Simulation of plasma accelerators with the Particle-In-Cell method

TL;DR

This paper details the electromagnetic Particle-in-Cell method for plasma accelerator simulations, covering algorithms, stability, accuracy, and practical applications including high-performance computing and advanced modeling techniques.

Contribution

It provides a comprehensive overview of the PIC method, including new insights into stability, accuracy, and specialized topics for plasma accelerator modeling.

Findings

Discussion of stability and accuracy in PIC algorithms

Analysis of numerical Cherenkov instability and mitigation strategies

Examples of laser-driven and beam-driven plasma accelerator simulations

Abstract

We present the standard electromagnetic Particle-in-Cell method, starting from the discrete approximation of derivatives on a uniform grid. The application to second-order, centered, finite-difference discretization of the equations of motion and of Maxwells equations is then described in one dimension, followed by two and three dimensions. Various algorithms are presented, for which we discuss the stability and accuracy, introducing and elucidating concepts like numerical stochastic heating, CFL limit and numerical dispersion. The coupling of the particles and field quantities via interpolation at various orders is detailed, together with its implication on energy and momentum conserving. Special topics of relevance to the modeling of plasma accelerators are discussed, such as moving window, optimal Lorentz boosted frame, the numerical Cherenkov instability and its mitigation. Examples of simulations of laser-driven and particle beam-driven accelerators are given, including with mesh refinement. We conclude with a discussion on high-performance computing and a brief outlook.