Diffusion modeling of an HF argon plasma discharge in a magnetic field

Using the basic moment equations (number density, how density, and energy density) for singly ionized argon and for electrons, a simple diffusion equation (essentially one proposed by Lieberman and Lichtenberg) is adopted (by comparison with experiment), together with an integrated power balance equation. The effects of scaling magnetic field and radius are then discussed first for simple cylinders, for which there are known analytic diffusion solutions. For specific cases having the more complicated geometry of two abutting coaxial cylinders with considerably different radii, the numerical results are well approximated and delimited by considering only the wider cylinder for low magnetic field, and at high magnetic field, where end effects dominate, using the total length and the smallest diameter of the system.