The Bohm Criterion in Collisional Plasmas: Can the Contoversy be solved?

The existence or non-existence of a collisionally modified Bohm criterion is the subject of intense discussion, with contributions by Godyak (\textit{Phys. Lett. A} 89 80, 1982), Riemann (J. Phys. D: Appl. Phys. 24 493, 1991), Valentini (\textit{Phys. Plasmas} \textbf{3} 1459, 1996), Chen (\textit{Phys. Plasmas} \textbf{5} 804, 1997), Sternberg (\textit{Phys. Plasmas} \textbf{9} 4427, 2002), Franklin (\textit{J. Phys. D: Appl. Phys.} \textbf{36} 2821, 2003), Benilov (\textit{IEEE TPS} \textbf{28} 2207, 2000), Brinkmann (\textit{J. Phys. D: Appl. Phys.} \textbf{44}, 042002, 2011), and others. All authors agree on the fact that that collisional plasmas do not obey a Bohm criterion in a strict sense, but are add odds whether (and how) such a criterion may be formulated in an approximate sense. This contribution will propose a solution to that controversy. In particular, it will show that Godyak's and Sternberg's thesis on the existence of a collisionally modified Bohm criterion (in the interpretation by Brinkmann) and Riemann's proof of its non-existence are mathematically not in contradiction: they just reflect different opinions on what constitutes a physically reasonable approximation.