Axisymmetric magnetically enhanced discharges described in terms of flux coordinates

Abstract

Magnetically enhanced glow discharges and arcs are widely used in materials processing and other branches of plasma technology. An important class—including, for example, circular magnetrons, Hall thrusters, and certain ion sources—is axisymmetric devices with a poloidal magnetic field. This paper discusses the representation of such fields using the so-called flux coordinates (ψ,θ,s), a system of field aligned spatial coordinates which include the flux label ψ of a magnetic field line, the azimuth angle θ, and the arc length s. After reviewing the formalism—which finds widespread use in fusion research and plasma astrophysics—a number of special amendments are introduced to make it suitable for technological plasmas. Focus is put on the description of internal and external domain boundaries (separatrices and walls). The flux coordinates are numerically constructed for the confinement region of a circular magnetron using an analytical field model that was obtained in earlier investigations by fitting a physically plausible ansatz to Hall probe measurements. As a first application, the dynamics of the energetic electron component in a high power impulse magnetron sputtering discharge is investigated on the basis of a linear kinetic model and the corresponding confinement is calculated by solving an eigenvalue problem.