# Convergence analysis of an explicit splitting method for laser plasma interaction simulations

## TL;DR

This paper rigorously analyzes a specialized explicit splitting method for laser plasma simulations, demonstrating its stability and convergence properties, and proposing modifications for improved second-order accuracy.

## Contribution

It provides a convergence analysis of a triple splitting method tailored for laser plasma interactions and introduces modifications for second-order convergence.

## Key findings

- The method overcomes stability restrictions of classical explicit integrators.
- A generalized version of the scheme is shown to be second order convergent.
- The analysis guides modifications to improve the original scheme's accuracy.

## Abstract

Convergence of a triple splitting method originally proposed by T. T\"uckmantel,et.al. [IEEE Transactions on Plasma Science, 38(9):2383--2389, 2010] for the solution of a simple Vlasov-Maxwell system, that describes laser plasma interactions with overdense plasmas, is analyzed. For classical explicit integrators it is the large density parameter that would impose a restriction on the time step size to make the integration stable. The triple splitting method contains an exponential integrator in its central component and was specifically designed for systems that describe laser plasma interactions and overcomes this restriction. We rigorously analyze a slightly generalized version of the original method. This analysis enables us to identify modifications of the original scheme, such that a second order convergent scheme is obtained.