The first mixed problem for the Vlasov–Poisson system in an infinite cylinder is considered. This problem describes the kinetics of charged particles of high-temperature plasma. It is shown that the characteristics of the Vlasov equations do not reach the boundary of the cylinder if the external magnetic field is sufficiently large. Sufficient conditions are obtained for the existence and uniqueness of classical solution of the Vlasov–Poisson system with ions and electrons density distribution functions supported at some distance from the boundary of the cylinder. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.