Comptes Rendus
Theoretical and numerical approaches for Vlasov–Maxwell equations
Modeling of relativistic plasmas with the Particle-In-Cell method
Comptes Rendus. Mécanique, Theoretical and numerical approaches for Vlasov-maxwell equations, Volume 342 (2014) no. 10-11, pp. 610-618.

Standard methods employed in relativistic electromagnetic Particle-In-Cell codes are reviewed, as well as novel techniques that were introduced recently. Advances in the analysis and mitigation of the numerical Cherenkov instability are also presented with comparison between analytical theory and numerical experiments. The algorithmic and numerical analytic advances are expanding the range of applicability of the method in the ultra-relativistic regime in particular, where the numerical Cherenkov instability is the strongest without corrective measures.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2014.07.006
Keywords: Particle-In-Cell, Plasma simulation, Special relativity, Numerical instability

Jean-Luc Vay 1 ; Brendan B. Godfrey 1, 2

1 Lawrence Berkeley National Laboratory, Berkeley, CA, USA
2 University of Maryland, College Park, MD, USA
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Jean-Luc Vay; Brendan B. Godfrey. Modeling of relativistic plasmas with the Particle-In-Cell method. Comptes Rendus. Mécanique, Theoretical and numerical approaches for Vlasov-maxwell equations, Volume 342 (2014) no. 10-11, pp. 610-618. doi : 10.1016/j.crme.2014.07.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.07.006/

[1] D. Grote; A. Friedman; J.-L. Vay; I. Haber The warp code: modeling high intensity ion beams, AIP Conference Proceedings, vol. 749, 2005, pp. 55-58

[2] J.-L. Vay; D. Grote; R. Cohen; A. Friedman Novel methods in the particle-in-cell accelerator code-framework warp, Comput. Sci. Discov., Volume 5 (2012), p. 014019 (20 p)

[3] C. Birdsall; A. Langdon Plasma Physics via Computer Simulation, Adam-Hilger, 1991

[4] J.-L. Vay; J.-C. Adam; A. Heron Asymmetric PML for the absorption of waves. Application to mesh refinement in electromagnetic particle-in-cell plasma simulations, Comput. Phys. Commun., Volume 164 (2004) no. 1–3, pp. 171-177 | DOI

[5] K. Yee Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas Propag., Volume 3 (1966), pp. 302-307

[6] J. Cole A high-accuracy realization of the Yee algorithm using non-standard finite differences, IEEE Trans. Microw. Theory Tech., Volume 45 (1997) no. 6, pp. 991-996

[7] J. Cole High-accuracy Yee algorithm based on nonstandard finite differences: new developments and verifications, IEEE Trans. Antennas Propag., Volume 50 (2002) no. 9, pp. 1185-1191 | DOI

[8] M. Karkkainen; E. Gjonaj; T. Lau; T. Weiland Low-dispersion wake field calculation tools, Chamonix, France (2006), pp. 35-40

[9] J.L. Vay; C.G.R. Geddes; E. Cormier-Michel; D.P. Grote Numerical methods for instability mitigation in the modeling of laser wakefield accelerators in a Lorentz-boosted frame, J. Comput. Phys., Volume 230 (2011) no. 15, pp. 5908-5929 | DOI

[10] B.M. Cowan; D.L. Bruhwiler; J.R. Cary; E. Cormier-Michel; C.G.R. Geddes Generalized algorithm for control of numerical dispersion in explicit time-domain electromagnetic simulations, Phys. Rev. ST Accel. Beams, Volume 16 (2013) no. 4, p. 041303 | DOI

[11] A. Pukhov Three-dimensional electromagnetic relativistic particle-in-cell code VLPL (Virtual Laser Plasma Lab), J. Plasma Phys., Volume 61 (1999) no. 3, pp. 425-433 | DOI

[12] R. Lehe; A. Lifschitz; C. Thaury; V. Malka; X. Davoine Numerical growth of emittance in simulations of laser-wakefield acceleration, Phys. Rev. ST Accel. Beams, Volume 16 (2013) no. 2, p. 021301 | DOI

[13] I. Haber; R. Lee; H. Klein; J. Boris Advances in electromagnetic simulation techniques, Berkeley, CA, USA (1973), pp. 46-48

[14] J.-L. Vay; I. Haber; B.B. Godfrey A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas, J. Comput. Phys., Volume 243 (2013), pp. 260-268 | DOI

[15] J. Dawson Particle simulation of plasmas, Rev. Mod. Phys., Volume 55 (1983) no. 2, pp. 403-447 | DOI

[16] Q. Liu The PSTD Algorithm: a time-domain method requiring only two cells per wavelength, Microw. Opt. Technol. Lett., Volume 15 (1997) no. 3, pp. 158-165 | DOI

[17] Y. Ohmura; Y. Okamura Staggered grid pseudo-spectral time-domain method for light scattering analysis, PIERS Online, Volume 6 (2010) no. 7, pp. 632-635

[18] J. Boris Relativistic plasma simulation–optimization of a hybrid code, Proc. Fourth Conf. Num. Sim. Plasmas, Naval Res. Lab., Wash., D.C., 1970, pp. 3-67

[19] J.L. Vay Simulation of beams or plasmas crossing at relativistic velocity, Phys. Plasmas, Volume 15 (2008) no. 5, p. 056701 | DOI

[20] H. Abe; N. Sakairi; R. Itatani; H. Okuda High-order spline interpolations in the particle simulation, J. Comput. Phys., Volume 63 (1986) no. 2, pp. 247-267

[21] A. Langdon On enforcing Gauss law in electromagnetic particle-in-cell codes, Comput. Phys. Commun., Volume 70 (1992) no. 3, pp. 447-450

[22] B. Marder A method for incorporating Gauss law into electromagnetic PIC codes, J. Comput. Phys., Volume 68 (1987) no. 1, pp. 48-55

[23] J.-L. Vay; C. Deutsch Charge compensated ion beam propagation in a reactor sized chamber, Phys. Plasmas, Volume 5 (1998) no. 4, pp. 1190-1197

[24] C. Munz; P. Omnes; R. Schneider; E. Sonnendrucker; U. Voss Divergence correction techniques for Maxwell solvers based on a hyperbolic model, J. Comput. Phys., Volume 161 (2000) no. 2, pp. 484-511 | DOI

[25] J. Villasenor; O. Buneman Rigorous charge conservation for local electromagnetic-field solvers, Comput. Phys. Commun., Volume 69 (1992) no. 2–3, pp. 306-316

[26] T. Esirkepov Exact charge conservation scheme for particle-in-cell simulation with an arbitrary form-factor, Comput. Phys. Commun., Volume 135 (2001) no. 2, pp. 144-153

[27] R. Morse; C. Nielson Numerical simulation of Weibel instability in one and 2 dimensions, Phys. Fluids, Volume 14 (1971) no. 4, p. 830 | DOI

[28] R. Hockney, J. Eastwood, Computer Simulation Using Particles, 1988.

[29] H. Lewis Variational algorithms for numerical simulation of collisionless plasma with point particles including electromagnetic interactions, J. Comput. Phys., Volume 10 (1972) no. 3, pp. 400-419 http://www.sciencedirect.com/science/article/pii/0021999172900447 | DOI

[30] B.B. Godfrey Numerical Cherenkov instabilities in electromagnetic particle codes, J. Comput. Phys., Volume 15 (1974) no. 4, pp. 504-521

[31] L. Sironi, A. Spitkovsky, Private communication, 2011.

[32] X. Xu; P. Yu; S.F. Martins; F. Tsung; V.K. Decyk; J. Vieira; R.A. Fonseca; W. Lu; L.O. Silva; W.B. Mori Numerical instability due to relativistic plasma drift in EM-PIC simulations, Comput. Phys. Commun., Volume 184 (2013), pp. 2503-2514

[33] B.B. Godfrey Canonical momenta and numerical instabilities in particle codes, J. Comput. Phys., Volume 19 (1975) no. 1, pp. 58-76

[34] B.B. Godfrey; J.-L. Vay Numerical stability of relativistic beam multidimensional pic simulations employing the Esirkepov algorithm, J. Comput. Phys., Volume 248 (2013), pp. 33-46 | DOI

[35] B.B. Godfrey, J.-L. Vay, Suppressing the numerical Cherenkov instability in FDTD PIC codes, 2014.

[36] B.B. Godfrey; J.-L. Vay; I. Haber Numerical stability analysis of the pseudo-spectral analytical time-domain PIC algorithm, J. Comput. Phys., Volume 258 (2014), pp. 689-704 | DOI

[37] B.B. Godfrey, J.-L. Vay, I. Haber, Numerical stability improvements for the pseudo-spectral EM PIC algorithm, 2013.

[38] A.B. Langdon Nonphysical modifications to oscillations, fluctuations, and collisions due to space-time differencing, Proceedings of the Fourth Conference on Numerical Simulation of Plasmas, 1970, pp. 467-495

[39] H. Okuda Nonphysical instabilities in plasma simulation due to small Debye length, Proceedings of the Fourth Conference on Numerical Simulation of Plasmas, 1970, pp. 511-525

[40] B. Godfrey, Time-biased field solver for electromagnetic PIC codes, in: Proceedings of the Ninth Conference on Numerical Simulation of Plasmas, 1980.

[41] A. Friedman A 2nd-order implicit particle mover with adjustable damping, J. Comput. Phys., Volume 90 (1990) no. 2, pp. 292-312

[42] A. Greenwood; K. Cartwright; J. Luginsland; E. Baca On the elimination of numerical Cerenkov radiation in PIC simulations, J. Comput. Phys., Volume 201 (2004) no. 2, pp. 665-684 | DOI

[43] T. Esirkepov Exact charge conservation scheme for particle-in-cell simulation with an arbitrary form-factor, Comput. Phys. Commun., Volume 135 (2001) no. 2, pp. 144-153

[44] J.-L. Vay; I. Haber; B.B. Godfrey A domain decomposition method for pseudo-spectral electromagnetic simulations of plasmas, J. Comput. Phys., Volume 243 (2013), pp. 260-268 | DOI

[45] http://www.wolfram.com/cdf/ Computable document format (CDF), 2012

[46] http://www.wolfram.com/mathematica/ (Mathematica, version nine, 2012)

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  • Edison Puig Maldonado; Rui Andrade Carvalho Nunes; Sávio Lima Morais, 2024 SBFoton International Optics and Photonics Conference (SBFoton IOPC) (2024), p. 1 | DOI:10.1109/sbfotoniopc62248.2024.10813485
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