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A fluid model of the edge plasma in low-temperature discharges containing beam electrons

The influence of mono-energetic beam electrons on the behaviour of a plane plasma boundary is investigated assuming that the ion, electron and beam electron components in the pre-sheath act as three coupled fluids. The sheath edge is identified by the singularity in the electric field appearing under the quasi-neutral assumption, and the Bohm criterion is solved for a range of beam and plasma parameters. Collisions between the plasma particles and the neutral species are considered in a regime in which Coulomb interactions are unimportant. The plasma is generated by beam and thermal electron impact ionization of the neutral gas. Under collision-free conditions, sheath-edge potentials and ion energies are found to increase with the ratio of beam to thermal electron density, up to a critical ratio of about 0.3, above which no sheath edge is predicted to exist. Ion - neutral species collisions further raise the Bohm speed; however, the attenuation of the electron beam through scattering and ionization does not appreciably alter the sheath-edge conditions, but changes the width of the boundary layer. The results of this model, which are relevant to industrial plasma discharges containing beam electrons, are compared with those found from other treatments of the beam - plasma boundary.