Collisional damping of plasma waves on a pure electron plasma column

Abstract

The collisional damping of electron plasma waves (or 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 relation 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. For large phase velocity, where Landau damping is negligible, the dispersion relation yields 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 expression spans from the weakly collisional regime (α⪡1) to the moderately collisional regime (α∼1) and in the weakly collisional limit yields a damping rate which is smaller than that for a neutral plasma by the factor k2λD2⪡1. In the strongly collisional limit (α⪢1), the damping is enhanced by long-range interactions that are not present in the kinetic theory (which assumes pointlike interactions); the effect of these long-range collisions on the damping is discussed.