L. F. Ziebell

Electromagnetic cyclotron-loss-cone instability associated with weakly relativistic electrons

The amplification of fast extraordinary mode waves with frequencies very close to the electron cyclotron frequency is investigated for a plasma which consists of a weakly relativistic electron component with a loss-cone type distribution and a cold background electron component. The basic mechanism of the amplification is attributed to a relativistic cyclotron resonance between the wave and the energetic electrons. The method employed in the present analysis enables us to solve the dispersion relation in a self-consistent manner for arbitrary ratio of the densities of the energetic and background electrons. It is found that the maximum growth rates occur at certain values of ω 2 pe /Ω 2 e and the angular dependence of the growth rate is sensitive to the ratios ω 2 pe /Ω 2 e and n e / n b . Here ω pe and Ω e are the electron plasma frequency and the electron cyclotron frequency, respectively, and n e and n b denote the number densities of the energetic and background electrons, respectively.

Nonlinear development of weak beam–plasma instability

Nonlinear interactions of tenuous electron beam, background, unmagnetized plasma, and self-consistently generated Langmuir and ion-sound waves are analyzed in the framework of plasma weak turbulence kinetic theory. Full numerical solutions of the complete weak turbulence equations are obtained for the first time, which show the familiar plateau formation in the electron beam distribution and concomitant quasi-saturation of primary Langmuir waves, followed by fully nonlinear processes which include three-wave decay and induced-scattering processes. A detailed analysis reveals that the scattering off ions is an important nonlinear process which leads to prominent backscattered and long-wavelength Langmuir wave components. However, it is found that the decay process is also important, and that the nonlinear development of weak Langmuir turbulence critically depends on the initial conditions. Special attention is paid to the electron-to-ion temperature ratio, Te/Ti, and the initial perturbation level. It is f...

NONLINEAR EVOLUTION OF BEAM-PLASMA INSTABILITY IN INHOMOGENEOUS MEDIUM

The problem of electron-beam propagation in inhomogeneous solar wind is intimately related to the solar type II and/or type III radio bursts. Many scientists have addressed this issue in the past by means of quasi-linear theory, but in order to fully characterize the nonlinear dynamics, one must employ weak-turbulence theory. Available numerical solutions of the weak-turbulence theory either rely on only one nonlinear process (either decay or scattering), or when both nonlinear terms are included, the inhomogeneity effect is generally ignored. The present paper reports the full solution of weak-turbulence theory that includes both decay and scattering processes, and also incorporating the effects of density gradient. It is found that the quasi-linear effect sufficiently accounts for the primary Langmuir waves, but to properly characterize the back-scattered Langmuir wave, which is important for eventual radiation generation, it is found that both nonlinear decay and scattering processes make comparable contributions. Such a finding may be important in the quantitative analysis of the plasma emission process with application to solar type II and/or type III radio bursts.

Two-dimensional nonlinear dynamics of beam–plasma instability

Numerical solutions for equations of weak turbulence theory that describe the beam–plasma interaction are obtained in two dimensions (2D). The self-consistent theory governs quasilinear processes as well as nonlinear decay and scattering processes. It is found that the Langmuir turbulence scatters into a quasi-circular ring spectrum in 2D wave number space, accompanied by quasi-isotropic heating of the electrons. When projected onto the one-dimensional (1D) space, 2D Langmuir turbulence spectrum appears as an inverse cascade, when in reality, the wavelength of the turbulence does not change but only the wave propagation angle changes. These findings are similar to those obtained in a previous analysis in which scattering processes were not taken into account, but it is found that the scattering term leads to a quantifiably higher scattering rate.

Asymmetric Solar Wind Electron Superthermal Distributions

Electron distributions with various degrees of asymmetry associated with the energetic tail population are commonly detected in the solar wind near 1 AU. By numerically solving one-dimensional electrostatic weak turbulence equations the present paper demonstrates that a wide variety of asymmetric energetic tail distributions may result. It is found that a wide variety of asymmetric tail formation becomes possible if one posits that the solar wind electrons are initially composed of thermal core plus field-aligned counterstreaming beams, instead of the customary thermal population plus a single beam. It is shown that the resulting nonlinear wave-wave and wave-particle interactions lead to asymmetric nonthermal tails. It is found that the delicate difference in the average beam speeds associated with the forward versus backward components is responsible for the generation of asymmetry in the energetic tail.

Dynamics of Langmuir wave decay in two dimensions

The present paper reports on the first two-dimensional (2D) self-consistent solution of weak turbulence equations describing the evolution of electron-beam-plasma interaction in which quasilinear as well as nonlinear three-wave decay processes are taken into account. It is found that the 2D Langmuir wave decay processes lead to the formation of a quasicircular ring spectrum in wave number space. It is also seen that the 2D ring-spectrum of Langmuir turbulence leads to a tendency to isotropic heating of the electrons. These findings contain some important ramifications. First, in the literature, isotropization of energetic electrons, detected in the solar wind for instance, is usually attributed to pitch-angle scattering. The present finding constitutes an alternative mechanism, whose efficiency for other parametric regimes has to be investigated. Second, when projected onto the one-dimensional (1D) space, the 2D ring spectrum may give a false impression of Langmuir waves inverse cascading to longer wavele...

Excitation of whistler waves by reflected auroral electrons

Abstract Excitation of electron cyclotron waves and whistlers by reflected auroral electrons which possess a loss-cone distribution is investigated. Based on a given magnetic field and density model, the instability problem is studied over a broad region along the auroral field lines. This region covers altitudes ranging from one quarter of an Earth radius to five Earth radii. It is found that the growth rate is significant only in the region of low altitude, say below the source region of the auroral kilometric radiation. In the high altitude region the instability is insignificant either because of low refractive indices or because of small loss cone angles.

Electron cyclotron emission from tokamak plasmas with mildly superthermal electrons

The emission of cyclotron radiation from a tokamak plasma in the presence of a high toroidal current is investigated. For the fundamental frequency, a theory of the radiation which consistently includes the hot plasma polarization effects is developed. The high current density electron system is described by a distribution function which is the sum of two Maxwellian functions representing the body of the electron population and a small fraction of superthermal drifting electrons, respectively. The emission of the ordinary and extraordinary modes in the equatorial plane of the torus for quasi‐perpendicular propagation is investigated numerically. It is found that the radiation temperature deduced from the emission of radiation on the high Bt side of the torus differs from that on the low Bt side, where Bt is the confining magnetic field.

A purely growing electromagnetic mode operative in the geomagnetic tail

This paper discusses a purely growing mode driven by a cross-field current. The study was motivated by a recent article by Chang et al. (1990). The present discussion pays special attention to two aspects. One is to generalize the analysis by Chang et al. (1990) so that the unmagnetized-ion approximation used by these authors is removed, and the other is to apply the theory to several regions in the magnetotail where the value of the plasma beta is in general very high. The present analysis is restricted to waves propagating along the ambient magnetic field. The high ion beta limit is discussed by considering two different situations. The first is to fix the strength of the ambient magnetic field but to increase the plasma temperature, and the second is to maintain the plasma temperature but to decrease the ambient magnetic field strength. It is found that in the former case the mode stabilizes when βi → ∞, but in the latter case the instability persists even if βi → ∞ (although the growth rate is significantly reduced). The present theory is applied to three regions in the magnetotail. These are: (1) the inner edge region, (2) the midtail region, and (3) the neutral sheet of a distant magnetotail. It is found that, among these three regions, for a given value of υ0 / αi, where υ0 is the net cross-field drift speed between the electrons and the ions and αi is the ion thermal speed, the growth rate in the neutral sheet is found to be the largest.

Effect of electron thermal anisotropy on the kinetic cross-field streaming instability

The investigation of the kinetic cross-field streaming instability, motivated by the research of collisionless shock waves and previously studied by Wu et al. (1983), is discussed more fully. Since in the ramp region of a quasi-perpendicular shock electrons can be preferentially heated in the direction transverse to the ambient magnetic field, it is both desirable and necessary to include the effect of the thermal anisotropy on the instability associated with a shock. It is found that Te-perpendicular greater than Te-parallel can significantly enhance the peak growth rate of the cross-field streaming instability when the electron beta is sufficiently high. Furthermore, the present analysis also improves the analytical and numerical solutions previously obtained.