TNSA proton maximum energy laws for 2D and 3D PIC simulations

TL;DR

This paper introduces empirical laws to interpret 2D PIC simulation results quantitatively and to determine when 3D PIC simulations are sufficiently converged, optimizing computational resources in laser-plasma research.

Contribution

It proposes new empirical laws that improve the understanding of proton energy scaling in PIC simulations and guide the use of 2D and 3D models effectively.

Findings

Empirical laws accurately estimate maximum proton energy in 2D PIC simulations.

Guidelines for when to stop 3D PIC simulations based on convergence criteria.

Reduction of computational costs by optimizing simulation dimensionality.

Abstract

Numerical simulations are a prominent tool in laser-plasma experiments. Their role, as a guide in new regime explorations and as a support for understanding laboratory results, is undisputed. But as the experiments themselves are growing in costs, setup time and complexity, so are the numerical counterparts. Nowadays it is often necessary to investigate, with great accuracy, a huge set of parameters, in order to explore interesting features. In literature, it is well known that two-dimensional particle in cell (2D PIC) simulations can only give a qualitative estimation of experimental results, often through a great layer of arbitrariness. On the other hand, three-dimensional (3D) PIC simulations, for the same setup, can typically require two orders of magnitude more of computational resources, to deliver results that, while being similar to laboratory results, are still far from being a real match, due to the many uncertainties, in the parameters and in the model, included in the physical engine. Following our recent published work, we discuss here a couple of empirical laws that we proposed, that can help giving quantitative insight into 2D PIC simulations and determining when 3D simulations should be stopped, if it is not really necessary to do a detailed exploration of the numerical results at long times.