Efficacy of a magnetic shield against a Vlasov-Poisson plasma

The aim of the paper is to test on a simple model how impenetrable may be a magnetic shield. We study the time evolution of a single species positive plasma, confined in the half-space $x_1>0$. The confinement is the result of a balance between a magnetic field and an external field, both singular at $x_1=0$; the magnetic field forbids the entrance of plasma particles in the region $x_1\le 0$, whereas the external field attracts the plasma particles towards $x_1=0$. The plasma has finite total charge and velocities distributed with a Maxwell-Boltzmann law.