Numerical Cherenkov Radiation Effects from Grid Dispersion in Finite Element Particle-in-Cell Simulations of Relativistic Electron Beams

Particle-in-cell algorithms (PIC) are widely used for plasma modeling. We provide a brief report on the performance of finite-element-based PIC algorithms on simplicial (i.e., based on triangular or tetrahedral cells) grids and compare it to the rectangular grid case. We pay particular attention to the issue of spurious numerical Cherenkov radiation affecting relativistic electron beams, which is produced by grid dispersion. We analyze finite-element grid dispersion on both simplicial and rectangular grids with respect to frequency and propagation directions to assess the conditions for the onset of spurious Cherenkov radiation. It is observed that simplicial grids produce less spurious Cherenkov radiation than rectangular grids with equivalent cell sizes.