The double sheath at the plasma-wall boundary

The relation between plasma parameters determining a steady-state charged sheath at a plasma-wall boundary was derived and analyzed using a fluid model, which accounted for inertia and partial pressure of both plasma components. The relation generalizes the well-known Bohm criterion and, in particular, shows that a steady-state sheath may be formed in some cases where the Bohm criterion is not satisfied. Conditions allowing formation of a double sheath structure were formulated and analyzed. It was shown that the structure may be formed only if a) the generalized Bohm criterion is satisfied, and b) the Sagdeev potential has a minimum. The double sheath structure consists of two sub-sheath of different polarity, which depends on the wall potential polarity and the relation between the plasma component temperatures and inertia. For positive wall potential, the sub-sheath adjacent to the plasma (the sheath edge) is enriched by negative particles, and the sub-sheath adjacent to the wall is enriched by positive particles, while the sub-sheath polarities are reversed for negative wall potential. An analytical theory was formulated and illustrated by numerical solutions of the Poisson equation for special cases.