On a Magnetically Confined Plasma with Infinite Charge

We consider a one-species plasma moving in an infinite cylinder, in which it is confined by means of a magnetic field diverging on the walls of the cylinder. It is assumed that initially the particles have bounded velocities and are distributed according to a density which is bounded, without any decreasing at infinity. The mutual interaction is of Yukawa type, i.e., Coulomb at short distance and exponentially decreasing at infinity. We prove the global in time existence and uniqueness of the time evolution of the plasma and its confinement.