Landau damping in space plasmas

Abstract

Space plasmas typically possess a particle distribution function with an enhanced high-energy tail that is well modeled by a generalized Lorentzian (or kappa) distribution with spectral index κ. The modified plasma dispersion function Z*κ(ξ) [Summers and Thorne, Phys. Fluids B 3, ■■■■ (1991)] is employed to analyze the Landau damping of (electrostatic) Langmuir waves and ion-acoustic waves in a hot, isotropic, unmagnetized, generalized Lorentzian plasma, and the solutions are compared with the classical results for a Maxwellian plasma. Numerical solutions for the real and imaginary parts of the wave frequency ω0−iγ are obtained as a function of the normalized wave number kλD, where λD is the electron Debye length. For both particle distributions the electrostatic modes are strongly damped, γ/ω0≫1, at short wavelengths, kλD≫1. This collisionless damping becomes less severe at long wavelengths, kλD≪1, but the attenuation of Langmuir waves is much stronger for a generalized Lorentzian plasma than for a Maxwellian plasma. This will further localize Langmuir waves to frequencies just above the electron plasma frequency in plasmas with a substantial high-energy tail. Landau damping of ion-acoustic waves is only slightly affected by the presence of a high-energy tail, but is strongly dependent on the ion temperature. Owing to the simple analytical form of the modified plasma dispersion function when κ=2 (corresponding to a pronounced high-energy tail), exact analytical results for the real and imaginary parts of the wave frequency can be found in this case; similar solutions are not available for a Maxwellian plasma.