Greifswald 2024 – scientific programme

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P: Fachverband Plasmaphysik

P 24: Codes and Modeling II

P 24.4: Talk

Thursday, February 29, 2024, 17:30–17:45, ELP 6: HS 4

The Poisson-Boltzmann equation and quasi-neutrality assumption in the presence of electron number perturbations — •Kevin Köhn¹, Lukas Vogelhuber¹, Dennis Krüger¹, Denis Eremin¹, Liang Xu², and Ralf Peter Brinkmann¹ — ¹Ruhr University Bochum, Germany — ²Soochow University, China

The Poisson-Boltzmann (PB) equation is a 3D elliptical partial differential equation used to determine the electric potential in a plasma chamber with appropriate boundary conditions. Solutions of the PB equation usually exhibit a typical bulk-sheath structure, with strong gradients in the sheath and approximately constant potential in the quasi-neutral bulk. In recent years, much research in the field of partially magnetized discharges, e.g. high power impulse magnetron sputtering, was dedicated to the so-called spoke phenomenon. These spokes can be characterized as self-emerging rotating structures of increased ionization, density and potential that rotate in the ExB direction. As these structures clearly break the discharge symmetry, researchers suggested that in order to fully capture the plasma potential dynamics of such a discharge the quasi-neutrality assumption in the bulk must be dropped and the full 3D PB equation would be required. In this talk, we present investigations of the PB equation in simple geometry with small and large scale periodic electron number perturbations to find a criterion if the quasi-neutrality assumption holds based on pertubation scale, bulk length and Debye length.

Keywords: Modeling; Poisson-Boltzmann; Quasi-neutrality