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 x1 > 0. The confinement is the result of a balance between a magnetic field and an external field, both singular at x1 = 0; the magnetic field forbids the entrance of plasma particles in the region x1 ≤ 0, whereas the external field attracts the plasma particles towards x1 = 0. The plasma has finite total charge and velocities distributed with a Maxwell—Boltzmann law.