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

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.