SMuK 2023 – scientific programme

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P: Fachverband Plasmaphysik

P 1: Low Pressure Plasmas and their Application I

P 1.2: Talk

Monday, March 20, 2023, 11:30–11:45, CHE/0089

On the role of the Poisson-Boltzmann equation in the modeling of high-power magnetrons — Kevin Köhn, Dennis Krüger, Denis Eremin, Liang Xu, and •Ralf Peter Brinkmann — Ruhr University Bochum, Theoretical Electrical Engineering

The Poisson-Boltzmann equation is a nonlinear differential equation that describes equilibria of conducting fluids. Using a variation principle based on the balances of particle number, entropy, and electromagnetic enthalpy, it can also be justified for a wide class of unmagnetized technological plasmas [Köhn et al., PSST 30, 105014 (2021)].

This study aims to extend the variation principle to magnetized discharges as used in high-power pulsed magnetron sputtering (HiPIMS). The example in focus is that of a high power circular magnetron. The discharge chamber and the magnetic field are assumed to be axisymmetric; the plasma dynamics need not share this symmetry. The domain is divided into the region of confinement, where the electrons can escape from their magnetic field lines only by slow processes such as drift and diffusion, and the remainder where the electrons are effectively free. A distinction is made between a fast thermodynamic and a slow dissipative regime. A variational principle is established for the fast regime which is similar in logic to its counterpart for unmagnetized plasmas but accounts for magnetic confinement by treating the individual flux tubes of the confinement domain as separate thermodynamic units. The resulting solutions obey a generalized Poisson-Boltzmann relation; they are thermodynamic equilibria of the fast regime but must be interpreted as dissipative structures in the slow regime.