A New Approach to Gas Discharge Theory with Sheath Boundaries

Classical theories of gas discharges have concentrated on the microscopic properties of collisions and diffusion coefficients, but few have considered the macroscopic observables such as the density and temperature profiles. Since practical devices cannot be approximated by infinite cylinders, we consider finite cylinders with endplates. There, the short-circuit effect permits electrons to be Maxwellian even in the presence of a DC magnetic field. For uniform electron temperature Te and pressure p, the radial density profile is found to have a “universal” shape independent of p. A code EQM is developed to solve for radial profiles when all quantities vary with r and includes ionization balance and neutral depletion. The profile Te(r) depends on the type of discharge and is found for helicon discharges by iterating with the code HELIC. Resulting n(r) profiles are flat or peaked on axis, as found in experiment, even when ionization is localized to the edge.