Instability of Langmuir-beam waves: Kappa-distributed electrons

Abstract

In space plasmas, electron populations exhibit non-equilibrium velocity distributions with high-energy tails that are reproduced by the Kappa power-laws and contrast with the Maxwellian distributions often used in theoretical and numerical analyses. In this work, we investigate typical electron beam-plasma systems and show the influence of Kappa tails on the linear dispersion and stability spectra of Langmuir-beam waves. The most common scenarios invoke instabilities of Langmuir waves at the origin of radio emissions in solar flares and interplanetary shocks. However, the parametric domain of these instabilities is narrow (i.e., energetic beams but with very low density, n b / n e ≲ 10 − 3 ), making their analytical and numerical characterization not straightforward, while the approximations used may lead to inconclusive results. Here, we provide exact numerical solutions of the Langmuir-beam mode, which distinguish from the classical ones (unaffected by the beam), and also from electron beam modes destabilized by more energetic and/or denser beams. Langmuir-beam solutions are only slightly modified by the Kappa distribution of the beam component, due to its very low density. However, if the main (core) population is Kappa distributed, the instability of the Langmuir-beam mode is strongly inhibited, if not suppressed. New analytical solutions are derived taking into account the more or less resonant involvement of the electron core and beam populations. As a result, the analytical solutions show an improved match with the exact solutions, making them applicable in advanced modeling of weak (weakly nonlinear) turbulence.