WENO schemes applied to the quasi-relativistic Vlasov--Maxwell model for laser-plasma interaction

TL;DR

This paper develops and tests WENO-based numerical schemes, including explicit and implicit methods, for simulating laser-plasma interactions using the 1D Quasi-Relativistic Vlasov--Maxwell model, demonstrating their effectiveness through preliminary experiments.

Contribution

It introduces novel WENO schemes with Runge--Kutta and Time-Splitting discretizations for the QRVM model, advancing numerical simulation techniques for laser-plasma interactions.

Findings

Effective non-oscillatory schemes demonstrated in preliminary tests

Both explicit and implicit WENO-based methods are viable

Potential for improved accuracy in laser-plasma interaction simulations

Abstract

In this paper we focus on WENO-based methods for the simulation of the 1D Quasi-Relativistic Vlasov--Maxwell (QRVM) model used to describe how a laser wave interacts with and heats a plasma by penetrating into it. We propose several non-oscillatory methods based on either Runge--Kutta (explicit) or Time-Splitting (implicit) time discretizations. We then show preliminary numerical experiments.