V. Y. Trakhtengerts

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...

Interrelation of noise‐like and discrete ELF/VLF emissions generated by cyclotron interactions

It is shown that quasi-monochromatic whistler waves (wavelets) can be caused by the strong cyclotron instability, stimulated by hiss emissions. The hiss, generated by the cyclotron instability of an anisotropic smooth energetic electron distribution, creates a step-like deformation of the distribution function at the boundary between resonant and nonresonant electrons. This deformation leads to the strong amplification of the wavelet whose frequency corresponds to that for cyclotron resonance with electrons at the step. Analytical calculations for this amplification have been made using the rigorous theory of the cyclotron instability in an inhomogeneous magnetic field. The wave amplification can be 2 orders of magnitude greater than that for a smooth distribution function. A self-consistent computational analysis of the cyclotron instability is developed on the basis of quasi-linear theory. This confirms both the formation of the step-like deformation of the distribution function and the wavelet generation.

Whistler and Alfvén mode cyclotron masers in space

Preface 1. Introduction 2. Basic theory of cyclotron masers (CMs) 3. Linear theory of the cyclotron instability (CI) 4. Backward wave oscillator (BWO) regime in CMs 5. Nonlinear cyclotron wave-particle interactions for a quasi-monochromatic wave 6. Nonlinear interaction of quasi-monochromatic whistler mode waves with gyroresonant electrons in an in homogeneous plasma 7. Wavelet amplification in an inhomogeneous plasma 8. Quasi-linear theory of cyclotron masers 9. Nonstationary generation regimes, and modulation effects 10. ELF/VLF noise-like emissions and electrons in the Earths radiation belts 11. Generation of discrete ELF/VLF whistler mode emissions 12. Cyclotron instability of the proton radiation belts 13. Cyclotron masers elsewhere in the solar system and in laboratory plasma devices Epilogue Glossary of terms List of acronyms References Index.

Cyclotron acceleration of radiation belt electrons by whistlers

The work consdiers the non linear scattering of energetic electrons in the earths radiation belts due to cyclotron interaction with VLF whistlers. In particular we consdier the acceleration of electrons which may result from trapping in the inhomogeneous medium. It is shown that considerable electron heating may result, and that the very anisotorpic electron distribution functions observed by Bell etal may be explained

Backward wave oscillator regime of the whistler cyclotron instability in an inhomogeneous magnetic field

A linear theory for the backward wave oscillator generation regime of whistler waves in the Earth’s magnetosphere is presented. Using a parabolic profile of the magnetic field and a linear expression for the resonant current in the case of a zeroth order distribution function with a step discontinuity in the velocity component parallel to the magnetic field, the modes of the system are investigated by means of a search procedure. The existence of at least one mode exponentially growing in time is indicative of absolute instability, and such modes have been found. Therefore, an earlier prediction of such a regime, based on the homogeneous magnetic field model, is confirmed. The dependence of growth rates on the frequency mismatch and energetic electron density has been studied. These results yield the characteristic spatial profile and temporal growth rate of small-amplitude whistler-wave disturbances, which are likely to be the seeds for chorus emissions.

Formation of electron beams by the interaction of a whistler wave packet with radiation belt electrons

Abstract The purpose of this paper is to discuss the properties of electron beams formed by cyclotron interactions between radiation belt electrons and a quasi-monochromatic whistler wave packet from a ground-based VLF transmitter. The beams are formed due to trapping of the electrons at the forward edge of the wave packet, their acceleration inside the wave packet, the escape of the accelerated electrons from the moving backward edge of the wave packet, and their following free motion in an inhomogeneous magnetic field. A combination of these processes provides the main features of the spatial-temporal evolution of the beams which are investigated both analytically and numerically. It is shown that one or two beams can appear at one point at the same time, and that the density of the beams increases during their expansion. Motion of the pumping wave packet in the inhomogeneous magnetic field provides the variations of the initial velocity and position of the beam injection which change the spatial and temporal gradients of the parallel velocity of the beam, in contrast with the case of the pure adiabatic motion of an individual electron. Such a behaviour can be significant for the generation of secondary emissions. Numerical calculations demonstrate a wide variety of the spatio–temporal patterns of the beam parallel velocity depending on the plasma and wave packet parameters. It is shown that the most significant parameters which determine the beam characteristics are the wave packet length about the equator, its group velocity, and the initial energy and pitch angle of the electrons.

Beam-plasma instability in inhomogeneous magnetic field and second order cyclotron resonance effects

A new analytical approach to cyclotron instability of electron beams with sharp gradients in velocity space (step-like distribution function) is developed taking into account magnetic field inhomogeneity and nonstationary behavior of the electron beam velocity. Under these conditions, the conventional hydrodynamic instability of such beams is drastically modified and second order resonance effects become important. It is shown that the optimal conditions for the instability occur for nonstationary quasimonochromatic wavelets whose frequency changes in time. The theory developed permits one to estimate the wave amplification and spatio-temporal characteristics of these wavelets.

Cellular automaton modeling of mesospheric optical emissions: Sprites

This paper presents a new attempt to model two-dimensional mesospheric optical emissions named sprites with the use of a cellular automaton network. A large-scale model of sprites based on the phenomenological percolation-like probabilistic approach is developed to model streamer discharges in sprites. It is shown that a sprite is a self-affine structure rather than a simple fractal one, and that this self-affine structure is tightly connected with directed percolation phenomena. The system is found to evolve in the vicinity of the percolation threshold, which results in a wide variety of sprite characteristics even under similar initial conditions. The approach developed allows us to estimate a maximum size of the discharge pattern to be formed.

Cyclotron amplification of whistler waves by electron beams in an inhomogeneous magnetic field

Cyclotron wave-particle interactions in the case of well-organized distributions of energetic electrons under an inhomogeneous magnetic field are studied. Step-like and δ function distributions over the field-aligned velocity are considered. The one-hop amplification of whistler waves is calculated by simple analytical solution and numerical computation based on strict approach. The strict consideration, taking into account third-order expansion of the spatial dependence of the electron phase with respect to the wave, reveals sonic new important features of the one-hop amplification Γ as a function of frequency and electron beam parameters. The main result is that Γ exhibits a quasi-periodic structure as a function of wave frequency or characteristic electron parallel velocity, remaining always positive in the case of the step-like distribution but being sign alternative for δ-function. Dependence of Γ on the parameters of energetic electrons such as their total energy, characteristic parallel velocity, position of the injection point in relation to the equator, and dispersion in parallel velocity is discussed.

Cyclotron amplification of whistler‐mode waves: A parametric study relevant to discrete VLF emissions in the Earth's magnetosphere

[1] We study the amplification of ducted whistler-mode waves in the Earth’s magnetosphere by the cyclotron instability for different types of energetic electron distributions in velocity space. Particular attention is paid to the comparison between cases of smooth distribution functions and those with sharp gradients (‘‘steps’’) in velocity space, which arise naturally owing to interactions with noise-like VLF emissions. We show that step-like features greatly favor the amplification of whistler-mode waves propagating along the Earth’s magnetic field line and hence the generation of narrowband VLF emissions even if the electron anisotropy is only moderate. The results obtained are discussed in light of observations of discrete VLF emissions from the magnetosphere, in particular those of Bell et al. [2000]. INDEX TERMS: 2720 Magnetospheric Physics: Energetic particles, trapped; 2730 Magnetospheric Physics: Magnetosphere—inner; 0654 Electromagnetics: Plasmas; 2772 Magnetospheric Physics: Plasma waves and instabilities; KEYWORDS: whistlers, amplification, anisotropic, electrons, step-like, chorus