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A one-dimensional two-fluid model is presented and used for numerical analysis of the asymptotic two-scale limit of the plasma-wall transition. Numerical results confirm that when the problem is treated on the pre-sheath scale, the sheath edge is determined by the electric field singularity. When the problem is approached on the sheath scale, electric field at the sheath edge must be larger than zero in order to obtain any solutions of the model equations. In this case the Bohm criterion is determined by two parameters: the electric field and the ion velocity at the sheath edge.

Numerical analysis of the asymptotic two-scale limit of the plasma-wall transition using a one-dimensional two-fluid model