On the analytical solution of the electrons motion equation in a cylindrical mirror when taking into account electrons having azimuthal velocity component

In this work, the solid angle was calculated by starting within which the electrons fall on the detector of a cylindrical mirror. The study of the solid angle, starting within which the electrons fall on the detector, showed that along the range of change of energy and along the range of change of the radius of emission, the maximum of the solid angle is observed. The radius of the largest deviation of electrons from the inner cylinder is obtained as a series, which provides good accuracy for angles up to 20°. The solution of the equation of motion of electrons in a cylindrical mirror, obtained as a Taylor series, showed good agreement with the results of direct integration of the modified equation of motion.