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Numerical simulations of Vlasov-Maxwell equations for laser plasmas based on Poisson structure

Yingzhe Li 1, 2, 3 Nicolas Crouseilles 1, 2 Yajuan Sun 3, * 
* Corresponding author
1 MINGUS - Multi-scale numerical geometric schemes
IRMAR - Institut de Recherche Mathématique de Rennes, ENS Rennes - École normale supérieure - Rennes, Inria Rennes – Bretagne Atlantique
Abstract : In this paper, a bracket structure is proposed for the laser-plasma interaction model introduced in [19], and it is proved by direct calculations that the bracket is Poisson which satisfies the Jacobi identity. Then splitting methods in time are proposed based on the Poisson structure. For the quasi-relativistic case, the Hamiltonian splitting leads to three subsystems which can be solved exactly. The conservative splitting is proposed for the fully relativistic case, and three one-dimensional conservative subsystems are obtained. Combined with the splittings in time, in phase space discretization we use the Fourier spectral and finite volume methods. It is proved that the discrete charge and discrete Poisson equation are conserved by our numerical schemes. Numerically, some numerical experiments are conducted to verify good conservations for the charge, energy and Poisson equation.
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Submitted on : Tuesday, December 3, 2019 - 7:55:42 PM
Last modification on : Friday, July 8, 2022 - 10:06:33 AM
Long-term archiving on: : Wednesday, March 4, 2020 - 9:22:11 PM


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Yingzhe Li, Nicolas Crouseilles, Yajuan Sun. Numerical simulations of Vlasov-Maxwell equations for laser plasmas based on Poisson structure. Journal of Computational Physics, 2020, 405, pp.1-20. ⟨10.1016/⟩. ⟨hal-02391668⟩



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