A semi-implicit, energy- and charge-conserving particle-in-cell algorithm for the relativistic Vlasov-Maxwell equations

Chen, Guangye; Chacon, Luis; Yin, Lin; Albright, Brian James; Stark, David James; Bird, Robert Francis

doi:10.1016/j.jcp.2020.109228

A semi-implicit, energy- and charge-conserving particle-in-cell algorithm for the relativistic Vlasov-Maxwell equations

Journal Article · Wed Jan 15 23:00:00 EST 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109228· OSTI ID:1770109

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Conventional explicit electromagnetic particle-in-cell (PIC) algorithms do not conserve discrete energy exactly. Time-centered fully implicit PIC algorithms can conserve discrete energy exactly, but may introduce large dispersion errors in the light-wave modes. This can lead to intolerable simulation errors where accurate light propagation is needed (e.g. in laser-plasma interactions). In this study, we selectively combine the leap-frog and Crank-Nicolson methods to produce an exactly energy- and charge-conserving relativistic electromagnetic PIC algorithm. Specifically, we employ the leap-frog method for Maxwell's equations, and the Crank-Nicolson method for the particle equations. The semi-implicit formulation still features a timestep CFL, but facilitates exact global energy conservation, exact local charge conservation, and preserves the dispersion properties of the leap-frog method for the light wave. The algorithm employs a new particle pusher designed to maximize efficiency and minimize wall-clock-time impact vs. the explicit alternative. It has been implemented in a code named iVPIC, based on the Los Alamos National Laboratory VPIC code (https://github.com/losalamos/vpic). We present numerical results that demonstrate the properties of the scheme with sample test problems: relativistic two-stream instability, Weibel instability, and laser-plasma instabilities.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC). Fusion Energy Sciences (FES)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1770109

Alternate ID(s):: OSTI ID: 1702395

Report Number(s):: LA-UR--19-21811

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 407; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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