Determining the Bohm criterion in plasmas with two ion species

Abstract

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≡ΔV≥ΔVc. The resultant instability-enhanced friction rapidly becomes so strong that ΔV cannot significantly exceed ΔVc. Using the condition provided by ΔV=ΔVc 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 et al., Phys. Rev. Lett. 103, 205002 (2009)] considered the cold ion limit (Ti→0), in which case ΔVc→0 and each ion species obtains a common “system” sound speed at the sheath edge. Finite ion temperatures are accounted for in this work. The result is that ΔVc depends on the density and thermal speed of each ion species; ΔVc 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 ΔVc increases, the speed of each ion species approaches its individual sound speed at the sheath edge.