Electron beam in the presence of a periodic magnetic field with allowance for the thermal velocities of electrons

Equations are derived to study the effect of the initial transverse thermal velocities of electrons on the configuration of an intense electron beam in an electron-optical system with a significant divergence for the case of the beam focusing by a periodic magnetic field. It is demonstrated that the minimization of the effect of thermal velocities of electrons in the electron-optical system with the given level of the periodic focusing field and the cathode radius and temperature and the limiting compression of the beam in the presence of such a field is reached with the shaping systems in which an optimal magnetic flux passes through the cathode and the flux depends on the parameters of the thermal beam and the focusing field.