Geometrized theory of plane electron beams and model of an electron-optical system of planar gyrotron

Abstract

Two approximations of the geometrized theory are constructed, which make it possible to consider nonparaxial plane relativistic beams emitted in the T-mode with an improved description of the nearcathode region with allowance for the third derivatives of the electric field on the emitting surface and the second derivative of its curvature. In the region of influence of the singularity, the cathode shape and the field on the cathode are related to the configuration of the basic current tube and the variation of the potential on it. The results are adapted to the case of a relativistic planar gyrotron.