Phase Portrait of a Beam of Charged Particles Reflected from a Material Medium

We report derivation of a distribution function of charges scattered due to an oblique incidence of a needle-shaped beam of charged particles from a vacuum onto a material medium, with the scattered particles landing up on the plane separating the medium and vacuum. To this end, the distribution function is used for multiple Coulomb scattering of a beam propagating in a homogeneous and unbounded medium. The phase plane shows the distributions of scattered charges corresponding to certain fixed values of the distribution function, i.e., phase portraits of a beam.