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Even today, solving numerically the time-dependent Vlasov–Maxwell equations is a challenging issue, and developing simpler but accurate approximate models is still worthwhile. Here, we propose a new family of paraxial asymptotic models that approximates the Vlasov–Maxwell system of equations. We introduce parameters in our models that allow us to handle relativistic cases, much slower beams or even non-relativistic cases. These models are derived by introducing a small parameter and provide static or quasi-static approximate equations that are 푛-th order accurate; 푛 may be chosen as required. Practically, one can select a model by determining the regime one is interested in and choosing the degree of accuracy needed. [ABSTRACT FROM AUTHOR]

We introduce a new family of paraxial asymptotic models that approximate the Vlasov-Maxwell equations in non-relativistic cases. This formulation is nth order accurate in a parameter n, which denotes the ratio between the characteristic velocity of the beam and the speed of light. This family of models is interesting, first because it is simpler than the complete Vlasov-Maxwell equation and then because it allows us to choose the model complexity according to the expected accuracy. [ABSTRACT FROM AUTHOR]