Friction-force model for Maxwellian drifting ions in weakly ionized plasmas.

Analytical expressions for the collision frequency for momentum transfer and the friction force experienced by a Maxwellian ion population drifting with respect to the uniform neutral atom background are derived. The calculations make use of different models for the collision cross section for momentum transfer accounting for the relative speed v_{r} between the colliding particles. These results are compared with the currently used semi-empirical equations for the friction force and collision frequency in the fluid equations for weakly ionized plasmas. The kinetic model calculations are in agreement for suprathermal ion flows while they present discrepancies of orders of magnitude for subthermal ion drift speeds u_{d} . However, for the collision cross section sigma_{m} approximately 1v_{r} , the magnitude of the friction force results proportional to u_{d} and the collision frequency becomes constant regardless of the magnitude of the ion drift speed in both cases. These results are relevant for ion populations drifting in a plasma which could be approximated by shifted Maxwellian distributions, as in collisional plasma sheaths or plasma double layers.