Unique solvability of the first mixed problem for the Vlasov–Poisson system in an infinite cylinder

We consider the first mixed problem for the Vlasov–Poisson system in an infinite cylinder. This problem describes the kinetics of charged particles of high-temperature plasma. We show 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 existence and uniqueness of the classical solution of the Vlasov–Poisson system with ions and electrons density distribution functions supported at some distance from the boundary of the cylinder.