The effects of Coulomb collisions on the propagation of cold-plasma waves

Explicit expressions for the corrections δε to the cold-plasma dielectric tensor due to Coulomb collisions have been obtained. These expressions, derived from the Fokker–Planck operator in the Landau form, are ‘‘exact’’ to first order in νcoll/ω, and can be used to evaluate the dissipation due to collisions between particles of arbitrary charge-to-mass ratios. Collisions between particles of the same species do not contribute to dissipation, as expected. In the high-frequency domain, when the ion mobility is negligible, electron–ion collisions can be accounted for by adding to the frequency an appropriate imaginary part, which coincides with νe/i up to a numerical factor close to unity. In the general case, collisional dissipation is proportional to the difference of the mobility of the two colliding species, again as expected from elementary considerations. The results obtained for arbitrary charge-to-mass ratios can be of practical relevance in the ion cyclotron and magnetohydrodynamic frequency ranges, where the perpendicular mobilities of ions and electrons are comparable, and in the case of collisions between hydrogen isotopes and impurities.