Two-Dimensional Plasma Density Distributions in Low-Pressure Gas Discharges

The plasma density distribution in a two-dimensional nonuniform positive column of a low-pressure gas discharge is studied in the hydrodynamic approximation with allowance for ion inertia. Exact solutions are derived for discharges in a rectangular and a cylindrical chamber. Asymptotic solutions near the coordinate origin and near the critical surface are considered. It is shown that, for potential plasma flows, the flow velocity component normal to the plasma boundary is equal to the ion acoustic velocity. The results obtained can be used to analyze the processes occurring in low-pressure plasmochemical reactors