Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

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

Abstract

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 additional main NCI modes well outside the range of physical interest with higher |k1|. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1ˆ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correctmore » the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss’ Law is satisfied. Lastly, we present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.« less

Authors:
 [1]; ORCiD logo [2];  [2];  [3];  [2];  [2];  [2];  [2];  [2];  [2];  [4];  [1];  [2]
+ Show Author Affiliations
  1. Tsinghua Univ., Beijing (China)
  2. Univ. of California, Los Angeles, CA (United States)
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  4. Univ. de Lisboa, Lisbon (Portugal); ISCTE - Instituto Univ. de Lisboa, Lisbon (Portugal)
Publication Date:
Research Org.:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1352201
Alternate Identifier(s):
OSTI ID: 1398307
Grant/Contract Number:  
11425521; 11535006; 11375006; ACI 1339893; 1500630; 1614949; SC0014260; SC0010064; SC0008316; AC02-76SF00515
Resource Type:
Accepted Manuscript
Journal Name:
Computer Physics Communications
Additional Journal Information:
Journal Volume: 214; Journal Issue: C; Journal ID: ISSN 0010-4655
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; PIC simulation; hybrid Maxwell solver; relativistic plasma drift; numerical Cerenkov instability; Lorentz boosted frame

Citation Formats

Li, Fei, Yu, Peicheng, Xu, Xinlu, Fiuza, Frederico, Decyk, Viktor K., Dalichaouch, Thamine, Davidson, Asher, Tableman, Adam, An, Weiming, Tsung, Frank S., Fonseca, Ricardo A., Lu, Wei, and Mori, Warren B. Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction. United States: N. p., 2017. Web. doi:10.1016/j.cpc.2017.01.001.
Copy to clipboard
Li, Fei, Yu, Peicheng, Xu, Xinlu, Fiuza, Frederico, Decyk, Viktor K., Dalichaouch, Thamine, Davidson, Asher, Tableman, Adam, An, Weiming, Tsung, Frank S., Fonseca, Ricardo A., Lu, Wei, & Mori, Warren B. Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction. United States. https://doi.org/10.1016/j.cpc.2017.01.001
Copy to clipboard
Li, Fei, Yu, Peicheng, Xu, Xinlu, Fiuza, Frederico, Decyk, Viktor K., Dalichaouch, Thamine, Davidson, Asher, Tableman, Adam, An, Weiming, Tsung, Frank S., Fonseca, Ricardo A., Lu, Wei, and Mori, Warren B. Thu . "Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction". United States. https://doi.org/10.1016/j.cpc.2017.01.001. https://www.osti.gov/servlets/purl/1352201.
Copy to clipboard
@article{osti_1352201,
title = {Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction},
author = {Li, Fei and Yu, Peicheng and Xu, Xinlu and Fiuza, Frederico and Decyk, Viktor K. and Dalichaouch, Thamine and Davidson, Asher and Tableman, Adam and An, Weiming and Tsung, Frank S. and Fonseca, Ricardo A. and Lu, Wei and Mori, Warren B.},
abstractNote = {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 additional main NCI modes well outside the range of physical interest with higher |k1|. These main NCI modes can be easily filtered out along with first spatial aliasing NCI modes which are also at the edge of the fundamental Brillouin zone. The customized solver has the possible advantage of improved parallel scalability because it can be easily partitioned along 1ˆ which typically has many more cells than other directions for the problems of interest. We show that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative. This ensures that Gauss’ Law is satisfied. Lastly, we present simulation examples of one relativistically drifting plasma, of two colliding relativistically drifting plasmas, and of nonlinear laser wakefield acceleration (LWFA) in a Lorentz boosted frame that show no evidence of the NCI can be observed when using this customized Maxwell solver together with its NCI elimination scheme.},
doi = {10.1016/j.cpc.2017.01.001},
journal = {Computer Physics Communications},
number = C,
volume = 214,
place = {United States},
year = {Thu Jan 12 00:00:00 EST 2017},
month = {Thu Jan 12 00:00:00 EST 2017}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1016/j.cpc.2017.01.001
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 24 works
Citation information provided by
Web of Science
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Numerical Cherenkov instabilities in electromagnetic particle codes
journal, August 1974

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

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

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

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

Laser Electron Accelerator
journal, July 1979

Ion Dynamics and Acceleration in Relativistic Shocks
journal, April 2009

Weibel-Instability-Mediated Collisionless Shocks in the Laboratory with Ultraintense Lasers
journal, June 2012

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

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

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

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

Modeling of laser wakefield acceleration in Lorentz boosted frame using EM-PIC code with spectral solver
journal, June 2014

Application of electromagnetic particle simulation to the generation of electromagnetic radiation
journal, January 1974

Particle simulation of plasmas
journal, April 1983

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

Closed-form expressions for the finite difference approximations of first and higher derivatives based on Taylor series
journal, July 1999

Mathematical proof of closed form expressions for finite difference approximations based on Taylor series
journal, January 2003

  • Khan, Ishtiaq Rasool; Ohba, Ryoji; Hozumi, Noriyuki
  • Journal of Computational and Applied Mathematics, Vol. 150, Issue 2
  • DOI: 10.1016/S0377-0427(02)00667-2

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

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
  • DOI: 10.1016/j.jcp.2008.11.017

Implementation of a hybrid particle code with a PIC description in r–z and a gridless description in ϕ into OSIRIS
journal, January 2015

Exact charge conservation scheme for Particle-in-Cell simulation with an arbitrary form-factor
journal, April 2001

Generating multi-GeV electron bunches using single stage laser wakefield acceleration in a 3D nonlinear regime
journal, June 2007

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Transverse phase space diagnostics for ionization injection in laser plasma acceleration using permanent magnetic quadrupoles
    journal, February 2018

    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

    High quality electron bunch generation using a longitudinal density-tailored plasma-based accelerator in the three-dimensional blowout regime
    journal, November 2017

    A new method for analyzing and visualizing plasma simulations using a phase-space tessellation
    journal, July 2018

    • Totorica, Samuel R.; Fiuza, Frederico; Abel, Tom
    • Physics of Plasmas, Vol. 25, Issue 7
    • DOI: 10.1063/1.5037348

    Multi-scale simulations of particle acceleration in astrophysical systems
    journal, March 2020

    • Marcowith, Alexandre; Ferrand, Gilles; Grech, Mickael
    • Living Reviews in Computational Astrophysics, Vol. 6, Issue 1
    • DOI: 10.1007/s41115-020-0007-6
      Sort by:
      [ × clear filter / sort ]

      Similar Records in DOE PAGES and OSTI.GOV collections: