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Geometric particle-in-cell methods for the Vlasov–Maxwell equations with spin effects

Part of: The Many Facets of the Vlasov Equation

Published online by Cambridge University Press:  28 May 2021

Nicolas Crouseilles ,
Paul-Antoine Hervieux ,
Yingzhe Li Open the ORCID record for Yingzhe Li [Opens in a new window] ,
Giovanni Manfredi Open the ORCID record for Giovanni Manfredi [Opens in a new window]  and
Yajuan Sun
Nicolas Crouseilles*
Affiliation:
Université de Rennes, Inria Rennes (Mingus team) and IRMAR UMR CNRS 6625, F-35042Rennes, France
Paul-Antoine Hervieux
Affiliation:
Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000Strasbourg, France
Yingzhe Li
Affiliation:
Max Planck Institute for Plasma Physics, Boltzmannstrasse 2, 85748Garching, Germany
Giovanni Manfredi*
Affiliation:
Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, F-67000Strasbourg, France
Yajuan Sun
Affiliation:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, University of Chinese Academy of Sciences, 100049Beijing, PR China
*
†Email addresses for correspondence: nicolas.crouseilles@inria.fr, giovanni.manfredi@ipcms.unistra.fr
†Email addresses for correspondence: nicolas.crouseilles@inria.fr, giovanni.manfredi@ipcms.unistra.fr
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Abstract

We propose a numerical scheme to solve the semiclassical Vlasov–Maxwell equations for electrons with spin. The electron gas is described by a distribution function $f(t,{\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ that evolves in an extended 9-dimensional phase space $({\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$, where $\boldsymbol s$ represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to five dimensions: $(x,{{p_x}}, {\boldsymbol s})$. It can be shown that the spin Vlasov–Maxwell equations enjoy a Hamiltonian structure that motivates the use of the recently developed geometric particle-in-cell (PIC) methods. Here, the geometric PIC approach is generalized to the case of electrons with spin. Total energy conservation is very well satisfied, with a relative error below $0.05\,\%$. As a relevant example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, where the electrons are partially or fully spin polarized. It is shown that the Raman instability is very effective in destroying the electron polarization.

Keywords

plasma simulationplasma instabilitiesquantum plasma
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 3 , June 2021 , 825870301
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

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