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P: Fachverband Plasmaphysik

P 9: Low Pressure Plasmas III

P 9.3: Talk

Wednesday, March 18, 2026, 11:45–12:00, KH 01.020

Global Clebsch coordinates for rectangular magnetron fields — •Ralf Peter Brinkmann, Dennis Krüger, Jens Kallähn, Kevin Köhn, Lukas Vogelhuber, Yulia Sharova, Liang Xu, and Denis Eremin — Ruhr-University Bochum

Large-scale rectangular magnetrons are the workhorses of modern high-throughput coating and other plasma-processing applications. This work introduces a tool to assist in the theoretical modeling and numerical simulation of such devices: global Clebsch coordinates [1].
Focusing on the region above the cathode, the magnetic field B(r) is shown to admit a divergence-free Clebsch formulation B = ∇Ψ × ∇ Θ, where Ψ(r) is a magnetic flux function whose constant values define nested flux surfaces, and Θ(r) is a generalized azimuth labeling individual magnetic field lines. A third coordinate S(r) measures the arc length along field lines and provides a natural parameterization.
The triplet (Ψ, Θ, S) defines a system of field-aligned flux coordinates suited for describing plasma behavior in large rectangular magnetrons.
The topological and geometrical principles of this construction are discussed and illustrated with a realistic rectangular magnetron field.
The resulting mathematical framework provides a rigorous foundation for self-consistent modeling and simulation of plasma dynamics in field-aligned flux coordinates, with direct relevance to industrial-scale plasma processing.

Keywords: High power magnetrons; Modeling and simulation; Clebsch coodinates