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

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.

References in corpus (7)

• Implementation of a hybrid particle code with a PIC description in r-z and a gridless description in $\varphi$ into OSIRIS
• Suppressing the Numerical Cherenkov Instability in FDTD PIC Codes
• Numerical stability analysis of the Pseudo-Spectral Analytical Time-Domain PIC algorithm
• Elimination of the numerical Cerenkov instability for spectral EM-PIC codes
• Modeling of Laser wakefield acceleration in Lorentz boosted frame using EM-PIC code with spectral solver
• Enhanced Stopping of Macro-Particles in Particle-in-Cell Simulations
• Numerical Stability Improvements for the Pseudo-Spectral EM PIC Algorithm

Cited by in corpus (15)

• A spectral, quasi-cylindrical and dispersion-free Particle-In-Cell algorithm
• High quality electron bunch generation using a longitudinal density-tailored plasma-based accelerator in the three-dimensional blowout regime
• Controlling the Numerical Cerenkov Instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction
• Elimination of Numerical Cherenkov Instability in flowing-plasma Particle-In-Cell simulations by using Galilean coordinates
• Stable discrete representation of relativistically drifting plasmas
• A Systematic Approach to Numerical Dispersion in Maxwell Solvers
• Accurately simulating nine-dimensional phase space of relativistic particles in strong fields
• On numerical errors to the fields surrounding a relativistically moving particle in PIC codes
• On the generation of ultra-bright and low energy spread electron beams in laser wakefield acceleration in a uniform plasma
• Lorentz boosted frame simulation of Laser wakefield acceleration in quasi-3D geometry
• Laser-plasma interactions with a Fourier-Bessel Particle-in-Cell method
• Overcoming timestep limitations in boosted-frame Particle-In-Cell simulations of plasma-based acceleration
• A new field solver for modeling of relativistic particle-laser interactions using the particle-in-cell algorithm
• An \mathcal{O}(N) Maxwell solver with improved numerical dispersion properties
• Modeling of Advanced Accelerator Concepts