A new paraxial asymptotic model for the relativistic Vlasov–Maxwell equations

Abstract

We introduce a new paraxial asymptotic model to approximate the Vlasov–Maxwell equations. This formulation is fourth order accurate in a parameter η which denotes the ratio between the transverse characteristic velocity of the beam and the speed of light. The model is interesting because it is simpler than the complete Vlasov–Maxwell equations, and is an accurate approximation of them. This model should give an accurate, fast and easy to implement numerical method of solution.