Scalable spectral solver in Galilean coordinates for eliminating the numerical Cherenkov instability in particle-in-cell simulations of streaming plasmas

Kirchen, Manuel; Lehe, Remi; Jalas, Soeren; Shapoval, Olga; Vay, Jean-Luc; Maier, Andreas R.

doi:10.1103/PhysRevE.102.013202

Title: Scalable spectral solver in Galilean coordinates for eliminating the numerical Cherenkov instability in particle-in-cell simulations of streaming plasmas

Abstract

Discretizing Maxwell's equations in Galilean (comoving) coordinates allows the derivation of a pseudospectral solver that eliminates the numerical Cherenkov instability for electromagnetic particle-in-cell simulations of relativistic plasmas flowing at a uniform velocity. Here we generalize this solver by incorporating spatial derivatives of arbitrary order, thereby enabling efficient parallelization by domain decomposition. This allows scaling of the algorithm to many distributed compute units. We derive the numerical dispersion relation of the algorithm and present a comprehensive theoretical stability analysis. The method is applied to simulations of plasma acceleration in a Lorentz-boosted frame of reference.

Authors:

; Lehe, Remi; Jalas, Soeren; Shapoval, Olga; Vay, Jean-Luc;

Publication Date:: Tue Jul 07 00:00:00 EDT 2020

Research Org.:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA); Federal Ministry of Education and Research (BMBF); USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1637566

Alternate Identifier(s):: OSTI ID: 1756341

Grant/Contract Number:: AC02-05CH11231; 05K19GUA

Resource Type:: Published Article

Journal Name:: Physical Review. E

Additional Journal Information:: Journal Name: Physical Review. E Journal Volume: 102 Journal Issue: 1; Journal ID: ISSN 2470-0045

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Laser wakefield acceleration; Plasma acceleration & new acceleration techniques; Relativistic plasmas; Particle-in-cell methods

Citation Formats


                    Kirchen, Manuel, Lehe, Remi, Jalas, Soeren, Shapoval, Olga, Vay, Jean-Luc, and Maier, Andreas R. Scalable spectral solver in Galilean coordinates for eliminating the numerical Cherenkov instability in particle-in-cell simulations of streaming plasmas.  United States: N. p., 2020. 
Web.  doi:10.1103/PhysRevE.102.013202.

Copy to clipboard


                    Kirchen, Manuel, Lehe, Remi, Jalas, Soeren, Shapoval, Olga, Vay, Jean-Luc, & Maier, Andreas R. Scalable spectral solver in Galilean coordinates for eliminating the numerical Cherenkov instability in particle-in-cell simulations of streaming plasmas.  United States.  https://doi.org/10.1103/PhysRevE.102.013202

Copy to clipboard


                    Kirchen, Manuel, Lehe, Remi, Jalas, Soeren, Shapoval, Olga, Vay, Jean-Luc, and Maier, Andreas R. Tue .  
"Scalable spectral solver in Galilean coordinates for eliminating the numerical Cherenkov instability in particle-in-cell simulations of streaming plasmas".  United States.  https://doi.org/10.1103/PhysRevE.102.013202.

Copy to clipboard


                    
@article{osti_1637566,

  title        = {Scalable spectral solver in Galilean coordinates for eliminating the numerical Cherenkov instability in particle-in-cell simulations of streaming plasmas},

  author       = {Kirchen, Manuel and Lehe, Remi and Jalas, Soeren and Shapoval, Olga and Vay, Jean-Luc and Maier, Andreas R.},

  abstractNote = {Discretizing Maxwell's equations in Galilean (comoving) coordinates allows the derivation of a pseudospectral solver that eliminates the numerical Cherenkov instability for electromagnetic particle-in-cell simulations of relativistic plasmas flowing at a uniform velocity. Here we generalize this solver by incorporating spatial derivatives of arbitrary order, thereby enabling efficient parallelization by domain decomposition. This allows scaling of the algorithm to many distributed compute units. We derive the numerical dispersion relation of the algorithm and present a comprehensive theoretical stability analysis. The method is applied to simulations of plasma acceleration in a Lorentz-boosted frame of reference.},

  doi          = {10.1103/PhysRevE.102.013202},

  journal      = {Physical Review. E},

  number       = 1,

  volume       = 102,

  place        = {United States},

  year         = {Tue Jul 07 00:00:00 EDT 2020},

  month        = {Tue Jul 07 00:00:00 EDT 2020}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
https://doi.org/10.1103/PhysRevE.102.013202

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 9 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Noninvariance of Space- and Time-Scale Ranges under a Lorentz Transformation and the Implications for the Study of Relativistic Interactions
journal, March 2007

Vay, J. -L.
Physical Review Letters, Vol. 98, Issue 13
DOI: 10.1103/PhysRevLett.98.130405

Generation of finite difference formulas on arbitrarily spaced grids
journal, January 1988

Fornberg, Bengt
Mathematics of Computation, Vol. 51, Issue 184
DOI: 10.1090/S0025-5718-1988-0935077-0

Elimination of the numerical Cerenkov instability for spectral EM-PIC codes
journal, July 2015

Yu, Peicheng; Xu, Xinlu; Decyk, Viktor K.
Computer Physics Communications, Vol. 192
DOI: 10.1016/j.cpc.2015.02.018

A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas
journal, June 2013

Vay, Jean-Luc; Haber, Irving; Godfrey, Brendan B.
Journal of Computational Physics, Vol. 243
DOI: 10.1016/j.jcp.2013.03.010

Numerical Stability Improvements for the Pseudospectral EM PIC Algorithm
journal, May 2014

Godfrey, Brendan B.; Vay, Jean-Luc; Haber, Irving
IEEE Transactions on Plasma Science, Vol. 42, Issue 5
DOI: 10.1109/TPS.2014.2310654

Numerical simulations of laser wakefield accelerators in optimal Lorentz frames
journal, May 2010

Martins, Samuel F.; Fonseca, Ricardo A.; Silva, Luís O.
Computer Physics Communications, Vol. 181, Issue 5
DOI: 10.1016/j.cpc.2009.12.023

Accurate modeling of plasma acceleration with arbitrary order pseudo-spectral particle-in-cell methods
journal, March 2017

Jalas, S.; Dornmair, I.; Lehe, R.
Physics of Plasmas, Vol. 24, Issue 3
DOI: 10.1063/1.4978569

The PSTD algorithm: A time-domain method requiring only two cells per wavelength
journal, June 1997

Liu, Q. H.
Microwave and Optical Technology Letters, Vol. 15, Issue 3
DOI: 10.1002/(SICI)1098-2760(19970620)15:3%3C158::AID-MOP11%3E3.0.CO;2-3

On numerical errors to the fields surrounding a relativistically moving particle in PIC codes
journal, July 2020

Xu, Xinlu; Li, Fei; Tsung, Frank S.
Journal of Computational Physics, Vol. 413
DOI: 10.1016/j.jcp.2020.109451

Novel methods in the Particle-In-Cell accelerator Code-Framework Warp
journal, January 2012

Vay, J-L; Grote, D. P.; Cohen, R. H.
Computational Science & Discovery, Vol. 5, Issue 1
DOI: 10.1088/1749-4699/5/1/014019

Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates
journal, November 2016

Lehe, Remi; Kirchen, Manuel; Godfrey, Brendan B.
Physical Review E, Vol. 94, Issue 5
DOI: 10.1103/PhysRevE.94.053305

Suppressing the numerical Cherenkov instability in FDTD PIC codes
journal, June 2014

Godfrey, Brendan B.; Vay, Jean-Luc
Journal of Computational Physics, Vol. 267
DOI: 10.1016/j.jcp.2014.02.022

Numerical growth of emittance in simulations of laser-wakefield acceleration
journal, February 2013

Lehe, R.; Lifschitz, A.; Thaury, C.
Physical Review Special Topics - Accelerators and Beams, Vol. 16, Issue 2
DOI: 10.1103/PhysRevSTAB.16.021301

Mitigation of numerical Cerenkov radiation and instability using a hybrid finite difference-FFT Maxwell solver and a local charge conserving current deposit
journal, December 2015

Yu, Peicheng; Xu, Xinlu; Tableman, Adam
Computer Physics Communications, Vol. 197
DOI: 10.1016/j.cpc.2015.08.026

Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction
journal, May 2017

Li, Fei; Yu, Peicheng; Xu, Xinlu
Computer Physics Communications, Vol. 214
DOI: 10.1016/j.cpc.2017.01.001

Particle Acceleration in Relativistic Collisionless Shocks: Fermi Process at Last?
journal, July 2008

Spitkovsky, Anatoly
The Astrophysical Journal, Vol. 682, Issue 1
DOI: 10.1086/590248

Generalized algorithm for control of numerical dispersion in explicit time-domain electromagnetic simulations
journal, April 2013

Cowan, Benjamin M.; Bruhwiler, David L.; Cary, John R.
Physical Review Special Topics - Accelerators and Beams, Vol. 16, Issue 4
DOI: 10.1103/PhysRevSTAB.16.041303

Numerical stability of relativistic beam multidimensional PIC simulations employing the Esirkepov algorithm
journal, September 2013

Godfrey, Brendan B.; Vay, Jean-Luc
Journal of Computational Physics, Vol. 248
DOI: 10.1016/j.jcp.2013.04.006

Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm
journal, February 2014

Godfrey, Brendan B.; Vay, Jean-Luc; Haber, Irving
Journal of Computational Physics, Vol. 258
DOI: 10.1016/j.jcp.2013.10.053

Stable discrete representation of relativistically drifting plasmas
journal, October 2016

Kirchen, M.; Lehe, R.; Godfrey, B. B.
Physics of Plasmas, Vol. 23, Issue 10
DOI: 10.1063/1.4964770

Warp-X: A new exascale computing platform for beam–plasma simulations
journal, November 2018

Vay, J. -L.; Almgren, A.; Bell, J.
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 909
DOI: 10.1016/j.nima.2018.01.035

A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm
journal, June 2016

Lehe, Rémi; Kirchen, Manuel; Andriyash, Igor A.
Computer Physics Communications, Vol. 203
DOI: 10.1016/j.cpc.2016.02.007

Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver
journal, March 2016

Vincenti, H.; Vay, J. -L.
Computer Physics Communications, Vol. 200
DOI: 10.1016/j.cpc.2015.11.009

Canonical momenta and numerical instabilities in particle codes
journal, September 1975

Godfrey, Brendan B.
Journal of Computational Physics, Vol. 19, Issue 1
DOI: 10.1016/0021-9991(75)90116-3

Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
journal, May 1966

Kane Yee,
IEEE Transactions on Antennas and Propagation, Vol. 14, Issue 3
DOI: 10.1109/TAP.1966.1138693

Physics of laser-driven plasma-based electron accelerators
journal, August 2009

Esarey, E.; Schroeder, C. B.; Leemans, W. P.
Reviews of Modern Physics, Vol. 81, Issue 3
DOI: 10.1103/RevModPhys.81.1229

Numerical instability due to relativistic plasma drift in EM-PIC simulations
journal, November 2013

Xu, Xinlu; Yu, Peicheng; Martins, Samual F.
Computer Physics Communications, Vol. 184, Issue 11
DOI: 10.1016/j.cpc.2013.07.003

Exploring laser-wakefield-accelerator regimes for near-term lasers using particle-in-cell simulation in Lorentz-boosted frames
journal, March 2010

Martins, S. F.; Fonseca, R. A.; Lu, W.
Nature Physics, Vol. 6, Issue 4
DOI: 10.1038/nphys1538

Interpenetrating Plasma Shells: Near-Equipartition Magnetic Field Generation and Nonthermal Particle Acceleration
journal, September 2003

Silva, L. O.; Fonseca, R. A.; Tonge, J. W.
The Astrophysical Journal, Vol. 596, Issue 1
DOI: 10.1086/379156

A high-accuracy realization of the Yee algorithm using non-standard finite differences
journal, June 1997

Cole, J. B.
IEEE Transactions on Microwave Theory and Techniques, Vol. 45, Issue 6
DOI: 10.1109/22.588615

Modeling of 10 GeV-1 TeV laser-plasma accelerators using Lorentz boosted simulations
journal, December 2011

Vay, J. -L.; Geddes, C. G. R.; Esarey, E.
Physics of Plasmas, Vol. 18, Issue 12
DOI: 10.1063/1.3663841

JUWELS: Modular Tier-0/1 Supercomputer at Jülich Supercomputing Centre
journal, February 2019

Support, Supercomputing
Journal of large-scale research facilities JLSRF, Vol. 5
DOI: 10.17815/jlsrf-5-171

Ultrahigh-order Maxwell solver with extreme scalability for electromagnetic PIC simulations of plasmas
journal, July 2018

Vincenti, Henri; Vay, Jean-Luc
Computer Physics Communications, Vol. 228
DOI: 10.1016/j.cpc.2018.03.018

Numerical Cherenkov instabilities in electromagnetic particle codes
journal, August 1974

Godfrey, Brendan B.
Journal of Computational Physics, Vol. 15, Issue 4
DOI: 10.1016/0021-9991(74)90076-X

Improved numerical Cherenkov instability suppression in the generalized PSTD PIC algorithm
journal, November 2015

Godfrey, Brendan B.; Vay, Jean-Luc
Computer Physics Communications, Vol. 196
DOI: 10.1016/j.cpc.2015.06.008

Generation of a Small-Scale Quasi-Static Magnetic Field and Fast Particles during the Collision of Electron-Positron Plasma Clouds
journal, May 1998

Kazimura, Y.; Sakai, J. I.; Neubert, T.
The Astrophysical Journal, Vol. 498, Issue 2
DOI: 10.1086/311316

Particle simulation of plasmas
journal, April 1983

Dawson, John M.
Reviews of Modern Physics, Vol. 55, Issue 2
DOI: 10.1103/RevModPhys.55.403

Pseudospectral Maxwell solvers for an accurate modeling of Doppler harmonic generation on plasma mirrors with particle-in-cell codes
journal, September 2017

Blaclard, G.; Vincenti, H.; Lehe, R.
Physical Review E, Vol. 96, Issue 3
DOI: 10.1103/PhysRevE.96.033305

Similar Records in DOE PAGES and OSTI.GOV collections:

Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates

Journal Article Lehe, Remi ; Kirchen, Manuel ; Godfrey, Brendan B. ; ... - Physical Review E

Particle-in-cell (PIC) simulations of relativistic flowing plasmas are of key interest to several fields of physics (including, e.g., laser-wakefield acceleration, when viewed in a Lorentz-boosted frame) but remain sometimes infeasible due to the well-known numerical Cherenkov instability (NCI). In this article, we show that, for a plasma drifting at a uniform relativistic velocity, the NCI can be eliminated by simply integrating the PIC equations in Galilean coordinates that follow the plasma (also sometimes known as comoving coordinates) within a spectral analytical framework. The elimination of the NCI is verified empirically and confirmed by a theoretical analysis of the instability. Moreover,more »« less
Cited by 23
https://doi.org/10.1103/PhysRevE.94.053305

Full Text Available
Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction

Journal Article Li, Fei ; Yu, Peicheng ; Xu, Xinlu ; ... - Computer Physics Communications

In this study we present a customized finite-difference-time-domain (FDTD) Maxwell solver for the particle-in-cell (PIC) algorithm. The solver is customized to effectively eliminate the numerical Cerenkov instability (NCI) which arises when a plasma (neutral or non-neutral) relativistically drifts on a grid when using the PIC algorithm. We control the EM dispersion curve in the direction of the plasma drift of a FDTD Maxwell solver by using a customized higher order finite difference operator for the spatial derivative along the direction of the drift (1ˆ direction). We show that this eliminates the main NCI modes with moderate |k₁|, while keeps additionalmore »« less
Cited by 24
https://doi.org/10.1016/j.cpc.2017.01.001

Full Text Available
Numerical methods for instability mitigation in the modeling of laser wakefield accelerators in a Lorentz-boosted frame

Journal Article Vay, J.-L., E-mail: jlvay@lbl.gov ; Geddes, C G.R. ; Cormier-Michel, E ; ... - Journal of Computational Physics

Modeling of laser-plasma wakefield accelerators in an optimal frame of reference has been shown to produce orders of magnitude speed-up of calculations from first principles. Obtaining these speedups required mitigation of a high-frequency instability that otherwise limits effectiveness. In this paper, methods are presented which mitigated the observed instability, including an electromagnetic solver with tunable coefficients, its extension to accommodate Perfectly Matched Layers and Friedman's damping algorithms, as well as an efficient large bandwidth digital filter. It is observed that choosing the frame of the wake as the frame of reference allows for higher levels of filtering or damping thanmore »« less
https://doi.org/10.1016/j.jcp.2011.04.003
Pseudospectral Maxwell solvers for an accurate modeling of Doppler harmonic generation on plasma mirrors with particle-in-cell codes

Journal Article Blaclard, G. ; Vincenti, H. ; Lehe, R. ; ... - Physical Review. E

With the advent of petawatt class lasers, the very large laser intensities attainable on target should enable the production of intense high-order Doppler harmonics from relativistic laser-plasma mirror interactions. At present, the modeling of these harmonics with particle-in-cell (PIC) codes is extremely challenging as it implies an accurate description of tens to hundreds of harmonic orders on a broad range of angles. In particular, we show here that due to the numerical dispersion of waves they induce in vacuum, standard finite difference time domain (FDTD) Maxwell solvers employed in most PIC codes can induce a spurious angular deviation of harmonicmore »« less
Cited by 17
https://doi.org/10.1103/physreve.96.033305

Full Text Available
Pseudospectral Maxwell solvers for an accurate modeling of Doppler harmonic generation on plasma mirrors with particle-in-cell codes

Journal Article Blaclard, G. ; Vincenti, H. ; Lehe, R. ; ... - Physical Review. E

With the advent of petawatt class lasers, the very large laser intensities attainable on target should enable the production of intense high-order Doppler harmonics from relativistic laser-plasma mirror interactions. At present, the modeling of these harmonics with particle-in-cell (PIC) codes is extremely challenging as it implies an accurate description of tens to hundreds of harmonic orders on a broad range of angles. In particular, we show here that due to the numerical dispersion of waves they induce in vacuum, standard finite difference time domain (FDTD) Maxwell solvers employed in most PIC codes can induce a spurious angular deviation of harmonicmore »« less
https://doi.org/10.1103/PhysRevE.96.033305

Similar Records

Title: Scalable spectral solver in Galilean coordinates for eliminating the numerical Cherenkov instability in particle-in-cell simulations of streaming plasmas

Abstract

Citation Formats

Noninvariance of Space- and Time-Scale Ranges under a Lorentz Transformation and the Implications for the Study of Relativistic Interactions journal, March 2007

Generation of finite difference formulas on arbitrarily spaced grids journal, January 1988

Elimination of the numerical Cerenkov instability for spectral EM-PIC codes journal, July 2015

A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas journal, June 2013

Numerical Stability Improvements for the Pseudospectral EM PIC Algorithm journal, May 2014

Numerical simulations of laser wakefield accelerators in optimal Lorentz frames journal, May 2010

Accurate modeling of plasma acceleration with arbitrary order pseudo-spectral particle-in-cell methods journal, March 2017

The PSTD algorithm: A time-domain method requiring only two cells per wavelength journal, June 1997

On numerical errors to the fields surrounding a relativistically moving particle in PIC codes journal, July 2020

Novel methods in the Particle-In-Cell accelerator Code-Framework Warp journal, January 2012

Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates journal, November 2016

Suppressing the numerical Cherenkov instability in FDTD PIC codes journal, June 2014

Numerical growth of emittance in simulations of laser-wakefield acceleration journal, February 2013

Mitigation of numerical Cerenkov radiation and instability using a hybrid finite difference-FFT Maxwell solver and a local charge conserving current deposit journal, December 2015

Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction journal, May 2017

Particle Acceleration in Relativistic Collisionless Shocks: Fermi Process at Last? journal, July 2008

Generalized algorithm for control of numerical dispersion in explicit time-domain electromagnetic simulations journal, April 2013

Numerical stability of relativistic beam multidimensional PIC simulations employing the Esirkepov algorithm journal, September 2013

Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm journal, February 2014

Stable discrete representation of relativistically drifting plasmas journal, October 2016

Warp-X: A new exascale computing platform for beam–plasma simulations journal, November 2018

A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm journal, June 2016

Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver journal, March 2016

Canonical momenta and numerical instabilities in particle codes journal, September 1975

Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media journal, May 1966

Physics of laser-driven plasma-based electron accelerators journal, August 2009

Numerical instability due to relativistic plasma drift in EM-PIC simulations journal, November 2013

Exploring laser-wakefield-accelerator regimes for near-term lasers using particle-in-cell simulation in Lorentz-boosted frames journal, March 2010

Interpenetrating Plasma Shells: Near-Equipartition Magnetic Field Generation and Nonthermal Particle Acceleration journal, September 2003

A high-accuracy realization of the Yee algorithm using non-standard finite differences journal, June 1997

Modeling of 10 GeV-1 TeV laser-plasma accelerators using Lorentz boosted simulations journal, December 2011

JUWELS: Modular Tier-0/1 Supercomputer at Jülich Supercomputing Centre journal, February 2019

Ultrahigh-order Maxwell solver with extreme scalability for electromagnetic PIC simulations of plasmas journal, July 2018

Numerical Cherenkov instabilities in electromagnetic particle codes journal, August 1974

Improved numerical Cherenkov instability suppression in the generalized PSTD PIC algorithm journal, November 2015

Generation of a Small-Scale Quasi-Static Magnetic Field and Fast Particles during the Collision of Electron-Positron Plasma Clouds journal, May 1998

Particle simulation of plasmas journal, April 1983

Pseudospectral Maxwell solvers for an accurate modeling of Doppler harmonic generation on plasma mirrors with particle-in-cell codes journal, September 2017

Noninvariance of Space- and Time-Scale Ranges under a Lorentz Transformation and the Implications for the Study of Relativistic Interactions
journal, March 2007

Generation of finite difference formulas on arbitrarily spaced grids
journal, January 1988

Elimination of the numerical Cerenkov instability for spectral EM-PIC codes
journal, July 2015

A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas
journal, June 2013

Numerical Stability Improvements for the Pseudospectral EM PIC Algorithm
journal, May 2014

Numerical simulations of laser wakefield accelerators in optimal Lorentz frames
journal, May 2010

Accurate modeling of plasma acceleration with arbitrary order pseudo-spectral particle-in-cell methods
journal, March 2017

The PSTD algorithm: A time-domain method requiring only two cells per wavelength
journal, June 1997

On numerical errors to the fields surrounding a relativistically moving particle in PIC codes
journal, July 2020

Novel methods in the Particle-In-Cell accelerator Code-Framework Warp
journal, January 2012

Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates
journal, November 2016

Suppressing the numerical Cherenkov instability in FDTD PIC codes
journal, June 2014

Numerical growth of emittance in simulations of laser-wakefield acceleration
journal, February 2013

Mitigation of numerical Cerenkov radiation and instability using a hybrid finite difference-FFT Maxwell solver and a local charge conserving current deposit
journal, December 2015

Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction
journal, May 2017

Particle Acceleration in Relativistic Collisionless Shocks: Fermi Process at Last?
journal, July 2008

Generalized algorithm for control of numerical dispersion in explicit time-domain electromagnetic simulations
journal, April 2013

Numerical stability of relativistic beam multidimensional PIC simulations employing the Esirkepov algorithm
journal, September 2013

Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm
journal, February 2014

Stable discrete representation of relativistically drifting plasmas
journal, October 2016

Warp-X: A new exascale computing platform for beam–plasma simulations
journal, November 2018

A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm
journal, June 2016

Detailed analysis of the effects of stencil spatial variations with arbitrary high-order finite-difference Maxwell solver
journal, March 2016

Canonical momenta and numerical instabilities in particle codes
journal, September 1975

Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
journal, May 1966

Physics of laser-driven plasma-based electron accelerators
journal, August 2009

Numerical instability due to relativistic plasma drift in EM-PIC simulations
journal, November 2013

Exploring laser-wakefield-accelerator regimes for near-term lasers using particle-in-cell simulation in Lorentz-boosted frames
journal, March 2010

Interpenetrating Plasma Shells: Near-Equipartition Magnetic Field Generation and Nonthermal Particle Acceleration
journal, September 2003

A high-accuracy realization of the Yee algorithm using non-standard finite differences
journal, June 1997

Modeling of 10 GeV-1 TeV laser-plasma accelerators using Lorentz boosted simulations
journal, December 2011

JUWELS: Modular Tier-0/1 Supercomputer at Jülich Supercomputing Centre
journal, February 2019

Ultrahigh-order Maxwell solver with extreme scalability for electromagnetic PIC simulations of plasmas
journal, July 2018

Numerical Cherenkov instabilities in electromagnetic particle codes
journal, August 1974

Improved numerical Cherenkov instability suppression in the generalized PSTD PIC algorithm
journal, November 2015

Generation of a Small-Scale Quasi-Static Magnetic Field and Fast Particles during the Collision of Electron-Positron Plasma Clouds
journal, May 1998

Particle simulation of plasmas
journal, April 1983

Pseudospectral Maxwell solvers for an accurate modeling of Doppler harmonic generation on plasma mirrors with particle-in-cell codes
journal, September 2017