Bohm criterion for the collisional plasma

Abstract

Summary form only given. As is known, in collisionless case for the electrode boundary sheath formation it is necessary that positive ions at the sheath edge have a velocity V/sub 1//spl ges/V/sub s/=/spl radic/kT/sub e//M where V/sub s/ is the ion sound speed, T/sub e/ is the electron temperature, M is the ion mass. Godyak (1982) has modified the Bohm's criterion for a collisional case neglecting the friction force acting on electrons and estimated the electric field at the sheath edge as E/sub 1/=kT/sub k///spl lambda//sub D/ where /spl lambda//sub 1/ is the electron Debye radius at the sheath edge. Riemann (1991) has shown this value to be too high and suggested to use in a collisional case the following expression E/sub 1/=kT/sub e//(e/spl lambda//sub D//sup 2/5//spl lambda//sub 1//sup 3/5/) where /spl lambda//sub 1/ is the ion mean-free path. Valenti has determined the Bohm criterion for a collision plasma. However, Riemann et al. have derived from Valentini's results the nonmonotonous behaviour of plasma parameters in the presheath. In this paper the equation for the ion velocity V/sub 1/ at the plasma-sheath interface is obtained.