Instability-Enhanced Collisional Friction Determines the Bohm Criterion in Multiple-Ion-Species Plasmas

Ion-ion streaming instabilities are excited in the presheath region of plasmas with multiple ion species if the ions are much colder than the electrons. Streaming instabilities onset when the relative fluid flow between ion species exceeds a critical speed, $\Delta V_c$, of order the ion thermal speeds. Using a generalized Lenard-Balescu theory that accounts for instability-enhanced collective responses [1], one is able to show the instabilities rapidly enhance the collisional friction between ion species far beyond the contribution from Coulomb collisions alone. This strong frictional force determines the relative fluid speed between species. When this condition is combined with the Bohm criterion generalized for multiple ion species, the fluid speed of each ion species is determined at the sheath edge. For each species, this speed differs from the common ``system'' sound speed by a factor that depends on the species concentrations, masses and $\Delta V_c$.\\[4pt] [1] S.D. Baalrud, J.D. Callen, and C.C. Hegna, Phys. Plasmas {\bf 15}, 092111 (2008).