Collisionless theory of a plasma sheath near an electrode

Abstract

The existing collisionless theory of a plasma sheath near an infinite planar electrode is examined in detail. Ranges of validity as well as difficulties with the existing sheath models are investigated. The assumption of monoenergetic particle distributions, as used for instance in "Bohm's sheath criterion," restricts the usual analysis. To remove this difficulty Maxwellian particle distribution functions are assumed. In addition, microscopic boundary conditions are assumed to incorporate the respective electrode and plasma parameters. A new sheath model is then developed without imposing the usual sheath criterion for the conditions specified at the sheath edge. Explicit results for the current-voltage relation and for the sheath thickness are obtained for the improved sheath model proposed in this study. Other important physical quantities are expressed in terms of the electrostatic potential, which can be calculated by a quadrature subject to the physical parameters to be specified. The general solution reduces to a simple analytic form for the special case where the temperature of the electrons, ions, and the electrode are identical.