pitch angles. Numerical calculations applying this formalism to parameters relevant to the plasmasphere and controlled VLF transmission experiments are presented.