A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm

Chen, G.; Chacón, L.

doi:10.1016/j.cpc.2015.08.008

Title: A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm

Abstract

For decades, the Vlasov–Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. We explore a fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space–time-centered, employing particle sub-cycling and orbit-averaging. This algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. Finally, we demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D–3V.

Authors:

Chen, G. ^[1]; Chacón, L. ^[1]

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

Publication Date:: Tue Aug 11 00:00:00 EDT 2015

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

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1329577

Alternate Identifier(s):: OSTI ID: 1246662

Report Number(s):: LA-UR-15-21463
Journal ID: ISSN 0010-4655

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Computer Physics Communications

Additional Journal Information:: Journal Volume: 197; Journal Issue: C; Journal ID: ISSN 0010-4655

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Implicit particle-in-cell; Energy conservation; Charge conservation; Canonical momentum conservation; Vlasov–Darwin; Multi-scale; JFNK; Physics-based preconditioner

Citation Formats


                    Chen, G., and Chacón, L. A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm.  United States: N. p., 2015. 
Web.  doi:10.1016/j.cpc.2015.08.008.

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                    Chen, G., & Chacón, L. A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm.  United States.  https://doi.org/10.1016/j.cpc.2015.08.008

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                    Chen, G., and Chacón, L. Tue .  
"A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm".  United States.  https://doi.org/10.1016/j.cpc.2015.08.008.  https://www.osti.gov/servlets/purl/1329577.

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@article{osti_1329577,

  title        = {A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm},

  author       = {Chen, G. and Chacón, L.},

  abstractNote = {For decades, the Vlasov–Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. We explore a fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space–time-centered, employing particle sub-cycling and orbit-averaging. This algorithm conserves total energy, local charge, canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. Finally, we demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D–3V.},

  doi          = {10.1016/j.cpc.2015.08.008},

  journal      = {Computer Physics Communications},

  number       = C,

  volume       = 197,

  place        = {United States},

  year         = {Tue Aug 11 00:00:00 EDT 2015},

  month        = {Tue Aug 11 00:00:00 EDT 2015}

}

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https://doi.org/10.1016/j.cpc.2015.08.008

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Title: A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm

Abstract

Citation Formats

Numerical Cherenkov instabilities in electromagnetic particle codes journal, August 1974

Some Electromagnetic Plasma Simulation Methods and Their Noise Properties journal, January 1972

The energy conserving particle-in-cell method journal, August 2011

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov–Darwin particle-in-cell algorithm journal, October 2014

A self-consistent magnetostatic particle code for numerical simulation of plasmas journal, March 1977

Hybrid simulations of quasineutral phenomena in magnetized plasma journal, June 1978

Low-frequency electromagnetic (Darwin) applications in plasma simulation journal, November 1994

The Darwin Direct Implicit Particle-in-Cell (DADIPIC) Method for Simulation of Low Frequency Plasma Phenomena journal, September 1995

Nonlinear perturbative electromagnetic (Darwin) particle simulation of high intensity beams journal, May 2001

Study of hot electron beam transport in high density plasma using 3D hybrid-Darwin code journal, December 2004

Simulations of electromagnetic effects in high-frequency capacitively coupled discharges using the Darwin approximation journal, February 2013

Darwin–Vlasov simulations of magnetised plasmas journal, May 2006

Boundary conditions for the Darwin model journal, October 1989

An analysis of the Darwin model of approximation to Maxwell’s equations journal, January 1992

An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm journal, August 2011

Development of a Consistent and Stable Fully Implicit Moment Method for Vlasov--Ampère Particle in Cell (PIC) System journal, January 2013

Jacobian-free Newton–Krylov methods: a survey of approaches and applications journal, January 2004

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations journal, February 2014

An efficient mixed-precision, hybrid CPU–GPU implementation of a nonlinearly implicit one-dimensional particle-in-cell algorithm journal, June 2012

Implicit moment particle simulation of plasmas journal, June 1981

Time-filtering particle simulations with ωpe Δt ⪢ 1 journal, August 1981

An implicit method for electromagnetic plasma simulation in two dimensions journal, May 1982

CELEST1D: an implicit, fully kinetic model for low-frequency, electromagnetic plasma simulation journal, March 1992

Direct implicit large time-step particle simulation of plasmas journal, July 1983

Electromagnetic direct implicit plasma simulation journal, September 1987

Implicit particle simulation of electromagnetic plasma phenomena journal, May 1992

Elimination of electromagnetic radiation in plasma simulation: The Darwin or magneto inductive approximation journal, October 1985

A hierarchy of approximate models for the Maxwell equations journal, May 1996

A unified approach to the Darwin approximation journal, October 2007

Hyperbolic Conservation Laws in Continuum Physics book, January 2000

The Origin of Spurious Solutions in Computational Electromagnetics journal, April 1996

One-Dimensional Plasma Model in the Presence of a Magnetic Field journal, January 1968

Divergence Correction Techniques for Maxwell Solvers Based on a Hyperbolic Model journal, July 2000

Accurate Numerical Solution of Charged Particle Motion in a Magnetic Field journal, February 1995

An analytical particle mover for the charge- and energy-conserving, nonlinearly implicit, electrostatic particle-in-cell algorithm journal, August 2013

Rigorous charge conservation for local electromagnetic field solvers journal, March 1992

The Darwin Model as a Tool for Electromagnetic Plasma Simulation journal, January 1971

Nested Iteration and First-Order Systems Least Squares for a Two-Fluid Electromagnetic Darwin Model journal, January 2015

Kinetic Alfvén waves and electron physics. I. Generation from ion-ion streaming journal, June 2007

An implicit “drift-Lorentz” mover for plasma and beam simulations journal, July 2009

A charge- and energy-conserving implicit, electrostatic particle-in-cell algorithm on mapped computational meshes journal, January 2013

Numerical Simulation of the Weibel Instability in One and Two Dimensions journal, January 1971

The energy conserving particle-in-cell method journal, August 2011

A finite element formulation of the Darwin PIC model for use on unstructured grids journal, October 1995

The Darwin Model as a Tool for Electromagnetic Plasma Simulation journal, January 1971

Assessment and Intervention Strategies for the Bilingual Language-Disordered Student journal, September 1983

Vlasov-Maxwell system with physical reasonableness constraints journal, May 2019

ViDA: a Vlasov–DArwin solver for plasma physics at electron scales journal, October 2019

Verification of long wavelength electromagnetic modes with a gyrokinetic-fluid hybrid model in the XGC code journal, May 2017

Interpolation-free particle simulation journal, January 2020

A Post-Newtonian Expansion Including Radiation Damping for a Collisionless Plasma journal, September 2019

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration journal, May 2018

A Semi-implicit Particle-in-cell Expanding Box Model Code for Fully Kinetic Simulations of the Expanding Solar Wind Plasma journal, January 2019

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Electromagnetic full-$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods text, January 2019

Numerical Cherenkov instabilities in electromagnetic particle codes
journal, August 1974

Some Electromagnetic Plasma Simulation Methods and Their Noise Properties
journal, January 1972

The energy conserving particle-in-cell method
journal, August 2011

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov–Darwin particle-in-cell algorithm
journal, October 2014

A self-consistent magnetostatic particle code for numerical simulation of plasmas
journal, March 1977

Hybrid simulations of quasineutral phenomena in magnetized plasma
journal, June 1978

Low-frequency electromagnetic (Darwin) applications in plasma simulation
journal, November 1994

The Darwin Direct Implicit Particle-in-Cell (DADIPIC) Method for Simulation of Low Frequency Plasma Phenomena
journal, September 1995

Nonlinear perturbative electromagnetic (Darwin) particle simulation of high intensity beams
journal, May 2001

Study of hot electron beam transport in high density plasma using 3D hybrid-Darwin code
journal, December 2004

Simulations of electromagnetic effects in high-frequency capacitively coupled discharges using the Darwin approximation
journal, February 2013

Darwin–Vlasov simulations of magnetised plasmas
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Boundary conditions for the Darwin model
journal, October 1989

An analysis of the Darwin model of approximation to Maxwell’s equations
journal, January 1992

An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm
journal, August 2011

Development of a Consistent and Stable Fully Implicit Moment Method for Vlasov--Ampère Particle in Cell (PIC) System
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Jacobian-free Newton–Krylov methods: a survey of approaches and applications
journal, January 2004

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations
journal, February 2014

An efficient mixed-precision, hybrid CPU–GPU implementation of a nonlinearly implicit one-dimensional particle-in-cell algorithm
journal, June 2012

Implicit moment particle simulation of plasmas
journal, June 1981

Time-filtering particle simulations with ωpe Δt ⪢ 1
journal, August 1981

An implicit method for electromagnetic plasma simulation in two dimensions
journal, May 1982

CELEST1D: an implicit, fully kinetic model for low-frequency, electromagnetic plasma simulation
journal, March 1992

Direct implicit large time-step particle simulation of plasmas
journal, July 1983

Electromagnetic direct implicit plasma simulation
journal, September 1987

Implicit particle simulation of electromagnetic plasma phenomena
journal, May 1992

Elimination of electromagnetic radiation in plasma simulation: The Darwin or magneto inductive approximation
journal, October 1985

A hierarchy of approximate models for the Maxwell equations
journal, May 1996

A unified approach to the Darwin approximation
journal, October 2007

Hyperbolic Conservation Laws in Continuum Physics
book, January 2000

The Origin of Spurious Solutions in Computational Electromagnetics
journal, April 1996

One-Dimensional Plasma Model in the Presence of a Magnetic Field
journal, January 1968

Divergence Correction Techniques for Maxwell Solvers Based on a Hyperbolic Model
journal, July 2000

Accurate Numerical Solution of Charged Particle Motion in a Magnetic Field
journal, February 1995

An analytical particle mover for the charge- and energy-conserving, nonlinearly implicit, electrostatic particle-in-cell algorithm
journal, August 2013

Rigorous charge conservation for local electromagnetic field solvers
journal, March 1992

The Darwin Model as a Tool for Electromagnetic Plasma Simulation
journal, January 1971

Nested Iteration and First-Order Systems Least Squares for a Two-Fluid Electromagnetic Darwin Model
journal, January 2015

Kinetic Alfvén waves and electron physics. I. Generation from ion-ion streaming
journal, June 2007

An implicit “drift-Lorentz” mover for plasma and beam simulations
journal, July 2009

A charge- and energy-conserving implicit, electrostatic particle-in-cell algorithm on mapped computational meshes
journal, January 2013

Numerical Simulation of the Weibel Instability in One and Two Dimensions
journal, January 1971

The energy conserving particle-in-cell method
journal, August 2011

A finite element formulation of the Darwin PIC model for use on unstructured grids
journal, October 1995

The Darwin Model as a Tool for Electromagnetic Plasma Simulation
journal, January 1971

Assessment and Intervention Strategies for the Bilingual Language-Disordered Student
journal, September 1983

Vlasov-Maxwell system with physical reasonableness constraints
journal, May 2019

ViDA: a Vlasov–DArwin solver for plasma physics at electron scales
journal, October 2019

Verification of long wavelength electromagnetic modes with a gyrokinetic-fluid hybrid model in the XGC code
journal, May 2017

Interpolation-free particle simulation
journal, January 2020

A Post-Newtonian Expansion Including Radiation Damping for a Collisionless Plasma
journal, September 2019

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-implicit Time Integration
journal, May 2018

A Semi-implicit Particle-in-cell Expanding Box Model Code for Fully Kinetic Simulations of the Expanding Solar Wind Plasma
journal, January 2019

A Post-Newtonian Expansion Including Radiation Damping for a Collisionless Plasma
text, January 2019

Kinetic Simulation of Collisional Magnetized Plasmas with Semi-Implicit Time Integration
preprint, January 2017

Electromagnetic full-$f$ gyrokinetics in the tokamak edge with discontinuous Galerkin methods
text, January 2019