Numerical investigation of Maxwell–Vlasov equations – Part I: Basic physics and algorithms

We present a numerical scheme to solve the fully 3D Maxwell–Vlasov equations. The aim is to investigate the interaction of a laser pulse with a plasma and the acceleration of electrons and ions. We choose the approach based on numerical particles to approximate the distribution function interpreted, according to the Klimontovich formalism, as a probability distribution function. The key points are a high order implicit scheme to approximate the space differential operators and a time evolution scheme of adequate accuracy.