The Bohm–Chodura plasma sheath criterion

Abstract

The ion flow velocity entering the Debye sheath is constrained to satisfy the Bohm criterion: velocity must be equal to or greater than sonic. The ion flow velocity entering the magnetic presheath (which arises upstream of the Debye sheath when a magnetic field, oblique to the solid surface is present) is constrained to satisfy the Chodura criterion: velocity-parallel to B must be equal to or greater than sonic. The Bohm criterion, in its marginal form where v=cs, is associated with a ‘‘gentle entry’’ into the sheath with Δne=Δni, while v≳cs corresponds to ‖Δne‖≳‖Δni‖. The magnetic presheath, in contrast with the Debye sheath, is a region of quasineutrality, and thus only Δne=Δni is permitted. This might appear to prohibit supersonic flow parallel to B at the entrance to the magnetic presheath, which the analysis of Chodura and Riemann has found to be permitted, in fact. This apparent contradiction is resolved by analyzing the magnetic presheath region to bring out more explicitly the role played by inertia in the E×B direction, thus confirming that such supersonic flow is permitted.