The plasma–sheath transition in an asymmetric collisionless plasma

The plasma–sheath problem (λD → 0) for an asymmetric warm collision-free plasma is solved in plane parallel geometry. To this end Emmert’s model source term [Phys. Fluids 23, 803 (1980)] is generalized to account for a superimposed plasma drift. The quasineutral plasma approximation results in a system of coupled integral equations that can be solved analytically. In contrast to Emmert’s symmetric model the upstream facing sheath edge shows the usual field singularity. At the downstream facing sheath edge, a finite field strength and an oversatisfied Bohm criterion are found. These results are in full agreement with general considerations on the Bohm criterion and on the sheath edge field singularity [Phys. Fluids B 1, 961 (1989)].