The electron attracting plasma sheath adjacent to the surfaces of a positively polarized electrode transforms into an anodic double layer over a threshold bias potential. The proposed one-dimensional model for this transition considers the contribution of the low production of charges by electron impact in the sheath, which develops a positive space charge in front of the electrode. The stationary electric field of this ionizing plasma sheath as well as the plasma potential spatial profile are obtained from the numerical solutions of a nonlinear integral equation derived from the Poisson equation. The stationary transition process is governed by a bifurcation driven by the bias potential of the electrode, which is the parameter controlled in the experiments. Below a bias potential threshold a single and stable ionizing plasma sheath is obtained. Past this critical voltage two possible values are found for the electric field close to the surface of the electrode. The double layer space plasma profile corresponds to low electric fields while a ionizing plasma sheath is found for higher values. It is conjectured that the abrupt transition occurs when the plasma sheath becomes unstable for bias voltage over a threshold and the double layer develops. The discontinuities in the current voltage characteristic curves observed in the experiments as the double layer upsurges or disappears would be explained as jumps between the two possible branches of this bifurcation.
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.
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