The RF vector potential in a gapped tunnel

The expressions given by Kosmahl and Branch for the RF fields in a gapped tunnel are combined and integrated to give the RF vector potential. The problem of evaluating the resulting expressions at the nodes of a suitable mesh is considered in detail. Different methods are used in different regions, and Shanks´s transformation is introduced to deal with the difficult gap-edge point. Buneman´s fast routine INTRA is used to evaluate the radial and axial fields at an arbitrary point, by nine-point interpolation and differencing of the potential matrix. The method is free from any paraxial approximations.