Boundary value problems for multi-component plasmas and a generalized Bohm criterion

A multi-fluid model for bounded plasmas containing positive species of ions yields a p + 2-point boundary value problem (BVP) if steady state conditions, space charge effects and simple geometries are taken into account. Assuming cold ions, a two-point one follows. The number of boundary points is not increased if negative ions are included. Neglecting the space charge effects, the sheath edge can be defined at a non-removable singular point of the problem. Taking into account the space charge density, a generalized Bohm criterion can be formulated. The resulting complicated expression is reduced to a practicable form.