Mitigation of numerical Cerenkov radiation and instability using a hybrid finite difference-FFT Maxwell solver and a local charge conserving current deposit

TL;DR

This paper introduces a hybrid Maxwell solver combining FFT and finite difference methods to eliminate numerical Cerenkov radiation and instability in relativistic particle-in-cell simulations, improving accuracy and stability.

Contribution

The paper presents a novel hybrid Maxwell solver that effectively removes numerical Cerenkov effects in relativistic PIC simulations, with theoretical analysis and validation in 2D and 3D geometries.

Findings

Eliminates numerical Cerenkov radiation in relativistic PIC simulations.

Successfully suppresses numerical Cerenkov instability using the hybrid solver.

Achieves good agreement with spectral and standard Yee solvers in benchmark tests.

Abstract

A hybrid Maxwell solver for fully relativistic and electromagnetic (EM) particle-in-cell (PIC) codes is described. In this solver, the EM fields are solved in $k$ space by performing an FFT in one direction, while using finite difference operators in the other direction(s). This solver eliminates the numerical Cerenkov radiation for particles moving in the preferred direction. Moreover, the numerical Cerenkov instability (NCI) induced by the relativistically drifting plasma and beam can be eliminated using this hybrid solver by applying strategies that are similar to those recently developed for pure FFT solvers. A current correction is applied for the charge conserving current deposit to correctly account for the EM calculation in hybrid Yee-FFT solver. A theoretical analysis of the dispersion properties in vacuum and in a drifting plasma for the hybrid solver is presented, and compared with PIC simulations with good agreement obtained. This hybrid solver is applied to both 2D and 3D Cartesian and quasi-3D (in which the fields and current are decomposed into azimuthal harmonics) geometries. Illustrative results for laser wakefield accelerator simulation in a Lorentz boosted frame using the hybrid solver in the 2D Cartesian geometry are presented, and compared against results from 2D UPIC-EMMA simulation which uses a pure spectral Maxwell solver, and from OSIRIS 2D lab frame simulation using the standard Yee solver. Very good agreement is obtained which demonstrates the feasibility of using the hybrid solver for high fidelity simulation of relativistically drifting plasma with no evidence of the numerical Cerenkov instability.