Some Properties of Characteristics for the Vlasov-Poisson System with External Magnetic Field

We consider the Vlasov-Poisson system of equations with external magnetic field in a half-space and in an infinite cylinder with the Dirichlet boundary condition for electric potential. The Vlasov-Poisson system describes evolution of electric potential and distribution functions for densities of charged particles in high-temperature rarefied plasma. The cylindrical shape of domain corresponds to thermonuclear reactor that is called "mirror trap". We obtain sufficient condition for external magnetic field under which characteristics of the Vlasov-Poisson system do not reach a boundary. There-fore we can study classical solutions with supports of distribution functions strictly inside domain. Such solutions are modelling plasma confinement. We obtain explicite relations providing existence and uniqueness of such solutions in Hölder spaces.relations providing existence and uniqueness of such solutions in Hölder spaces.