Two-Dimensional Low-Pressure Discharge Theory

It is shown that a pressure theory, modified to take into account ion generation, can be used to describe the steady-state collisionless discharge. Both planar and cylindrical geometry one-dimensional cases are solved for various types of ion generation using this fluid-type of approach. The parameters found by this approximate technique are shown to be in good agreement with the values obtained from the more exact formulation developed by Langmuir. The analysis leads to partial differential equations which are easily generalized to describe two-dimensional problems. For the particular case of ion generation proportional to electron density, the discharge parameters of a two-dimensional rectangular box and a finite-length cylinder are obtained.