A comprehensive theory has been developed to describe all manifestations of Coulomb interactions between charged particles in low- and medium-density nonrelativistic beams, e.g., as found in electron beam pattern generators and scanning electron microscopes. A survey is given of the analytical prescriptions for the calculation of the Boersch effect, trajectory displacement effect, and space-charge effect occurring in the drift space of a column. The theory is applied to the IBM EL3 and the Perkin–Elmer aeble 150 shaped spot lithography machines. The results are in close agreement with Monte Carlo simulations as well as the available experimental data.