Temporal resolution criterion for correctly simulating relativistic electron motion in a high-intensity laser field

TL;DR

This paper establishes a new temporal resolution criterion for accurately simulating relativistic electron motion in high-intensity laser fields, highlighting the need for adaptive sub-cycling to maintain numerical accuracy.

Contribution

It introduces a novel analytical criterion for time-step selection in particle-in-cell simulations involving relativistic electrons in intense laser fields.

Findings

Numerical accuracy deteriorates with increasing laser amplitude at fixed time-step.

The time-step must be less than λ/(c a_0) for accurate simulations.

Adaptive electron sub-cycling effectively improves simulation accuracy.

Abstract

Particle-in-cell codes are now standard tools for studying ultra-intense laser-plasma interactions. Motivated by direct laser acceleration of electrons in sub-critical plasmas, we examine temporal resolution requirements that must be satisfied to accurately calculate electron dynamics in strong laser fields. Using the motion of a single electron in a perfect plane electromagnetic wave as a test problem, we show surprising deterioration of the numerical accuracy with increasing wave amplitude $a_0$ for a given time-step. We go on to show analytically that the time-step must be significantly less than $\lambda/c a_ 0$ to achieve good accuracy. We thus propose adaptive electron sub-cycling as an efficient remedy.