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Title: Energy-conserving perfect-conductor boundary conditions for an implicit, curvilinear Darwin particle-in-cell algorithm

Abstract

We propose here a conservative prescription for perfect-conductor boundary conditions for a Darwin particle-in-cell (PIC) model on curvilinear meshes and arbitrarily shaped boundaries. The Darwin model is a subset of Maxwell's equation in which the electromagnetic mode (light wave) has been analytically removed. This renders the Darwin formulation elliptic, instead of hyperbolic. Historically, Darwin-PIC practitioners have had difficulty implementing a well-posed set of boundary conditions for realistic applications. In this study, we demonstrate the well-posedness and effectiveness of a simple boundary-condition prescription for perfect conductors of specified potential and of arbitrary shape in multiple dimensions, using a recently developed conservative, implicit Darwin-PIC algorithm. The boundary conditions conserve the electromagnetic energy, and preserve the Coulomb gauge of the vector potential, · A = 0 exactly. We demonstrate that global energy is exactly conserved in curvilinear, simply-connected domains in the specific case of particles reflecting off perfect conductors.

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1511229
Report Number(s):
LA-UR-18-21246
Journal ID: ISSN 0021-9991
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 391; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; particle in cell; curvilinear meshes; implicit timestepping; nonlinear solvers; energy conservation

Citation Formats

Chacón, L., and Chen, G.. Energy-conserving perfect-conductor boundary conditions for an implicit, curvilinear Darwin particle-in-cell algorithm. United States: N. p., 2019. Web. doi:10.1016/j.jcp.2019.04.032.
Chacón, L., & Chen, G.. Energy-conserving perfect-conductor boundary conditions for an implicit, curvilinear Darwin particle-in-cell algorithm. United States. doi:10.1016/j.jcp.2019.04.032.
Chacón, L., and Chen, G.. Thu . "Energy-conserving perfect-conductor boundary conditions for an implicit, curvilinear Darwin particle-in-cell algorithm". United States. doi:10.1016/j.jcp.2019.04.032.
@article{osti_1511229,
title = {Energy-conserving perfect-conductor boundary conditions for an implicit, curvilinear Darwin particle-in-cell algorithm},
author = {Chacón, L. and Chen, G.},
abstractNote = {We propose here a conservative prescription for perfect-conductor boundary conditions for a Darwin particle-in-cell (PIC) model on curvilinear meshes and arbitrarily shaped boundaries. The Darwin model is a subset of Maxwell's equation in which the electromagnetic mode (light wave) has been analytically removed. This renders the Darwin formulation elliptic, instead of hyperbolic. Historically, Darwin-PIC practitioners have had difficulty implementing a well-posed set of boundary conditions for realistic applications. In this study, we demonstrate the well-posedness and effectiveness of a simple boundary-condition prescription for perfect conductors of specified potential and of arbitrary shape in multiple dimensions, using a recently developed conservative, implicit Darwin-PIC algorithm. The boundary conditions conserve the electromagnetic energy, and preserve the Coulomb gauge of the vector potential, ∇·A=0 exactly. We demonstrate that global energy is exactly conserved in curvilinear, simply-connected domains in the specific case of particles reflecting off perfect conductors.},
doi = {10.1016/j.jcp.2019.04.032},
journal = {Journal of Computational Physics},
number = ,
volume = 391,
place = {United States},
year = {2019},
month = {4}
}

Journal Article:
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This content will become publicly available on April 18, 2020
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