Approximation technique for solving the Vlasov–Poisson problem

In this paper, we describe the beam distribution in particle accelerators in the framework of a Vlasov–Poisson scheme. A new approach to the investigation and numerical simulation is based on the property of an universality of Maxwell equations, and Ł -moment problem. In this scheme, it is possible to reduce a problem of an optimal stabilization of the given motion to the Ł -moment problem using its regular approximation technique and well developed computational procedures.