Volume 55, Number 6, November-December 2021
|Page(s)||2609 - 2642|
|Published online||11 November 2021|
A variational sheath model for stationary gyrokinetic Vlasov–Poisson equations
Université de Nantes, CNRS UMR 6629, 2 rue de la Houssinière, 44332 Nantes, France
2 Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany
3 Laboratoire Jacques Louis Lions, Sorbonne Université, 4 place Jussieu, 75005 Paris, France
4 Università degli Studi di Torino, dipartimento di Matematica, Giuseppe Peano. Via Carlo Alberto 10, Torino, TO 10123, Italia
* Corresponding author: firstname.lastname@example.org
Accepted: 5 October 2021
We construct a stationary gyrokinetic variational model for sheaths close to the metallic wall of a magnetized plasma, following a physical extremalization principle for the natural energy. By considering a reduced set of parameters we show that our model has a unique minimal solution, and that the resulting electric potential has an infinite number of oscillations as it propagates towards the core of the plasma. We prove this result for the non linear problem and also provide a simpler analysis for a linearized problem, based on the construction of exact solutions. Some numerical illustrations show the well-posedness of the model after numerical discretization. They also exhibit the oscillating behavior.
Mathematics Subject Classification: 78A30 / 49J05 / 34C10
Key words: Plasma-wall interaction / Vlasov–Poisson equation / gyrokinetic model / gyroaverage operator / Bohm criterion / floating potential / stationary solutions
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://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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