Conditions for the existence of strong double layers

Abstract

We present the results of a theoretical investigation of the conditions for the existence of a stationary, strong, monotonic double layer. A model that includes finite temperatures both of the particle species accelerated by the double layer and of those reflected by it is developed on the basis of the general theory of double layers due to Andrews and Allen. A numerical solution of the model equations is presented and analysed. Explicit approximate formulae for the electron-to-ion current ratio (i.e. the Langmuir factor) and for the initial velocities (i.e. directional energies of the accelerated particles at the double-layer boundaries before acceleration) are also derived that fit almost exactly the exact numerical solution over a wide range of double-layer potentials. It is shown that in the cases in which the standard results of Langmuir and Bohm are an oversimplification, approximate formulae may be used instead of exact numerical solutions to obtain quite accurate results in a simple manner.