Collisional Damping Of Plasma Waves On A Pure Electron Plasma Column

Abstract

The collisional damping of electron plasma waves (or, more precisely, Trivelpiece‐Gould waves) on a pure electron plasma column is discussed. The damping in a pure electron plasma differs from that in a neutral plasma, since there are no ions to provide collisional drag. A dispersion equation for the complex wave frequency is derived from Poisson’s equation and the drift‐kinetic equation with the Dougherty collision operator—a Fokker‐Planck operator that conserves particle number, momentum, and energy yet is analytically tractable. In the limit of weak collisionality, for phase velocity comparable to the thermal velocity, Landau damping is recovered. For larger phase velocity, where Landau damping is negligible, the dispersion equation can be solved analytically, yielding the complex frequency ω = (kzωp/k)[1+(3/2)(kλD)2(1+10iα/9)(1+2iα)−1], where ωp is the plasma frequency, kz is the axial wavenumber, k is the total wavenumber, λD is the Debye length, ν is the collision frequency, and α≡νk/ωpkz. This expr...