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: $V1−V2≡ΔV≥ΔVc$⁠. 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.