The Bohm Criterion in Collisional Plasmas -- A Comparison of Different Approaches

The plasma sheath transition in stationary low temperature plasmas is investigated for arbitrary levels of collisionality. The model under study contains the equations of continuity and motion for a single ion species, Boltzmann's equilibrium for the electrons and Poisson's equation for the field. Within this simple but self-consistent model, the arguments of various authors with respect to the existence or non-existence of a collisional modified Bohm criterion are compared. Godyak (1982 Phys. Lett. A 89 80), Valentini (1996 Phys. Plasmas 3 1459), Chen (1997 Phys. Plasmas 5 804) and Brinkmann (2011, J. Phys. D: Appl. Phys. 44, 042002) argued in favor of such a concept, Riemann (1991 J. Phys. D: Appl. Phys. 24 493) and Franklin (2003 J. Phys. D: Appl. Phys. 36 2821) disputed it.