Abstract
We present a multi-stream model obtained from the Vlasov-Maxwell system of equations based on the invariance of the canonical momentum in the perpendicular direction in a 1D-2V phase space. The model is conceived for the study of the Weibel and current filamentation instability in the relativistic regime, but turns out to be of more general importance. It can be used numerically for the study of the non-linear, kinetic dynamics with a drastic reduction of the computational cost with respect to the integration of the corresponding Vlasov-Maxwell system.