Numerical paraxial approximation for highly relativistic beams

Franck Assous, Felix Tsipis

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


This paper is concerned with the numerical simulation of highly relativistic beams. We developed a particle-in-cell code for highly relativistic beams, based on the paraxial Vlasov-Maxwell formulation of Laval et al. This formulation follows the beam in a speed-of-light frame. It is fourth order accurate in the small characteristic velocity of the beam. The formulation is simpler than standard particle-in-cell codes in the lab frame or in the beam frame and gives a fast and easy to implement algorithm. Numerical examples illustrate the accuracy of the method.

Original languageEnglish
Pages (from-to)1086-1097
Number of pages12
JournalComputer Physics Communications
Issue number7
StatePublished - Jul 2009


  • Asymptotic methods
  • Numerical schemes
  • Paraxial approximation
  • Relativistic beams
  • Vlasov-Maxwell equations


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