Multi-Scale Paraxial Models to Approximate Vlasov–Maxwell Equations

Abstract

Abstract 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; 𝑛 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.