| Issue |
ESAIM: ProcS
Volume 64, 2018
SMAI 2017 - 8e Biennale Française des Mathématiques Appliquées et Industrielles
|
|
|---|---|---|
| Page(s) | 17 - 36 | |
| DOI | https://doi.org/10.1051/proc/201864017 | |
| Published online | 20 November 2018 | |
Numerical stability of a plasma sheath*,**,***,****
1
Institut de Mathématiques de Toulouse, UMR 5219, Université Toulouse 3, 118 Route de Narbonne, 31400 Toulouse
2
Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67000 Strasbourg, France, INRIA Nancy-Grand Est, TONUS Project, Strasbourg, France
3
Institut de Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, 7 rue René Descartes, 67000 Strasbourg, France, INRIA Nancy-Grand Est, TONUS Project, Strasbourg, France
We are interested in developing a numerical method for capturing stationary sheaths, that a plasma forms in contact with a metallic wall. This work is based on a bi-species (ion/electron) Vlasov-Ampère model proposed in [3]. The main question addressed in this work is to know how accurately classical time-dependent Vlasov-Ampère numerical schemes preserve in long time these non-homogeneous stationary solutions with emission/absorption boundary conditions. In the context of high-order semi-Lagrangian methods, due to their large stencil, interpolation near the boundary of the domain requires also a specific treatment.
Résumé
Nous sommes intéressés à développer une méthode numérique pour capturer les gaines stationnaires qu'un plasma forme au contact d'un mur métallique. Ce travail est basé sur un modèle de Vlasov-Ampère proposé dans [3]. La question principale posée dans ce travail est de savoir dans quelle mesure les schémas numériques classiques pour le système Vlasov-Ampère préservent ces solutions stationnaires non-homogènes avec conditions aux bords d'émission/absorption. Dans le contexte de la méthode semi-Lagrangienne d'ordre élevé, à cause du stencil large, l'interpolation près du bord du domaine nécessite aussi un traitement spécifique.
This work comes from discussions during the SMAI conference. We thank all the organizers of the conference and also all the speakers of the MULTIKIN mini-symposium.
Thanks to the Selalib team http://selalib.gforge.inria.fr/ and in particular Pierre Navaro
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom Research and Training Programme 2014- 2018 under Grant Agreement No. 633053. Computing facilities were provided by the EUROfusion Marconi supercomputer facility. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
© EDP Sciences, SMAI 2018
This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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