Multifluid equations of a plasma with various species of positive ions and the Bohm criterion

An explicit formula is found for the determinant of the system of multifluid equations of a quasi-neutral plasma. A close relation is revealed between this determinant and the Bohm criterion. A one-dimensional multifluid theory of a quasi-neutral plasma with M species of positive ions results in a (M + 1)-point boundary-value problem, one boundary condition referring to the sheath edge, M to the plasma-side boundary, and 2M - 2 to M - 1 free internal boundaries. The Bohm criterion is marginally satisfied not only at the sheath edge, but also at each internal boundary, and the sheath edge is distiguished by some additional conditions (the mean velocity of every ion species entering the sheath should exceed the velocity of sound of this species).