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 found that higher values of Te/Ti promote the generation of backscattered Langmuir wave component, and that a higher initial wave intensity suppresses the backscattered component while significantly enhancing the long-wavelength Langmuir wave component.

The plasma emission, or electromagnetic (EM) radiation at the plasma frequency and/or its harmonic(s), is generally accepted as the radiation mechanism responsible for solar type II and III radio bursts. Identification and characterization of these solar radio burst phenomena were done in the 1950s. Despite many decades of theoretical research since then, a rigorous demonstration of the plasma emission process based upon first principles was not available until recently, when, in a recent Letter, Ziebell et al. reported the first complete numerical solution of EM weak turbulence equations; thus, quantitatively analyzing the plasma emission process starting from the initial electron beam and the associated beam-plasma (or Langmuir wave) instability, as well as the subsequent nonlinear conversion of electrostatic Langmuir turbulence into EM radiation. In the present paper, the same problem is revisited in order to elucidate the detailed physical mechanisms that could not be reported in the brief Letter format. Findings from the present paper may be useful for interpreting observations and full-particle numerical simulations.

Numerical solutions for equations of weak turbulence theory that describe the beam-plasma interaction are obtained in two dimensions (2D). The selfconsistent 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 quasiisotropic 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.

Generation of electrostatic multiple harmonic Langmuir modes during beam-plasma interaction process has been observed in laboratory and spaceborne active experiments, as well as in computer simulation experiments. Despite earlier efforts, such a phenomenon has not been completely characterized both theoretically and in terms of numerical simulations. This paper is a first in a series of three papers in which analytic expressions for harmonic Langmuir mode dispersion relations are derived and compared against the numerical simulation result.

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.