Equilibrium theory of cylindrical discharges with special application to helicons

Abstract

Radiofrequency discharges used in industry often have centrally peaked plasma density profiles n(r) although ionization is localized at the edge, even in the presence of a dc magnetic field. This can be explained with a simple cylindrical model in one dimension as long as the short-circuit effect at the endplates causes a Maxwellian electron distribution. Surprisingly, a universal profile can be obtained, which is self-similar for all discharges with uniform electron temperature Te and neutral density nn. When all collisions and ionizations are radially accounted for, the ion drift velocity toward the wall reaches the Bohm velocity at a radius which can be identified with the sheath edge, thus obviating a pre-sheath calculation. For non-uniform Te and nn, the profiles change slightly but are always peaked on axis. For helicon discharges, iteration with the HELIC code for antenna-wave coupling yields profiles consistent with both energy deposition and diffusion profiles. Calculated density is in absolute-value agreement with experiment.