VALIS: A split-conservative scheme for the relativistic 2D Vlasov–Maxwell system

An accurate treatment of the relativistic Vlasov–Maxwell system is of fundamental importance to a broad range of plasma physics topics, including laser–plasma interaction, transport in solar and magnetospheric plasmas and magnetically confined plasmas. This paper introduces VALIS: an algorithm for the numerical solution of the Vlasov–Maxwell system in two spatial dimensions and two momentum dimensions. Particular attention is given to the problems of particle gyromotion on Eulerian momentum grids, satisfying Poisson’s equation without introducing additional workload or altering the dispersion properties of the solver and the potential problems of applying time-splitting algorithms to relativistic systems. This work demonstrates that by adopting a conservative, split-Eulerian scheme based on the Piecewise Parabolic Method for the update of the particle distribution function and utilising the exact particle fluxes to calculate the current in the solution of Maxwell’s equations, these concerns can easily be addressed.