Stochastic variational principles for the collisional Vlasov–Maxwell and Vlasov–Poisson equations

Tomasz M. Tyranowski*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)
5 Downloads (Pure)

Abstract

In this work, we recast the collisional Vlasov–Maxwell and Vlasov–Poisson equations as systems of coupled stochastic and partial differential equations, and we derive stochastic variational principles which underlie such reformulations. We also propose a stochastic particle method for the collisional Vlasov–Maxwell equations and provide a variational characterization of it, which can be used as a basis for a further development of stochastic structure-preserving particle-in-cell integrators.
Original languageEnglish
Article number20210167
Number of pages23
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume477
Issue number2252
DOIs
Publication statusPublished - 25 Aug 2021
Externally publishedYes

Keywords

  • stochastic variational principles
  • Vlasov-Maxwell equation
  • Vlasov-Poisson equation
  • collisions
  • Fokker-Planck equation
  • particle methods

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