Finite grid instability and spectral fidelity of the electrostatic Particle-In-Cell algorithm

• Published in: Computer physics communications Vol. 207; pp. 123 - 135
• Main Authors: Huang, C.-K., Zeng, Y., Wang, Y., Meyers, M.D., Yi, S., Albright, B.J.
• Format: Journal Article
• Language: English
• Published: United States Elsevier B.V 01.10.2016; Elsevier
• Subjects: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Finite grid instability; Mathematics; MATHEMATICS AND COMPUTING; Numerical instability; Particle-In-cell; Spectral fidelity; Spectral fidelity; Numerical instability; Finite grid instability; Particle-In-cell
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2016.05.021

The origin of the Finite Grid Instability (FGI) is studied by resolving the dynamics in the 1D electrostatic Particle-In-Cell (PIC) model in the spectral domain at the single particle level and at the collective motion level. The spectral fidelity of the PIC model is contrasted with the underlying physical system or the gridless model. The systematic spectral phase and amplitude errors from the charge deposition and field interpolation are quantified for common particle shapes used in the PIC models. It is shown through such analysis and in simulations that the lack of spectral fidelity relative to the physical system due to the existence of aliased spatial modes is the major cause of the FGI in the PIC model.