Geometric Properties of a Beam Formed from a Radionuclide Positron Source by Stochastic Electron Optics

In the earlier experiments with electron beams, partial reflection of the beams falling obliquely on a foil was observed. This effect was studied theoretically using stochastic electron optics methods to show, in particular, that the reflection coefficient and the average angle of the reflected beam do not depend on the beam parameters and the material of the reflecting medium. Here, the dynamics of a beam falling obliquely from a vacuum onto a flat interface of a medium and a vacuum is studied in more detail. The flow line model is used to obtain the beam distribution function at the specified boundary. This approach makes it possible to study the dynamics of the reflected beam in detail. At the same time, it is proven that the distribution function for a semi-infinite medium coincides with that for an infinite medium, which justifies the previously developed model of flow lines for multiple Coulomb scattering. A differential equation describing the surface of rotation for the formation of a beam from a point isotropic source is derived, and its solution is presented. The phase dynamics of the charge flow formed by the reflecting surface is investigated.