On the problem of magnetic focusing of a beam of electrons emitted with thermal velocities

The current passing through the anode opening is determined for the case of a beam of electrons focused by a longitudinal homogeneous magnetic field and simultaneously accelerated towards the anode by a longitudinal electrostatic field. A point cathode, or a strip or circular plane cathode, is located in the magnetic field. At the cathode a Maxwell-Boltzmann distribution of velocities is assumed. The criterion of sufficient focusing is determined first for a magnetic field and then for an electrostatic field as the variable.