VLF Chorus Research Articles

Simultaneous satellite observations of VLF chorus, hot and relativistic electrons in a magnetic storm “recovery” phase

The mechanism for formation of the Earth's radiation belts has been an outstanding issue for utilization of the geospace environment. We present a magnetic storm recovery phase that occurred from 10 to 19 October 1990, in which there is a clear correlation among continuous injection of hot electrons, generation of chorus, geomagnetic AE activity (all for ∼8 days) and the acceleration of electrons to relativistic energies. We propose a following scenario to explain the observations: the continuous injection of hot electrons associated with the continuous AE activity. The hot electrons with Tperp/Tpara > 1 temperature anisotropies excite whistler‐mode chorus waves. The chorus interacts with energetic electrons accelerating them to MeV energies forming a flux of “killer electrons” in the outer radiation belt.

Effects of latitudinal distributions of particle density and wave power on cyclotron resonant diffusion rates of radiation belt electrons

Abstract We evaluate cyclotron resonant interactions of radiation belt electrons with VLF chorus, plasmaspheric ELF hiss and electromagnetic ion cyclotron (EMIC) waves. We assume that the Earth’s magnetic field is dipolar and that each wave mode has a Gaussian spectral density. The dependence of the resonant electron diffusion rates on the latitudinal distributions of particle density and wave power is examined. We find that while the diffusion rates can be sensitive to the latitudinal distributions of density and wave power, in general the sensitivity depends on wave mode, equatorial pitch-angle, electron energy and L-shell. We determine the effects of the latitudinal distributions of density and wave power on the electron precipitation loss timescale due to combined scattering by VLF chorus, ELF hiss and EMIC waves. Accurate modeling of radiation belt electron dynamics requires observational data on the global distributions of particle number density and wave power.

Timescales for radiation belt electron acceleration and loss due to resonant wave‐particle interactions: 2. Evaluation for VLF chorus, ELF hiss, and electromagnetic ion cyclotron waves

Outer zone radiation belt electrons can undergo gyroresonant interaction with various magnetospheric wave modes including whistler‐mode chorus outside the plasmasphere and both whistler‐mode hiss and electromagnetic ion cyclotron (EMIC) waves inside the plasmasphere. To evaluate timescales for electron momentum diffusion and pitch angle diffusion, we utilize bounce‐averaged quasi‐linear diffusion coefficients for field‐aligned waves with a Gaussian frequency spectrum in a dipole magnetic field. Timescales for momentum diffusion of MeV electrons due to VLF chorus can be less than a day in the outer radiation belt. Equatorial chorus waves (∣λW∣ < 15 deg) can effectively accelerate MeV electrons. Efficiency of the chorus acceleration mechanism is increased if high‐latitude waves (∣λW∣ > 15 deg) are also present. Our calculations confirm that chorus diffusion is a viable mechanism for generating relativistic (MeV) electrons in the outer zone during the recovery phase of a storm or during periods of prolonged substorm activity when chorus amplitudes are enhanced. Radiation belt electrons are subject to precipitation loss to the atmosphere due to resonant pitch angle scattering by plasma waves. The electron precipitation loss timescale due to scattering by each of the wave modes, chorus, hiss, and EMIC waves, can be 1 day or less. These wave modes can separately, or in combination, contribute significantly to the depletion of relativistic (MeV) electrons from the outer zone over the course of a magnetic storm. Efficient pitch angle scattering by whistler‐mode chorus or hiss typically requires high latitude waves (∣λW∣ > 30 deg). Timescales for electron acceleration and loss generally depend on the spectral properties of the waves, as well as the background electron number density and magnetic field. Loss timescales due to EMIC wave scattering also depend on the ion (H+, He+, O+) composition of the plasma. Complete models of radiation belt electron transport, acceleration and loss should include, in addition to radial (cross‐L) diffusion, resonant diffusion due to gyroresonance with VLF chorus, plasmaspheric hiss, and EMIC waves. Comprehensive observational data on the spectral properties of these waves are required as a function of spatial location (L, MLT, MLAT) and magnetic activity.

Formation of VLF chorus frequency spectrum: Cluster data and comparison with the backward wave oscillator model

The dependence of the frequency spectrum of individual chorus elements on the position of the observation point in and near the generation region is analyzed using recent Cluster data obtained on two different geomagnetically active days. The source of night‐side chorus is localized using multicomponent measurements of the wave electric and magnetic fields. We have revealed that the spectrum of the chorus elements lacks the lower frequencies at the center of the source region. One possible explanation of this effect is provided by applying the backward wave oscillator model of chorus generation to these data. According to this model, the chorus frequency is determined by the parallel velocity corresponding to a step‐like deformation in the distribution function of resonant electrons. This velocity decreases during the generation of an element as the electrons move through the source region. Thus, only a part of a chorus element is visible inside this region. For the typical case of rising‐tone chorus elements, the lower frequencies are generated downstream with respect to the chorus propagation and, hence, disappear as a receiver is moved upstream towards the center of the source region.

Acceleration mechanism responsible for the formation of the new radiation belt during the 2003 Halloween solar storm

Observations of the relativistic electron flux increases during the first days of November, 2003 are compared to model simulations of two leading mechanisms for electron acceleration. It is demonstrated that radial diffusion driven by ULF waves cannot explain the formation of the new radiation belt in the slot region and instead predicts a decay of fluxes during the recovery phase of the October 31st storm. Compression of the plasmasphere during the main phases of the storm created preferential conditions for local acceleration during interactions with VLF chorus. Local acceleration of electrons at L = 3 is modelled with a 2‐D pitch‐angle, energy diffusion code. We show that the energy diffusion driven by whistler mode waves can explain the gradual build up of fluxes to energies exceeding 3 MeV in a new radiation belt which is formed in the slot region normally devoid of high energy electrons.

Quasi‐linear diffusion coefficients for field‐aligned electromagnetic waves with applications to the magnetosphere

Much current research in magnetospheric physics is directed toward understanding the dramatic variations in relativistic (>1 MeV) electron fluxes that can take place in the Earth's outer zone during magnetic storms. The behavior of outer‐zone energetic electrons is partly controlled by the competing mechanisms of acceleration and loss that result from wave‐particle interactions, in particular electron gyroresonance with ELF, VLF, and electromagnetic ion cyclotron (EMIC) waves. Powerful techniques for treating gyroresonant wave‐particle interactions are provided by quasi‐linear diffusion theory. In this paper, we derive formulae for the quasi‐linear (momentum, mixed, and pitch‐angle) diffusion coefficients for cyclotron resonance with field‐aligned electromagnetic waves of any mode and general spectral density. The formulae are fully exact, expressed in closed analytical form, and easily computable. Our results can therefore be readily used to determine accurate diffusion rates for many forms of wave‐particle interaction in the magnetosphere and other space plasmas. We find that momentum diffusion rates for MeV electrons in gyroresonance with VLF chorus can be less than a day in the lower‐density regions outside the plasmasphere. The mechanism of stochastic acceleration by VLF chorus could therefore be instrumental in generating relativistic electrons during the recovery phase of a magnetic storm. Pitch‐angle diffusion rates of MeV electrons scattered by EMIC waves along the plasmapause can approach the limit of strong diffusion. EMIC wave scattering could hence contribute significantly to electron precipitation loss over the course of a storm. Codes designed to model electron dynamics in the radiation belts need to incorporate, in addition to radial (cross‐L) diffusion, resonant diffusion due to electron gyroresonance with ELF, VLF, and EMIC waves. In order to determine the quasi‐linear diffusion coefficients for such codes, observational data are required on the power spectral density, spatial distribution, and temporal variation of these wave modes. Currently, only limited wave data sets are available. In addition, problems of numerical instability associated with diffusion codes need to be solved. The development of fully comprehensive models of radiation belt electron dynamics remains a considerable scientific challenge.

Vlasov Hybrid Simulation—An Efficient and Stable Algorithm for the Numerical Simulation of Collision‐Free Plasma

This paper presents a highly efficient and stable algorithm for the numerical simulation of collision free plasma. The algorithm has been successfully used to numerically model non linear electron cyclotron resonance in VLF band radio waves in space, and has produced good simulations of radio emissions such as ‘dawn chorus’ and ‘triggered VLF emissions’. The algorithm fills the phase box with simulation particles which represent phase space trajectories. Particle trajectories are followed forwards continuously in time without restarts, and these particles are followed until either the simulation ends or the particles exit from the phase box. Liouville’s theorem states that distribution function F is conserved along these trajectories, and so F is known at the phase space points represented by the particle positions. No phase space volume is associated with these particles. At each time step F is truly interpolated, and not distributed from particles to the regular phase space grid, solely for the purpose of calculating plasma charge and current fields. For this operation a cheap low order interpolation is useable. The algorithm is simple, robust and highly efficient. There is NO diffusion in phase space whatsoever, and fine structure is merely undersampled and does not cause any instability problems. Regions of phase space where F=0 are cost free as no particles need be provided. The algorithm readily accomodates situations where phase fluid flows into or out of the phase box. The paper presents the latest simulations of VLF chorus and VLF triggered emissions from the VHS/VLF code, which are in excellent agreement with observations.

Modelling substorm chorus events in terms of dispersive azimuthal drift

Abstract. The Substorm Chorus Event (SCE) is a radio phenomenon observed on the ground after the onset of the substorm expansion phase. It consists of a band of VLF chorus with rising upper and lower cutoff frequencies. These emissions are thought to result from Doppler-shifted cyclotron resonance between whistler mode waves and energetic electrons which drift into a ground station's field of view from an injection site around midnight. The increasing frequency of the emission envelope has been attributed to the combined effects of energy dispersion due to gradient and curvature drifts, and the modification of resonance conditions and variation of the half-gyrofrequency cutoff resulting from the radial component of the ExB drift. A model is presented which accounts for the observed features of the SCE in terms of the growth rate of whistler mode waves due to anisotropy in the electron distribution. This model provides an explanation for the increasing frequency of the SCE lower cutoff, as well as reproducing the general frequency-time signature of the event. In addition, the results place some restrictions on the injected particle source distribution which might lead to a SCE. Key words. Space plasma physics (Wave-particle interaction) – Magnetospheric physics (Plasma waves and instabilities; Storms and substorms)

Generation mechanism for VLF chorus emissions observed at a low-latitude ground station

Abstract. A detailed spectral analysis of VLF chorus emissions observed at the low-latitude ground station Gulmarg (geomag. lat., 24° 26' N, geomag. long., 147° 9' E, L=1.28) during the strong magnetic activity on 7-8 March 1986 have been carried out, which shows that each chorus element originates from the upper edge of the underlying hiss band. To explain various temporal and spectral features of these emissions, a possible generation mechanism has been presented based on the backward wave oscillator regime of the magnetospheric cyclotron maser. On the basis of this model, we have computed various chorus parameters as well as some magnetospheric parameters affecting the generation process. A comparison of the observed chorus characteristics with the proposed generation mechanism shows a good agreement.

Verification of the backward wave oscillator model of VLF chorus generation using data from MAGION 5 satellite

Abstract. We present a detailed study of chorus emissions in the magnetosphere detected on board Magion 5, when the satellite was not far from the magnetic equator. We determine the frequency sweep rate of more than 8500 electromagnetic VLF chorus elements. These results are compared with the backward wave oscillator (BWO) regime of chorus generation. Comparison of the frequency sweep rate with the BWO model shows: (i) There is a correlation between the frequency sweep rates and the chorus amplitudes. The frequency sweep rate increases with chorus amplitude, in accordance with expectations from the BWO model; (ii) The chorus growth rate, estimated from the frequency sweep rate, is in accord with that inferred from the BWO generation mechanism; (iii) The BWO regime of chorus generation ensures the observed decrease in the frequency sweep rate of the chorus elements with increasing L-shell.Key words. Magnetospheric physics (VLF emissions, energetic particles) – Space plasma physics (wave-particle interactions)

VLF, magnetic bay, and Pi2 substorm signatures at auroral and midlatitude ground stations

A superposed epoch analysis of 100–300 substorms is performed to determine the median size and shape of the substorm‐associated VLF chorus, magnetic bay, and Pi2 pulsation burst observed at the near‐auroral Halley research station, Antarctica, and at the midlatitude Faraday station at three different local times (2230, 2330, 0130 MLT). The spatial and temporal properties of the magnetic bay signatures are compared with the University of York implementation of the Kisabeth–Rostoker substorm current wedge (SCW) model and the Weimer pulse model, respectively. These constitute the best analytical models of the substorm to date. It is shown that the polarities and relative amplitudes of the observed magnetic bays in the H, D, and Z components at Halley at midnight MLT and at Faraday in the premidnight sector are consistent with the York model for a SCW 3 hours wide in MLT with its westward electrojet at 67°S magnetic latitude. In particular the little‐discussed Z component of the bay agrees with the model and is shown to be the clearest substorm signature of the three components, especially at midlatitude. The midnight and postmidnight bays are similar to the premidnight case but progressively smaller and cannot be fully reconciled with the model. The shape of the H and Z bays at Halley and the D bays at Faraday fit a normalized Weimer pulse well, with Weimer's 2 h−1 recovery rate, but the other components do not. The D component at Halley and H at Faraday do fit the Weimer pulse shape but with a faster recovery rate of 4 h−1. It is proposed that this is due to the effect of a decaying current in the SCW combining with the geometrical effect of changing SCW configuration and position relative to the observing station. The Z component at Faraday recovers more slowly than the 2 h−1 Weimer prediction; we cannot explain this. Secondary bays at Halley and Faraday show a clear tendency to recur after 2 hours. Inflection points just prior to onset at Halley and Faraday are argued to be related to reduced convection associated with northward turning of the IMF. The median substorm signature at Halley in the Pi2 frequency band (7–25 mHz) is well correlated with the bay structure, showing that it is part of a broader band, possibly turbulent, spectrum in the substorm‐dependent DP2 current. There is evidence of a minor additional narrow band component occurring at substorm onset. This is the dominant signal at Faraday which shows the classic midlatitude substorm signature, a short Pi2 pulsation burst at onset, that decreases progressively in intensity with increasing local time, implying a source region biased to the evening side or else preferred propagation to the east from a near‐midnight source.

Dynamic cell models of VLF chorus generation

We consider some cell models to explain a power-law distribution of time intervals between VLF chorus elements, revealed by the MAGION satellite data. This form of a distribution function usually used as an evidence that collective dynamics of a system is in “punctuated equilibrium” mode of self-organization. However, by physical reasons the punctuated equilibrium model cannot be used directly to explain self-similarity of VLF/ULF chorus emissions. To explain dynamics of chorus generation we worked out two mathematical models and found, that the observed power-law distribution in these models results from non-linearity of chorus generation mechanism.

Observations of relativistic electron microbursts in association with VLF chorus

The Solar, Anomalous and Magnetospheric Particle Explorer (SAMPEX) satellite frequently observes relativistic (> 1 MeV) electron precipitation in the radiation belts at L shells of 4–6 with bursty temporal structure lasting < 1 s. This phenomenon can occur at all local times but is most often seen between 0200 and 1000 magnetic local time. VLF chorus is also observed to occur preferentially at these same local times. Using electron observations from the SAMPEX satellite Heavy Ion Large Telescope and data from the Polar satellite plasma wave instrument, we show correlation between observations of relativistic electron microbursts and VLF chorus with frequencies <2 kHz. In addition, the duration of the individual rising frequency chorus elements is comparable to the duration of the relativistic electron microbursts. It has been speculated that relativistic electron microbursts are caused by wave‐particle interactions, which strongly scatter electrons into the loss cone for a short period. Lower‐energy electron microbursts in the range from tens to hundreds of keV have long been associated with chorus waves, since these lower‐energy electrons can resonate at the equator with whistler‐mode waves at chorus frequencies. Electrons of MeV energies do not satisfy the first‐order cyclotron resonance condition with chorus wave frequencies at the equator. However, MeV electrons may interact with chorus through higher‐order resonances or off‐equatorial interactions.

Auroral pulsations and accompanying VLF emissions

Abstract. Results of simultaneous TV observations of pulsating auroral patches and ELF-VLF-emissions in the morning sector carried out in Sodankylä (Finland) on February 15, 1991 are presented. Auroral pulsating activity was typical having pulsating patches with characteristic periods of about 7 s. Narrow-band hiss emissions and chorus elements at intervals of 0.3–0.4 s formed the main ELF-VLF activity in the frequency range 1.0–2.5 kHz at the same time. The analysis of auroral images with time resolution of 0.04 s allowed perfectly separate analysis of spatial and temporal variations in the auroral luminosity. Mutual correspondence between the behaviour of the luminous auroral patches and the appearance of ELF noise type hiss emissions and VLF chorus trains was found in two intervals chosen for analysis. While the hiss emissions were associated with the appearance of luminosity inside a limited area close to the zenith, the structured VLF emissions were accompanied by rapid motion of luminosity inside the area. The spatial dimension of the pulsating area was about 45–50 km and luminosity propagated inside it with velocity of about 10–12 kms. We discuss a new approach to explain the 5–15 s auroral pulsation based on the theory of flowing cyclotron maser and relaxation characteristics of ionosphere.Key words. Magnetospheric physics (auroral phenomena; magnetosphere-ionosphere interactions) · Space plasma physics (wave-particle interactions)

VLF chorus emissions observed by Polar during the January 10, 1997, magnetic cloud

VLF chorus emissions occur near the dawn meridian in fast response (<60 s) to magnetospheric perturbations caused by sudden fluctuations in solar wind dynamic pressure and southward turnings of the interplanetary magnetic field (IMF) at the arrival of the Jan. 10, 1997 magnetic cloud. Raytracing analysis indicates the likely chorus source region to be near the magnetic equator with rays launched at oblique wave normal angles, for which likely resonant electron energies are in the range E∼14–30 keV, consistent with observed particle data.

The numerical simulation of VLF chorus and discrete emissions observed on the Geotail satellite using a Vlasov code

The Geotail satellite skims the dayside magnetosphere in the equatorial region at about L = 10. During such passes the WFC (Waveform Capture Receiver) observes VLF chorus and discrete emissions in the band 200 ∼ 1200 Hz. The most common waveforms observed are rising tones and rising chorus, with hooks and fallers being seen occasionally. Analysis shows that the k vectors are closely parallel to the ambient magnetic field. The Geotail satellite has available comprehensive wave and particle data observed in the vicinity of the generation regions of such VLF emissions. A well‐established Vlasov simulation code has been used to simulate the observed emissions, using detailed data from Geotail. The code readily simulates rising frequency VLF emissions with a steep frequency gradient. With appropriate parameter values the code will produce fallers and hooks in good agreement with those observed on Geotail. These self‐consistent simulations suggest that nonlinear trapping of cyclotron resonant electrons is the underlying mechanism behind VLF chorus and VLF emissions.

Correction to “Postmidnight VLF chorus events, a substorm signature observed at the ground near L = 4” by A. J. Smith, M.P. Freeman, and G. D. Reeves

Correction to “Postmidnight VLF chorus events, a substorm signature observed at the ground near <i>L</i> = 4” by A. J. Smith, M.P. Freeman, and G. D. Reeves

Post midnight VLF chorus events, a substorm signature observed at the ground near L = 4

Clouds of energetic electrons, injected sporadically into the nightside magnetosphere during substorm expansion phase onsets, can generate VLF whistler mode noise through the gyroresonance instability, which may then be observed on the ground or in space. Although these substorm‐related chorus events (SCEs) have been reported occasionally in the literature, there seems to have been no systematic study, probably because of the lack, until now, of a well‐adapted experimental technique. The VLF/ELF Logger Experiment (VELOX) instrument, located at Halley, Antarctica (76°S, 26°W, L = 4.3), is, however, particularly well suited to a systematic study of this aspect of the substorm phenomenon. The data exist almost continuously from January 1992 onward, at 1‐s time resolution in eight quasi‐logarithmically spaced frequency bands covering the range 0.25–10 kHz. For this paper, 327 days of continuous data from 1992 have been analyzed. The 243 SCEs identified were observed on about 50% of days, almost exclusively in the 2300–0600 MLT local time range, and were characterized by limited duration (typically, ∼10 min at 1.5 kHz) and upward frequency drift of a band of usually weak and relatively unstructured chorus at a rate of ∼200 Hz min−1 between 0.5 and 5 kHz (corresponding to parallel electron energies in the range ∼10–100 keV). This drift is consistent with the combined eastward and inward motion of the resonant electrons due to azimuthal gradient‐curvature drift and radial E × B drift under the action of substorm‐enhanced westward electric fields of order l mVm−1 near the equatorial plane. The limited MLT viewing window of the station implies an overall detection efficiency for SCEs of ∼20%. The inferred annual mean substorm rate, 1366 ± 188 year−1, and inter substorm interval, 5.5 ± 0.8 hours, are similar to the values derived using other techniques. However, the distribution of intervals between successive SCEs is different from that for substorm‐related particle injections at geostationary orbit; in particular, the models around 1 hour rather than 2–3 hours. The SCE as seen by a VELOX‐type VLF receiver with a wide field of view is an important alternative ground‐observable substorm signature, complementary to those (such as bays and Pi 2 pulsations) indicated by magnetometers.

A cyclotron resonance model of VLF chorus emissions detected during electron microburst precipitation

VLF chorus, consisting of narrowband rising frequency emissions, has often been observed in association with microburst electron precipitation. We present the first simultaneous rocket observations of these two phenomena, with emphasis on understanding the source of the VLF emissions. The rocket experiment was launched on May 6, 1993, from Poker Flat, Alaska (L = 5.6). In this work, the observed 1–4 kHz chorus emissions are interpreted in terms of a cyclotron resonance interaction. The frequency range of the risers and the observed electron energy range agree with those required for this interaction. Using a criterion derived from the conservation of energy during an interaction, it is shown that a cold plasma cyclotron resonance interaction can produce the lower‐frequency portions of the observed chorus risers, from ≈1000 Hz to ≈2500 Hz, while a warm plasma model is required to produce frequencies &gt; 2500 Hz. The warm plasma model assumes a two‐component plasma, with an isotropic cold component and a bi‐Maxwellian warm component. The effect of the warm component is to change the wave dispersion relation, allowing the production of the higher‐frequency risers. A portion of the anisotropy required to produce the high‐frequency emissions can also be provided by a loss cone distribution. The chorus source is estimated from this cyclotron resonance theory to be located near the equatorial plane.

Direction‐finding measurements of magnetospheric vlf chorus emissions and analysis of their generation and propagation mechanism

AbstractChorus is one of the most important VLF/ELF emissions in the magnetosphere, but several points are still unsolved concerning their generation and propagation mechanisms.In this paper, the near‐equatorial direction‐finding measurements made on board a satellite are studied first and it is confirmed that the rising tone chorus (frequency of the chorus increases with time) is generated at θ (the angle between the wave normal and earth's magnetic field) ˜ 0° by the cyclotron resonance interaction with the energetic electrons.These results support the previous theory of Helliwell. Moreover, the direction‐finding measurements of the rising tone chorus are carried out aboard the GEOS 1 satellite in the off‐equatorial regions. Their generation and propagation mechanism are studied with the help of three‐dimensional ray‐tracing computations and these results are compared with the corresponding results of OGO 5 direction‐finding measurements by Burton et al.As a result, the observations by OGO 5 indicate that after the generation of chorus at the equator with wave‐normal direction θ0 ˜ 0°, it reaches the satellite in ducted propagation along the magnetic field line, whereas the results of GEOS 1 suggest that the waves are generated in a wider region near the equator with comparatively smaller θ0 (30° ˜ 40°, at the most 50°) and that the subsequent propagation is nonducted in the magnetosphere.Finally, the direction finding measurements and the ray‐tracing computation are suggested to be very important in the study of generation and propagation of various emissions generated in the magnetosphere.