On the Existence of Global Solutions for the Vlasov-Poisson System in a Half-space and Plasma Confinement

We consider the Vlasov-Poisson system with external magnetic field in a half-space with the Neumann boundary condition for the electric potential and specular reflection on a boundary. For arbitrary compactly supported initial density distribution functions, we obtain sufficient conditions for external magnetic field, which provide global existence of density distribution functions with compact supports lying at some distance from a boundary.