A fluid description of plasma double-layers

This paper describes the space-charge double-layer that forms between two plasmas with different densities and thermal energies. Three progressively more realistic models are treated by fluid theory, taking into account four species of particles: electrons and ions reflected by the double-layer, and electrons and ions transmitted through it. First, the two plasmas are assumed to be cold, and the self-consistent potential, electric field and space-charge distributions within the double-layer are determined. Second, the effects of thermal velocities are taken into account for the reflected particles, and the modifications to the cold plasma solutions are established. Third, the further modifications due to thermal velocities of the transmitted particles are examined. The applicability of a one-dimensional fluid description, rather than plasma kinetic theory, is discussed. One valuable product of this description is the potential difference across the double- layer in terms of the parameters of the two plasmas which it separates. A useful length parameter is defined characterizing the distance over which most of this potential is dropped. Comparisons are then made between theoretical predictions, and double-layer potentials and lengths deduced from laboratory and space plasma experiments.