Collisional Damping of Plasma Waves on a Pure Electron Plasma Column.

Collisional damping of electron plasma waves (Trivelpiece-Gould waves) on a magnetized pure electron plasma column is discussed. Damping in a pure electron plasma differs from damping in a neutral plasma, since there are no ions to provide a collisional drag on the oscillating electrons. A dispersion relation for the complex frequency, $\omega$, is derived from Poisson's equation and the drift-kinetic equation with the Dougherty collision operator. This approximate Fokker-Planck operator conserves particle number, momentum, and energy, and also is analytically tractable. For large phase velocity, where Landau damping is negligible, the dispersion relation yields the complex frequency $\omega \! = \! (k_z \omega_p / k)[1\! + \! (3/2)(k \lambda_D)^2 (1 \! + \! i 10 \alpha / 9) (1 \!+ \! i 2 \alpha )^{-1}]$, where $\omega_p$ is the plasma frequency, $k_z$ is the axial wave number, $k$ is the total wave number, $\lambda_D$ is the Debye length, $\nu$ is the collision frequency and $\alpha \! \equiv \! \nu k / \omega_p k_z$. This expression spans uniformly from the weakly collisional regime $( \alpha \! \ll \! 1 )$ to the strongly collisional regime $(\alpha > 1 )$, matching onto fluid results in the latter limit. For comparison, note that in the weakly collisional regime, the damping rate is given by ${\mathrm Im} (\omega) \! = \! - 4 \nu k^2 \lambda_D^2 / 3$, which is suppressed from the damping rate for the case of a neutral plasma [i.e., ${\mathrm Im} (\omega ) \simeq - \nu $] by the small factor $( k \lambda_D)^2 \ll 1$.