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Geometric electrostatic particle-in-cell algorithm on unstructured meshes

Published online by Cambridge University Press:  21 July 2021

Zhenyu Wang Open the ORCID record for Zhenyu Wang [Opens in a new window] ,
Hong Qin Open the ORCID record for Hong Qin [Opens in a new window] ,
Benjamin Sturdevant Open the ORCID record for Benjamin Sturdevant [Opens in a new window]  and
C.S. Chang Open the ORCID record for C.S. Chang [Opens in a new window]
Zhenyu Wang*
Affiliation:
Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA
Hong Qin
Affiliation:
Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA
Benjamin Sturdevant
Affiliation:
Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA
C.S. Chang
Affiliation:
Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, USA
*
†Email address for correspondence: [email protected]
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Abstract

We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

Keywords

plasma simulationplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 4 , August 2021 , 905870406
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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