Superluminal phase velocity approach for suppression of Numerical Cherenkov Instability in Maxwell solver

Abstract

A modification of a standard finite-difference time-domain (FDTD) Maxwell solver is proposed based on the inclusion of the terms of the higher order in the finite differences approximation. By selecting the coefficients of this hybrid scheme the numeric dispersion of the electromagnetic waves can be fine-tuned. It is shown that a particular choice of the coefficients leads to the phase velocity of all the waves being slightly larger than speed of light. Results of the 3D Particles-In-Cells (PIC) simulations demonstrate that the proposed scheme of the Maxwell solver is efficient to mitigate the Numerical Cherenkov Instability (NCI) when simulating ultrarelativistic charged beams.