Linear theory of electron-plasma waves at arbitrary collisionality

The dynamics of electron-plasma waves is described at arbitrary collisionality by considering the full Coulomb collision operator. The description is based on a Hermite–Laguerre decomposition of the velocity dependence of the electron distribution function. The damping rate, frequency and eigenmode spectrum of electron-plasma waves are found as functions of the collision frequency and wavelength. A comparison is made between the collisionless Landau damping limit, the Lenard–Bernstein and Dougherty collision operators and the electron–ion collision operator, finding large deviations in the damping rates and eigenmode spectra. A purely damped entropy mode, characteristic of a plasma where pitch-angle scattering effects are dominant with respect to collisionless effects, is shown to emerge numerically, and its dispersion relation is analytically derived. It is shown that such a mode is absent when simplified collision operators are used, and that like-particle collisions strongly influence the damping rate of the entropy mode.