Modeling of relativistic plasmas with the Particle-In-Cell method

Standard methods employed in relativistic electromagnetic Particle-In-Cell codes are reviewed, as well as novel techniques that were introduced recently. Advances in the analysis and mitigation of the numerical Cherenkov instability are also presented with comparison between analytical theory and numerical experiments. The algorithmic and numerical analytic advances are expanding the range of applicability of the method in the ultra-relativistic regime in particular, where the numerical Cherenkov instability is the strongest without corrective measures.