The plasma-sheath transition with a constant mean free path model and the applicability of the Bohm criterion

The fluid model for positive ions is used together with the assumption of a constant ion mean free path to examine the structure of the plasma-wall sheath at low and medium pressures in plasmas where ionization is by electron impact and the ion temperature is set to zero. It is shown that in the near collisionless regime there is the same structure as was found with the constant collision frequency for momentum transfer model with the Bohm speed playing the same role and similar scaling of the transitional layer. At higher pressures there is again no transitional layer, only plasma joining smoothly to a collisional sheath, thus the Bohm criterion has no significance, but the scaling is with a different exponent than for the mobility case. No fundamental differences are found between the two models. An expression is derived to describe the boundary between the parameter region where the Bohm criterion applies and that where it does not.