High-order exponential solver method for particle-in-cell simulations

TL;DR

This paper introduces a high-order exponential solver method for particle-in-cell simulations that combines the accuracy of spectral methods with the locality of finite difference methods, improving modeling of laser-plasma interactions.

Contribution

The paper presents a novel finite difference exponential time domain solution that bridges finite difference and spectral methods for PIC simulations, enhancing accuracy and locality.

Findings

Verified accuracy and convergence in benchmarks

Simulated laser propagation, electron injection, and high-harmonic generation

Compared results with standard PIC codes

Abstract

Outstanding advances in solid-state laser technology, employing the optical parametric chirped-pulse-amplification (OPCPA) technique, have led physicists to focus laser pulses to highly-relativistic intensities which led to novel schemes for charged-particle acceleration and radiation generation in laser-driven plasmas. Microscopic understanding of these highly nonlinear processes is possible via accurate modeling of the laser-plasma interaction using particle-in-cell (PIC) simulations. Numerous codes are available and they rely on finite difference time domain methods on Yee-grids or on the analytical solution of the Maxwell-equations in spectral space. In this work, we present a solution bridging these two methods, which we call finite difference exponential time domain solution. This method could provide a very high accuracy even in 3D, but with improved locality, similar to the pseudospectral analytical methods without relying on transformation to special basis functions. We verified the accuracy and the convergence of the method in various benchmarks, including laser propagation in vacuum and in underdense plasma. We also simulated electron injection in a non-linear laser-plasma wakefield acceleration and surface high-harmonic generation in the overdense regime. The results are then compared with those obtained from standard PIC codes.