The simple accurate calculation of cylinder lens potentials and focal properties

By use of a variational principle it is shown that the potential inside two coaxial cylinders separated by a gap g may be expressed in a form which can be evaluated very easily. For g=0.1 diameters the potential on the axis of cylinders having potentials 1 and 0 is everywhere within 0.0001 of the true value and the focal properties of the lens so formed agree with the most accurate calculations to within 0.1%. For large values of g the accuracy is reduced, but is still enough for practical use, because of problems in the practical realization of such lenses.