E. E. Titova

Interpretation of Cluster data on chorus emissions using the backward wave oscillator model

The measurements of chorus emissions by four closely separated Cluster spacecraft provide important information concerning the chorus generation mechanism. They confirm such properties of the wave source as their strong localization near the equatorial cross section of a magnetic flux tube, an almost parallel average wave-vector direction with respect to the geomagnetic field, and an energy flux direction pointing outward from the generation region. Inside this region, Cluster discovered strong temporal and spatial variations in the amplitude with correlation scale lengths of the order of 100 km across the magnetic flux. The wave electric field reached 30 mV/m, and the maximum growth and damping rates are of the order of a few hundreds of s−1. These and other properties of the detected chorus emissions are discussed here in relation with the backward wave oscillator mechanism. According to this mechanism, a succession of whistler wave packets is generated in a small near-equatorial region with temporal an...

Observations of the relationship between frequency sweep rates of chorus wave packets and plasma density

[1] Chorus emissions are generated by a nonlinear mechanism involving wave‐particle interactions with energetic electrons. Discrete chorus wave packets are narrowband tones usually rising (sometimes falling) in frequency. We investigate frequency sweep rates of chorus wave packets measured by the Wideband data (WBD) instrument onboard the Cluster spacecraft. In particular, we study the relationship between the sweep rates and the plasma density measured by the WHISPER active sounder. We have observed increasing values of the sweep rate for decreasing plasma densities. We have compared our results with results of simulations of triggered emissions as well as with estimates based on the backward wave oscillator model for chorus emissions. We demonstrate a reasonable agreement of our experimental results with theoretical ones. Citation: Macusova, E., et al. (2010), Observations of the relationship between frequency sweep rates of chorus wave packets and plasma density,

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

[1] 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 steplike 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. Citation: Trakhtengerts, V. Y., A. G. Demekhov, E. E. Titova, B. V. Kozelov, O. Santolik, E. Macusova, D. Gurnett, J. S. Pickett, M. J. Rycroft, and D. Nunn (2007), Formation of VLF chorus frequency spectrum: Cluster data and comparison with the backward wave oscillator model, Geophys. Res. Lett., 34, L02104, doi:10.1029/2006GL027953.

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

We 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.

Identification of the source of quasiperiodic VLF emissions using ground‐based and Van Allen Probes satellite observations

We report on simultaneous spacecraft and ground-based observations of quasiperiodic VLF emissions and related energetic-electron dynamics. Quasiperiodic emissions in the frequency range 2–6 kHz were observed during a substorm on 25 January 2013 by Van Allen Probe-A and a ground-based station in the Northern Finland. The spacecraft detected the VLF signals near the geomagnetic equator in the night sector at L = 3.0–4.2 when it was inside the plasmasphere. During the satellite motion toward higher latitudes, the time interval between quasiperiodic elements decreased from 6 min to 3 min. We find one-to-one correspondence between the quasiperiodic elements detected by Van Allen Probe-A and on the ground, which indicates the temporal nature of the observed variation in the time interval between quasiperiodic elements. Multiсomponent measurements of the wave electric and magnetic fields by the Van Allen Probe-A show that the quasiperiodic emissions were almost circularly right-hand polarized whistler mode waves and had predominantly small (below 30°) wave vector angles with respect to the magnetic field. In the probable source region of these signals (L about 4), we observed synchronous variations of electron distribution function at energies of 10–20 keV and the quasiperiodic elements. In the pause between the quasiperiodic elements pitch angle distribution of these electrons had a maximum near 90°, while they become more isotropic during the development of quasiperiodic elements. The parallel energies of the electrons for which the data suggest direct evidence of the wave-particle interactions is in a reasonable agreement with the estimated cyclotron resonance energy for the observed waves.

Spectral features of lightning‐induced ion cyclotron waves at low latitudes: DEMETER observations and simulation

[1] We use a comprehensive analysis of 6-component ELF wave data from the DEMETER satellite to study proton whistlers, placing emphasis on low-latitude events originating from lightning strokes in the hemisphere opposite to the hemisphere of observation. In this case, the formation of proton whistlers does not involve mode conversion caused by a strong mode coupling at a crossover frequency, although a polarization reversal remains an important element in formation of the phenomenon. DEMETER measurements of the six electromagnetic field components in the frequency band below 1000 Hz make it possible to determine not only the dynamic spectrum, but also the wave polarization, the wave normal angle, and the normalized parallel component of the Poynting vector. This permits us to address fine features of proton whistlers, in particular, we show that the deviation of the upper cutoff frequency from the equatorial cyclotron frequency is related to the Doppler shift. Experimental study of proton whistlers is supplemented by an investigation of ion cyclotron wave propagation in a multicomponent magnetoplasma and by numerical modeling of spectrograms, both in the frame of geometrical optics.

Testing of the backward wave oscillator model by using the spectral characteristics of VLF chorus elements

A generation mechanism for chorus was suggested by Trakhtengerts (1995) on the basis of the backward wave oscillator (BWO) regime of the magnetospheric cyclotron maser. According to this model, step-like deformation on the electron distribution function is the most important factor of chorus generation, but such a feature is very difficult to observe. By measuring the frequency sweep rates in chorus elements detected by the Cluster spacecraft we determine the mean values and distributions of a dimensionless parameter characterizing the step feature. These values are in agreement with the results of numerical simulations of chorus elements based on the BWO model.

U‐Shaped Spectrograms Registered by the DEMETER Satellite: Observational Features and Formation Mechanism

U-shaped spectrograms observed by the DEMETER satellite in the equatorial region of the upper ionosphere are presented and explained for the first time. These spectra are characterized by the latitude-dependent upper cutoff frequency that increases with the latitude during nighttime. The observations suggest that this very low frequency wave phenomenon is closely connected with the anomalous increase in cold plasma density at and below the satellite. We show that restricting the analysis to propagation effects is insufficient to explain U-shaped spectra, and other effects, in particular, the collisional wave damping should be taken into consideration. To calculate the wave damping, we use the method of successive approximations. In the first approximation, we calculate the ray trajectory and the wave normal vector along it, using the equations of geometrical optics neglecting collisions. In the second approximation we calculate the collisional wave damping along the precalculated trajectory. We show that the effects of very low frequency wave propagation and attenuation in the equatorial region of the upper ionosphere explain the main features of the phenomenon under discussion.

Variety of proton whistlers: Satellite observation and theoretical analysis

Based on observations from the DEMETER satellite, we present and investigate various types of proton whistlers, including ionospherically reflected proton whistlers, which have not been discussed so far. The observations are complemented by theoretical analysis and numerical simulations. A side result of the analysis consists in that the region in the Earth-ionosphere waveguide illuminated by a lightning stroke, which serves as an effective source of the emission, spreads more than 30 degrees over latitude in meridian plane.

On statistical distribution of characteristics of chorus element generation

A generation mechanism for VLF chorus was suggested by V. Yu. Trakhtengerts [1, 2] on the basis of the backward wave oscillator (BWO) regime of magnetospheric cyclotron maser. Up to now many predictions of the BWO regime were supported by observations. In this report we discuss a statistical distribution of the dimensionless parameter q, quantifying an excess of the electron flux over the absolute-instability threshold. Typically the q parameter values deduced from VLF chorus elements observed by WBD instrument onboard the CLUSTER spacecraft exhibit significant scatter, while their mean values were ∼10. We suppose that so large excess of the instability threshold cannot be permanently supported in the magnetospheric plasma. On the basis of the discrete numerical model we demonstrate that if the noised “on-off” intermittency regime generation is realized, then the observed q values deduced from chorus elements should be extreme ones, but the average value over the entire event can be much smaller. We stress an importance of taking the noise-induced type of chorus generation into account.