Central peaking of magnetized gas discharges

Partially ionized gas discharges used in industry are often driven by radiofrequency (rf) power applied at the periphery of a cylinder. It is found that the plasma density n is usually flat or peaked on axis even if the skin depth of the rf field is thin compared with the chamber radius a. Previous attempts at explaining this did not account for the finite length of the discharge and the boundary conditions at the endplates. A simple 1D model is used to focus on the basic mechanism: the short-circuit effect. It is found that a strong electric field (E-field) scaled to electron temperature T_e, drives the ions inward. The resulting density profile is peaked on axis and has a shape independent of pressure or discharge radius. This "universal" profile is not affected by a dc magnetic field (B-field) as long as the ion Larmor radius is larger than a.