Splitting methods for Fourier spectral discretizations of the strongly magnetized Vlasov-Poisson and the Vlasov-Maxwell system

TL;DR

This paper develops and compares splitting methods for Fourier spectral discretizations of magnetized Vlasov systems, demonstrating their accuracy and conservation properties through plasma instability simulations.

Contribution

It introduces new splitting methods tailored for strongly magnetized Vlasov systems and extends Fourier spectral discretizations to higher dimensions with improved conservation.

Findings

Effective splitting methods for 4D magnetized Vlasov--Poisson system.

Comparison with fluid models in turbulence scenarios.

Charge-conserving Hamiltonian splitting for Vlasov--Maxwell system.

Abstract

Fourier spectral discretizations belong to the most straightforward methods for solving the unmagnetized Vlasov--Poisson system in low dimensions. In this article, this highly accurate approach is extended two the four-dimensional magnetized Vlasov--Poisson system with new splitting methods suited for strong magnetic fields. Consequently, a comparison to the asymptotic fluid model is provided at the example of a turbulent Kelvin--Helmholtz instability. For the three dimensional electromagnetic Vlasov--Maxwell system different novel charge conserving implementations of a Hamiltonian splitting are discussed and simulation results of the Weibel streaming instability are presented.