Optimization of parameters of a collector electron flow based on the geometrized theory of dense beams

On the basis of the geometrized theory of higher-order approximations of electron beams, it is shown that, in requiring the discovery of the current density from the uniform distribution to be minimum and the collecting surface to be equipotential and cylindrical in the case of the normal incidence of electrons, one has to consider three different functionals. The collector's geometry and the parameters of the collector electron flow can be optimized using the analysis of a combination of these functionals. The simultaneous fulfillment of these three requirements is impossible in principle.