Multi-Scale Paraxial Models to Approximate Vlasov-Maxwell Equations

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 n-Th order accurate; 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.