A model of the electron-optical system of a finite-width ribbon beam in the case of approximation of the initial rectangular contour by an ellipse

A model of the electron-optical system with straight axis and a finite-width ribbon beam is constructed on the basis of exact solution of partial differential equations describing a narrow relativistic beam in axisymmetric external magnetic field in the case when the initial rectangular contour is approximated by an ellipse. Rotating and nonrotating beams and curved or planar cathode in the case of emission in the T mode are considered.