The exact form of the Bohm criterion for a collisional plasma
  A long-standing debate in the literature about the kinetic form of the Bohm criterion is resolved for plasmas with single positive ion species when transport is dominated by charge exchange collisions. The solution of the Boltzmann equation for the ions gives the exact form free of any divergence and contains an additional term that is not included in the classical result. This term includes collisional and geometric effects and leads to a noticeable correction. Further, the question is addressed whether the space charge argument at the bottom of the Bohm criterion can actually lead to a meaningful definition of the transition point between bulk and sheath. The analysis is supported by a numerical model and experiments, showing excellent agreement throughout. As a novelty in diagnostics, the theoretical results allow from the ion velocity distribution function (IVDF), measured at the wall, a reconstruction of the IVDF and the electric field at any point in the plasma. This property is used to reconstruct non-intrusively also the ion density, flow velocity, mean energy and effective temperature and the electron density and temperature as functions of the spatial coordinate and potential. Finally, the fluid equation for ion momentum balance is verified. 
Tsanko Vaskov Tsankov and Uwe Czarnetzki
physics.plasm-ph