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Title: Formulation of the relativistic moment implicit particle-in-cell method

Abstract

A new formulation is presented for the implicit moment method applied to the time-dependent relativistic Vlasov-Maxwell system. The new approach is based on a specific formulation of the implicit moment method that allows us to retain the same formalism that is valid in the classical case despite the formidable complication introduced by the nonlinear nature of the relativistic equations of motion. To demonstrate the validity of the new formulation, an implicit finite difference algorithm is developed to solve the Maxwell's equations and equations of motion. A number of benchmark problems are run: two stream instability, ion acoustic wave damping, Weibel instability, and Poynting flux acceleration. The numerical results are all in agreement with analytical solutions.

Authors:
; ; ;  [1];  [2];  [3];  [4]
  1. Physics and Astronomy Department, Rice University, Houston, Texas 77005 (United States)
  2. (United Kingdom) and TERA Foundation, V. Puccini 11, 28100 Novara (Italy)
  3. (United States) and DISMIC, Politecnico di Torino, Corso Duca degli Abruzzi 10129, Turin (Italy)
  4. (Belgium)
Publication Date:
OSTI Identifier:
20976604
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 4; Other Information: DOI: 10.1063/1.2721083; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ACCELERATION; ALGORITHMS; ANALYTICAL SOLUTION; BENCHMARKS; BOLTZMANN-VLASOV EQUATION; EQUATIONS OF MOTION; FINITE DIFFERENCE METHOD; ION ACOUSTIC WAVES; MAXWELL EQUATIONS; MOMENTS METHOD; NONLINEAR PROBLEMS; PARTICLES; PLASMA SIMULATION; RELATIVISTIC PLASMA; RELATIVISTIC RANGE; TIME DEPENDENCE; TWO-STREAM INSTABILITY

Citation Formats

Noguchi, Koichi, Tronci, Cesare, Zuccaro, Gianluca, Lapenta, Giovanni, Mathematics Department, Imperial College London, 180 Queen's Gate, SW7 2AZ London, Plasma Theory Group, Theoretical Division, Los Alamos National Laboratory, Mail Stop: K717, Los Alamos, New Mexico 87545, and Centrum voor Plasma-Astrofysica, Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven. Formulation of the relativistic moment implicit particle-in-cell method. United States: N. p., 2007. Web. doi:10.1063/1.2721083.
Noguchi, Koichi, Tronci, Cesare, Zuccaro, Gianluca, Lapenta, Giovanni, Mathematics Department, Imperial College London, 180 Queen's Gate, SW7 2AZ London, Plasma Theory Group, Theoretical Division, Los Alamos National Laboratory, Mail Stop: K717, Los Alamos, New Mexico 87545, & Centrum voor Plasma-Astrofysica, Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven. Formulation of the relativistic moment implicit particle-in-cell method. United States. doi:10.1063/1.2721083.
Noguchi, Koichi, Tronci, Cesare, Zuccaro, Gianluca, Lapenta, Giovanni, Mathematics Department, Imperial College London, 180 Queen's Gate, SW7 2AZ London, Plasma Theory Group, Theoretical Division, Los Alamos National Laboratory, Mail Stop: K717, Los Alamos, New Mexico 87545, and Centrum voor Plasma-Astrofysica, Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven. Sun . "Formulation of the relativistic moment implicit particle-in-cell method". United States. doi:10.1063/1.2721083.
@article{osti_20976604,
title = {Formulation of the relativistic moment implicit particle-in-cell method},
author = {Noguchi, Koichi and Tronci, Cesare and Zuccaro, Gianluca and Lapenta, Giovanni and Mathematics Department, Imperial College London, 180 Queen's Gate, SW7 2AZ London and Plasma Theory Group, Theoretical Division, Los Alamos National Laboratory, Mail Stop: K717, Los Alamos, New Mexico 87545 and Centrum voor Plasma-Astrofysica, Departement Wiskunde, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven},
abstractNote = {A new formulation is presented for the implicit moment method applied to the time-dependent relativistic Vlasov-Maxwell system. The new approach is based on a specific formulation of the implicit moment method that allows us to retain the same formalism that is valid in the classical case despite the formidable complication introduced by the nonlinear nature of the relativistic equations of motion. To demonstrate the validity of the new formulation, an implicit finite difference algorithm is developed to solve the Maxwell's equations and equations of motion. A number of benchmark problems are run: two stream instability, ion acoustic wave damping, Weibel instability, and Poynting flux acceleration. The numerical results are all in agreement with analytical solutions.},
doi = {10.1063/1.2721083},
journal = {Physics of Plasmas},
number = 4,
volume = 14,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
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