The Bohm criterion and boundary conditions for a multicomponent system

In the asymptotic limit λ_D→O (small Debye length) the boundary layer problem of a plasma is split up into the separate problems of a: quasineutral presheath and a collision free planar sheath. The formation of a stationary sheath requires that the ions fulfil a sheath condition (“Bohm criterion”). In this paper, the boundary layer problem of a multicomponent system is investigated. Both in the frames of a hydrodynamic and of a kinetic theory, a generalized sheath condition is derived accounting for various ion components and arbitrary electron- and ion distributions. It is shown that the sheath condition is usually fulfilled marginally (in the equality form) and provides a boundary condition for the plasma analysis