Suppressing the numerical Cherenkov radiation in the Yee numerical scheme

The next generation of laser facilities will routinely produce relativistic particle beams from the interaction of intense laser pulses with solids and/or gases. Their modeling with Particle-In-Cell (PIC) codes needs dispersion-free Maxwell solvers in order to properly describe the interaction of electromagnetic waves with relativistic particles. A particular attention is devoted to the suppression of the numerical Cherenkov instability, responsible for the noise generation. It occurs when the electromagnetic wave is artificially slowed down because of the finite mesh size, thus allowing for the high energy particles to propagate with super-luminous velocities. In the present paper, we show how a slight increase of the light velocity in the Maxwell's equations enables to suppress this instability while keeping a good overall precision of calculations.