Methods and algorithm for calculating the focal parameters of a hollow conical electron beam in high-voltage glow discharge electron guns with a focusing magnetic lens

The algorithm is considered for calculating the focal distance of a hollow conical electron beam generated by high-voltage glow discharge electron guns with magnetic focusing of the beam in the drift region, as well as a method for calculating the diameter of the focal ring and its thickness for such a beam. The proposed algorithm is based on the theory of electron drift in the field of a focusing magnetic lens and is designed using the methods of discrete mathematics and the minimax analysis. The obtained simulation results made it possible to establish the influence of the magnetic lens current on the focal diameter of a hollow conical electron beam and on its focal ring thickness. It is shown that the change in the focal parameters of a hollow conical electron beam can be effectively provided through the regulation of the magnetic lens current.