You cannot patch active plasma and collisionless sheath

The fluid equations for the plasma-sheath are examined over the range of collisionality from collisionless to fully collisional. The method of "patching" plasma to sheath is examined critically in comparison with matched asymptotic approximations and solutions computed without approximation. It is concluded that it is necessary to include a transition layer in order to smoothly join plasma and collisionless sheath-and then the Bohm Criterion applies. When the sheath is collisional, the orderings are different and there is no transitional layer but equally there is no collisionally modified Bohm Criterion. Nevertheless, a method is given for calculating the ion flux to the wall under conditions where the sheath is collisional