Numerical double layer solutions with ionisation

Maxwell's equation div D= rho in one dimension is solved numerically, taking ionisation into account. Time independent anode sheath and double-layer solutions are obtained. By varying voltage, neutral gas pressure, temperature of the trapped ions on the cathode side and density and temperature of the trapped electrons on the anode side, diagrams are constructed that show permissible combinations of these parameters. Results from a recent experiment form a subset. Distribution functions, the Langmuir condition, some scaling laws and a possible application to the lower ionosphere are discussed.