Abstract
A new version of the geometrized theory of electron beams is presented in which the originally unknown coordinate system is connected with trajectories (or current tubes) and equipotential surfaces and, in the case of emission in the ρ-mode, has a singular metric. Equations of 3D and 2D nonmonoenergetic flows in the presence of a magnetic field and in the electrostatic version, which admits full geometrization of the problem, are derived. Solution for the cases of emission in the ρ- and T-modes in the vicinity of an arbitrary smooth emitting surface are constructed.
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