The results of the geometrized theory of dense electron beams are analyzed. This theory is a new branch of modern corpuscular optics that considers the synthesis of nonparaxial relativistic flows, construction of the methods of approximate solution and numerical integration of the geometrized beam equations, and description of three-dimensional flows. Within the framework of the hydrodynamic approach, the laminar flows in the arbitrarily oriented inhomogeneous external magnetic field are considered taking into account the intrinsic magnetic field, as well as mono-energy beams that start from the cathode.
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