Variational calculation of the focusing properties of electrostatic lenses

A variational principle is derived for the electrode voltages in an electrostatic lens when the Green's function is known; the method can be used to calculate the potential for specified object and image positions. Systems of test functions are suggested, and specific calculations show that just two variational parameters suffice for accuracies to within a few percent if the beam crosses the axis of the lens once (the error is a fraction of a percent if the beam does not cross the axis inside the lens).