Diagnosing numerical Cherenkov instabilities in relativistic plasma simulations based on general meshes

•Study of spurious Cherenkov radiation in particle-in-cell (PIC) simulations.•A generalized grid-dispersion analysis accounts for different mesh element shapes.•Key behavior differences across mesh types and mesh layouts are examined.•Results help in assessing PIC simulations of kinetic plasmas. Numerical Cherenkov radiation (NCR) or instability is a detrimental effect frequently found in electromagnetic particle-in-cell (EM-PIC) simulations involving relativistic plasma beams. NCR is caused by spurious coupling between electromagnetic-field modes and multiple beam resonances. This coupling may result from the slow down of poorly-resolved waves due to numerical (grid) dispersion and from aliasing mechanisms. NCR has been studied in the past for finite-difference-based EM-PIC algorithms on regular (structured) meshes with rectangular elements. In this work, we extend the analysis of NCR to finite-element-based EM-PIC algorithms implemented on unstructured meshes. The influence of different mesh element shapes and mesh layouts on NCR is studied. Analytic predictions are compared against results from finite-element-based EM-PIC simulations of relativistic plasma beams on various mesh types.