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Parallel implementation of a relativistic semi-Lagrangian Vlasov–Maxwell solver

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Abstract

We describe the parallel implementation of a semi-Lagrangian relativistic VLasov ElectroMagnetic (VLEM) code for the numerical investigation of the dynamics of charged particle distribution in their self-consistent electromagnetic fields. This paper introduces the numerical solution of the Vlasov–Maxwell system in two spatial dimensions, and two or three momentum dimensions. Accuracy, stability, efficiency properties and the implementation of a new algorithm of charge conservation when solving Maxwell equations are discussed. The performances of the code are tested by studying the evolution of Weibel-type instabilities in the relativistic regime. Application to the coupling between Current Filamentation (CFI) and Two-Stream (TSI) instabilities is presented showing the importance of pair-wise vortex merging scenario in the saturation mechanism.

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References

  1. J.M. Dawson, Rev. Mod. Phys. 55, 403 (1983)

    Article  ADS  Google Scholar 

  2. C.A. Birdsall, A.B. Langdon, Plasma physics via computer simulations (McGraw-Hill, New York, 1985)

  3. G. Lapenta, J. Comput. Phys. 231, 795 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  4. P. Bertrand, A. Ghizzo, T.W. Johnston, M. Shoucri, E. Fijalkow, M.R. Feix, Phys. Fluids B 2, 1028 (1990)

    Article  ADS  Google Scholar 

  5. T.W. Johnston, P. Bertrand, A. Ghizzo, M. Shoucri, E. Fijalkow, M.R. Feix, Phys. Fluids B 4, 2523 (1992)

    Article  ADS  Google Scholar 

  6. A. Ghizzo, P. Bertrand, J. Lebas, T.W. Johnston, M. Shoucri, Phys. Plasmas 3, 650 (1996)

    Article  ADS  Google Scholar 

  7. M. Albrecht-Marc, A. Ghizzo, T.W. Johnston, T. Reveille, D. Del Sarto, P. Bertrand, Phys. Plasmas 14, 072704 (2007)

    Article  ADS  Google Scholar 

  8. E. Sonnendrücker, J. Roche, P. Bertrand, A. Ghizzo, J. Comput. Phys. 149, 201 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  9. M.L. Begue, A. Ghizzo, P. Bertrand, E. Sonnendrücker, O. Coulaud, J. Plasma Phys. 62, 367 (1999)

    Article  ADS  Google Scholar 

  10. M.L. Begue, A. Ghizzo, P. Bertrand, J. Comput. Phys. 151, 458 (1999)

    Article  ADS  Google Scholar 

  11. A. Ghizzo, F. Huot, P. Bertrand, J. Comput. Phys. 186, 47 (2003)

    Article  ADS  Google Scholar 

  12. T. Nakamura, T. Yabe, Comput. Phys. Commun. 120, 122 (1999)

    Article  ADS  Google Scholar 

  13. E. Fijalkow, Comput. Phys. Commun. 116, 319 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  14. F. Filbet, E. Sonnendrücker, P. Bertrand, J. Comput. Phys. 172, 166 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  15. F. Filbet, E. Sonnendrücker, Comput. Phys. Commun. 150, 247 (2003)

    Article  ADS  Google Scholar 

  16. R. Bermejo, Numer. Math. 60, 163 (1991)

    Article  MathSciNet  Google Scholar 

  17. M. Falcone, R. Ferreti, SIAM J. Numer. Anal. 35, 909 (1998)

    Article  MathSciNet  Google Scholar 

  18. P. Bartello, S.J. Thomas, Mon. Weather Rev. 124, 2883 (1996)

    Article  ADS  Google Scholar 

  19. N. Besse, SIAM J. Numer. Anal. 42, 350 (2004)

    Article  MathSciNet  Google Scholar 

  20. A. Staniforth, J. Coté, Mon. Weather Rev. 119, 206 (1991)

    Article  Google Scholar 

  21. C.G. Cheng, G. Knorr, J. Comput. Phys. 22, 330 (1976)

    Article  ADS  Google Scholar 

  22. N. Crouseilles, G. Latu, E. Sonnendrücker, Int. J. Appl. Math. Comput. Sci. 17, 335 (2007)

    Article  MathSciNet  Google Scholar 

  23. X. Garbet, Y. Idomura, L. Villard, T.H. Watanabe, Nucl. Fusion 50, 043002 (2010)

    Article  ADS  Google Scholar 

  24. V. Grandgirard, M. Brunetti, P. Bertrand, N. Besse, X. Garbet, P. Ghendrih, E. Sonnendrücker, J. Vaclavik, L. Villard, J. Comput. Phys. 217, 395 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  25. A.J. Klimas, W.M. Farrell, J. Comput. Phys. 110, 150 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  26. M.C. Pinto, E. Sonnendrücker, A. Friedman, D.P. Grote, S.M. Lund, J. Comput. Phys. 275, 236 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  27. N. Crouseilles, M. Mehrenberger, E. Sonnendrücker, J. Comput. Phys. 229, 1927 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  28. F. Huot, A. Ghizzo, P. Bertrand, E. Sonnendrücker, O. Coulaud, J. Comput. Phys. 185, 512 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  29. L.K.S. Daldorff, B. Eliasson, Parallel Comput. 35, 109 (2009)

    Article  MathSciNet  Google Scholar 

  30. T. Umeda, K. Togano, T. Ogino, Comput. Phys. Commun. 180, 365 (2009)

    Article  ADS  Google Scholar 

  31. T. Minoshima, Y. Matsumoto, T. Amano, J. Comput. Phys. 230, 6800 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  32. Y. Cheng, A.J. Christlieb, X. Zhang, J. Comput. Phys. 279, 145 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  33. F. Valentini, P. Travnicek, F. Califano, P. Hellinger, A. Mangeney, J. Comput. Phys. 225, 753 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  34. A. Mangeney, F. Califano, C. Cavazzoni, P. Travnicek, J. Comput. Phys. 179, 495 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  35. O. Coulaud, E. Sonnendrücker, E. Dillon, P. Bertrand, A. Ghizzo, J. Plasma Phys. 3, 435 (1999)

    Article  ADS  Google Scholar 

  36. A. Ghizzo, T.W. Johnston, T. Reveille, P. Bertrand, M. Albrecht-Marc, Phys. Rev. E 74, 046407 (2006)

    Article  ADS  Google Scholar 

  37. A. Ghizzo, D. Del Sarto, R. Reveille, N. Besse, R. Klein, Phys. Plasmas 14, 062702 (2007)

    Article  ADS  Google Scholar 

  38. K. Yee, IEEE Trans. Ant. Prop. 14, 302 (1966)

    Article  ADS  Google Scholar 

  39. T.Zh. Esirkepov, Comput. Phys. Commun. 135, 144 (2001)

    Article  ADS  Google Scholar 

  40. N. Crouseilles, P. Navaro, E. Sonnendrücker, CR Mécanique 342, 636 (2014)

    Article  Google Scholar 

  41. B.D. Fried, Phys. Fluids 2, 337 (1959)

    Article  ADS  Google Scholar 

  42. E.W. Weibel, Phys. Rev. Lett. 2, 83 (1959)

    Article  ADS  Google Scholar 

  43. G.A. Askar Yan, S.V. Bulanov, F. Pegoraro, A.M. Pukhov, JETP Lett. 60, 251 (1994)

    ADS  Google Scholar 

  44. R. Sudan, Phys. Rev. Lett. 70, 3075 (1993)

    Article  ADS  Google Scholar 

  45. A. Bret, L. Gremillet, D. Bénisti, E. Lefebvre, Phys. Rev. Lett. 100, 205008 (2008)

    Article  ADS  Google Scholar 

  46. F. Pegoraro, S.V. Bulanov, F. Califano, M. Lontano, Phys. Scripta T63, 262 (1996)

    Article  ADS  Google Scholar 

  47. Y. Kaziura, F. Califano, J.-I. Sakai, T. Neubert, F. Pegoraro, S. Bulanov, J. Phys. Soc. Jpn 67, 1079 (1998)

    Article  ADS  Google Scholar 

  48. R. Schlickeiser, P.K. Shukla, Astrophys. J. 599, L60 (2003)

    Article  ADS  Google Scholar 

  49. F. Califano, R. Prandi, F. Pegoraro, S. Bulanov, Phys. Rev. E 58, 7837 (1998)

    Article  ADS  Google Scholar 

  50. G. Kalman, C. Montes, D. Guemada, Phys. Fluids 11, 1797 (1968)

    Article  ADS  Google Scholar 

  51. A. Ghizzo, B. Izrar, P. Bertrand, E. Fijalkow, M.R. Feix, M.M. Shoucri, Phys. Fluids 31, 72 (1988)

    Article  ADS  Google Scholar 

  52. A. Ghizzo, B. Izrar, P. Bertrand, E. Fijalkow, M.R. Feix, M.M. Shoucri, Phys. Lett. A 120, 191 (1987)

    Article  ADS  Google Scholar 

  53. A. Bret, L. Gremillet, D. Benisti, Phys. Rev. E 81, 036402 (2010)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Institut Jean Lamour, UMR 7198, Université de Lorraine, BP 70239, 54506, Vandoeuvre les Nancy Cedex, France

    Mathieu Sarrat, Alain Ghizzo, Daniele Del Sarto & Laurent Serrat

Authors
  1. Mathieu Sarrat
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  2. Alain Ghizzo
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  3. Daniele Del Sarto
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  4. Laurent Serrat
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Corresponding author

Correspondence to Alain Ghizzo.

Additional information

Contribution to the “Topical Issue Relativistic Laser Plasma Interactions”, edited by Tünde Fülöp, Francesco Pegoraro, and Vladimir Tikhonchuk.

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Sarrat, M., Ghizzo, A., Del Sarto, D. et al. Parallel implementation of a relativistic semi-Lagrangian Vlasov–Maxwell solver. Eur. Phys. J. D 71, 271 (2017). https://doi.org/10.1140/epjd/e2017-80188-4

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  • DOI: https://doi.org/10.1140/epjd/e2017-80188-4

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