Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates
Abstract
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, it is shown that this method is applicable both to Cartesian geometry and to cylindrical geometry with azimuthal Fourier decomposition.
- Authors:
-
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Univ. of Hamburg, Hamburg (Germany)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of Maryland, College Park, MD (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP)
- OSTI Identifier:
- 1398439
- Alternate Identifier(s):
- OSTI ID: 1332030
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review E
- Additional Journal Information:
- Journal Volume: 94; Journal Issue: 5; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
Lehe, Remi, Kirchen, Manuel, Godfrey, Brendan B., Maier, Andreas R., and Vay, Jean -Luc. Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates. United States: N. p., 2016.
Web. doi:10.1103/PhysRevE.94.053305.
Lehe, Remi, Kirchen, Manuel, Godfrey, Brendan B., Maier, Andreas R., & Vay, Jean -Luc. Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates. United States. https://doi.org/10.1103/PhysRevE.94.053305
Lehe, Remi, Kirchen, Manuel, Godfrey, Brendan B., Maier, Andreas R., and Vay, Jean -Luc. Mon .
"Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates". United States. https://doi.org/10.1103/PhysRevE.94.053305. https://www.osti.gov/servlets/purl/1398439.
@article{osti_1398439,
title = {Elimination of numerical Cherenkov instability in flowing-plasma particle-in-cell simulations by using Galilean coordinates},
author = {Lehe, Remi and Kirchen, Manuel and Godfrey, Brendan B. and Maier, Andreas R. and Vay, Jean -Luc},
abstractNote = {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, it is shown that this method is applicable both to Cartesian geometry and to cylindrical geometry with azimuthal Fourier decomposition.},
doi = {10.1103/PhysRevE.94.053305},
journal = {Physical Review E},
number = 5,
volume = 94,
place = {United States},
year = {Mon Nov 14 00:00:00 EST 2016},
month = {Mon Nov 14 00:00:00 EST 2016}
}
Web of Science
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
Laser Electron Accelerator
journal, July 1979
- Tajima, T.; Dawson, J. M.
- Physical Review Letters, Vol. 43, Issue 4
Modeling Laser Wakefield Accelerators in a Lorentz Boosted Frame
conference, January 2010
- Vay, J. -L.; Geddes, C. G. R.; Benedetti, C.
- ADVANCED ACCELERATOR CONCEPTS: 14th Advanced Accelerator Concepts Workshop, AIP Conference Proceedings
Laser-plasma interactions with a Fourier-Bessel particle-in-cell method
journal, March 2016
- Andriyash, Igor A.; Lehe, Remi; Lifschitz, Agustin
- Physics of Plasmas, Vol. 23, Issue 3
Review and recent advances in PIC modeling of relativistic beams and plasmas
conference, January 2016
- Godfrey, Brendan B.
- ADVANCED ACCELERATOR CONCEPTS 2016: 16th Advanced Accelerator Concepts Workshop, AIP Conference Proceedings
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
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
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
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
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
Magnetic Field Evolution in Relativistic Unmagnetized Collisionless Shocks
journal, February 2009
- Keshet, Uri; Katz, Boaz; Spitkovsky, Anatoly
- The Astrophysical Journal, Vol. 693, Issue 2
Implementation of a hybrid particle code with a PIC description in r–z and a gridless description in ϕ into OSIRIS
journal, January 2015
- Davidson, A.; Tableman, A.; An, W.
- Journal of Computational Physics, Vol. 281
Simulation of beams or plasmas crossing at relativistic velocity
journal, May 2008
- Vay, J. -L.
- Physics of Plasmas, Vol. 15, Issue 5
Suppressing the numerical Cherenkov instability in FDTD PIC codes
journal, June 2014
- Godfrey, Brendan B.; Vay, Jean-Luc
- Journal of Computational Physics, Vol. 267
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
Particle Acceleration in Relativistic Collisionless Shocks: Fermi Process at Last?
journal, July 2008
- Spitkovsky, Anatoly
- The Astrophysical Journal, Vol. 682, Issue 1
Ion Dynamics and Acceleration in Relativistic Shocks
journal, April 2009
- Martins, S. F.; Fonseca, R. A.; Silva, L. O.
- The Astrophysical Journal, Vol. 695, Issue 2
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
New Developments in the Simulation of Advanced Accelerator Concepts
conference, January 2009
- Bruhwiler, David L.; Cary, John R.; Cowan, Benjamin M.
- ADVANCED ACCELERATOR CONCEPTS: Proceedings of the Thirteenth Advanced Accelerator Concepts Workshop, AIP Conference Proceedings
Numerical methods for instability mitigation in the modeling of laser wakefield accelerators in a Lorentz-boosted frame
journal, July 2011
- Vay, J. -L.; Geddes, C. G. R.; Cormier-Michel, E.
- Journal of Computational Physics, Vol. 230, Issue 15
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
Stable discrete representation of relativistically drifting plasmas
journal, October 2016
- Kirchen, M.; Lehe, R.; Godfrey, B. B.
- Physics of Plasmas, Vol. 23, Issue 10
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
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
Canonical momenta and numerical instabilities in particle codes
journal, September 1975
- Godfrey, Brendan B.
- Journal of Computational Physics, Vol. 19, Issue 1
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
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
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
Effects of hyperbolic rotation in Minkowski space on the modeling of plasma accelerators in a Lorentz boosted frame
journal, March 2011
- Vay, J. -L.; Geddes, C. G. R.; Cormier-Michel, E.
- Physics of Plasmas, Vol. 18, Issue 3
Particle-in-Cell modelling of laser–plasma interaction using Fourier decomposition
journal, March 2009
- Lifschitz, A. F.; Davoine, X.; Lefebvre, E.
- Journal of Computational Physics, Vol. 228, Issue 5
Numerical Cherenkov instabilities in electromagnetic particle codes
journal, August 1974
- Godfrey, Brendan B.
- Journal of Computational Physics, Vol. 15, Issue 4
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
Summary report of working group 2: Computations for accelerator physics
conference, January 2016
- Vay, Jean-Luc; Arefiev, Alexey
- ADVANCED ACCELERATOR CONCEPTS 2016: 16th Advanced Accelerator Concepts Workshop, AIP Conference Proceedings
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
Works referencing / citing this record:
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
Efficient start-to-end 3D envelope modeling for two-stage laser wakefield acceleration experiments
journal, October 2019
- Massimo, F.; Beck, A.; Derouillat, J.
- Plasma Physics and Controlled Fusion, Vol. 61, Issue 12
Numerical studies on electron beam quality optimization in a laser-driven plasma accelerator with external injection at SINBAD for ATHENA e
journal, November 2019
- Svystun, E. N.; Assmann, R. W.; Dorda, U.
- Journal of Physics: Conference Series, Vol. 1350
Numerical Studies on Electron Beam Quality Optimization in a Laser-Driven Plasma Accelerator with External Injection at SINBAD for ATHENA
text, January 2019
- Svystun, Elena; Assmann, R. W.; Dorda, U.
- Deutsches Elektronen-Synchrotron, DESY, Hamburg
Numerical Studies on Electron Beam Quality Optimization in a Laser-Driven Plasma Accelerator with External Injection at SINBAD for ATHENAe
text, January 2019
- Svystun, Elena; Aßmann, Ralph; Dorda, Ulrich
- JACoW Publishing, Geneva, Switzerland