On a Vlasov-Poisson plasma confined in a torus by a magnetic mirror

We study the time evolution of a Vlasov-Poisson plasma moving in a torus, in which it is confined by an unbounded external magnetic field. This field depends on the distance from the border of the torus, is tangent to the border and singular on it. We prove the existence and uniqueness of the solution, and also its confinement inside the torus for all times, i.e. the external field behaves like a magnetic mirror.