Plasmas with more than one species of positive ion and the Bohm Criterion

The fluid equations for an active plasma generated by electron impact containing more than one species of positive ion are examined in detail when the ionization frequencies are assumed to be spatially constant with a view to generalizing the Bohm Criterion. It is shown that in this specific situation the various ion spatial distributions and transverse ion speed distributions are geometrically similar and thus each species arrives at the sheath with its own Bohm speed, when the plasma is collisionless. The collisional situation is also examined with the conclusion that in that case as well, ion densities and ion speeds are again geometrically similar. The transition between the collisionless and collisional cases is discussed but not examined in detail.