UW-CPTC 10-2 rev Determining the Bohm criterion in plasmas with two ion species

A model that uniquely determines the flow speed of each ion species at the sheath edge of two ion species plasmas is developed. In this analysis, ion-ion two-stream instabilities can play an important role because they significantly enhance the friction between ion species. Two-stream instabilities arise when the difference in flow speeds between the ion species exceeds a critical value: V1−V2 ≡ ∆V ≥ ∆Vc. The resultant instability-enhanced friction rapidly becomes so strong that ∆V cannot significantly exceed ∆Vc. Using the condition provided by ∆V = ∆Vc and the generalized Bohm criterion, the speed of each ion species is uniquely determined as it leaves a quasineutral plasma and enters a sheath. Previous work [S. D. Baalrud, C. C. Hegna and J. D. Callen, Phys. Rev. Lett. 103, 205002 (2009)] considered the cold ion limit (Ti → 0), in which case ∆Vc → 0 and each ion species obtains a common “system” sound speed at the sheath edge. In this work, we extend the previous calculation to account for finite ion temperatures. The result is that ∆Vc depends on the density and thermal speed of each ion species; ∆Vc has a minimum when the density ratio of the two ion species is near one, and becomes larger as the density ratio deviates from unity. As ∆Vc increases, the speed of each ion species approaches its individual sound speed