Contemporary particle-in-cell approach to laser-plasma modelling

TLDR

Particle‑in‑cell (PIC) methods, originally based on Yee grids and Boris particle pushing, have evolved to include high‑order shape functions, Poisson‑preserving updates, collisions, ionisation, hybrid solid‑density schemes, and QED effects, and modern computing now enables full 3D, real mass‑ratio, multi‑speckle simulations. The paper reviews core algorithms of contemporary laser‑plasma PIC codes and summarizes recent applications such as SRS, short‑pulse laser‑solid interactions, fast‑electron transport, and QED effects. The authors examine algorithmic components—field solvers, particle pushers, collision models, ionisation, hybrid solid‑density schemes, and QED modules—within modern PIC codes. The review provides estimates of self‑heating rates, convergence of collisional routines, tests of ionisation models, and highlights recent applications in SRS, short‑pulse laser‑solid interactions, fast‑electron transport, and QED effects.

Abstract

Particle-in-cell (PIC) methods have a long history in the study of laser-plasma interactions. Early electromagnetic codes used the Yee staggered grid for field variables combined with a leapfrog EM-field update and the Boris algorithm for particle pushing. The general properties of such schemes are well documented. Modern PIC codes tend to add to these high-order shape functions for particles, Poisson preserving field updates, collisions, ionisation, a hybrid scheme for solid density and high-field QED effects. In addition to these physics packages, the increase in computing power now allows simulations with real mass ratios, full 3D dynamics and multi-speckle interaction. This paper presents a review of the core algorithms used in current laser-plasma specific PIC codes. Also reported are estimates of self-heating rates, convergence of collisional routines and test of ionisation models which are not readily available elsewhere. Having reviewed the status of PIC algorithms we present a summary of recent applications of such codes in laser-plasma physics, concentrating on SRS, short-pulse laser-solid interactions, fast-electron transport, and QED effects.