Abstract: The first mixed problem for the Vlasov–Poisson system in an infinite cylinder is considered. This problem describes the kinetics of charged particles in a high-temperature two-component plasma under an external magnetic field. For an arbitrary electric field potential and a sufficiently strong external magnetic field, it is shown that the characteristics of the Vlasov equations do not reach the boundary of the cylinder. It is proved that the Vlasov–Poisson system with ion and electron distribution density functions supported at some distance from the cylinder boundary has a unique classical solution. © 2019, Pleiades Publishing, Ltd.