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The origin of the Finite Grid Instability (FGI) is studied by resolving thedynamics in the 1D electrostatic Particle-In-Cell (PIC) model in spectraldomain at the single particle level and at the collective motion level. Thespectral fidelity of the PIC model is contrasted with the underlying physicalsystem or the gridless model. The systematic spectral phase and amplitudeerrors from the charge deposition and field interpolation are quantified forcommon particle shapes used in the PIC models. It is shown through suchanalysis and in simulations that the lack of spectral fidelity relative to thephysical system due to the existence of aliased spatial modes is the majorcause of the FGI in the PIC model.

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