Global magnetic confinement for the 1.5D Vlasov-Maxwell system

We establish the global-in-time existence and uniqueness of classi- cal solutions to the "one and one-half" dimensional relativistic Vlasov-Maxwell systems in a bounded interval, subject to an external magnetic field which is infinitely large at the spatial boundary. We prove that the large external mag- netic field confines the particles to a compact set away from the boundary. This excludes the known singularities that typically occur due to particles that repeatedly bounce offthe boundary. In addition to the confinement, we follow the techniques introduced by Glassey and Schaeffer, who studied the Cauchy problem without boundaries.