RUDI GAELZER

A recent paper [Ziebell et al., Phys. Plasmas 21, 010701 (2014)] discusses a new type of radiation emission process for plasmas in a state of quasi-equilibrium between the particles and enhanced Langmuir turbulence. Such a system may be an example of the so-called “turbulent quasi-equilibrium.” In the present paper, it is shown on the basis of electromagnetic weak turbulence theory that an initial thermal equilibrium state (i.e., only electrostatic fluctuations and Maxwellian particle distributions) transitions toward the turbulent quasi-equilibrium state with enhanced electromagnetic radiation spectrum, thus demonstrating that the turbulent quasi-equilibrium discussed in the above paper correctly describes the weakly turbulent plasma dynamically interacting with electromagnetic fluctuations, while maintaining a dynamical steady-state in the average sense.

Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes are limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.

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.

Solar wind electrons near 1 AU feature wide-ranging asymmetries in the superthermal tail distribution. Gaelzer et al. (2008) recently demonstrated that a wide variety of asymmetric distributions results if one considers a pair of counterstreaming electron beams interacting with the core solar wind electrons. However, the nonlinear dynamics was investigated under the simplifying assumption of one dimensionality. In the present paper, this problem is revisited by extending the analysis to two dimensions. The classic bump-on-tail instability involves a single electron beam interacting with the background population. The bidirectional or counterstreaming beams excite Langmuir turbulence initially propagating in opposite directions. It is found that the nonlinear mode coupling leads to the redistribution of wave moments along concentric arcs in wave number space, somewhat similar to the earlier findings by Ziebell et al. (2008) in the case of one beam-plasma instability. However, the present result also shows distinctive features. The similarities and differences in the nonlinear wave dynamics are discussed. It is also found that the initial bidirectional beams undergo plateau formation and broadening in perpendicular velocity space. However, the anisotropy persists in the nonlinear stage, implying that an additional pitch angle scattering by transverse electromagnetic fluctuations is necessary in order to bring the system to a truly isotropic state.

Beam–plasma instability of inhomogeneous media is an important problem associated with practical applications in space and laboratory plasmas. Previous investigations of the spatially inhomogeneous beam–plasma instability problem assumed one-dimensional velocity and wave number space. This paper extends the available theory to two-dimensional velocity and wave number space. A fully self-consistent set of quasilinear particle and wave kinetic equations is solved for two-dimensional velocity and wave number space in both time and one-dimensional spatial inhomogeneity scale length. The analytical equations include induced and spontaneous emission processes, as well as convective and dispersive effects.