The magnetic vector potential in a gapped tunnel

The problem of computing a matrix of magnetic vector potentials in a gapped tunnel is studied. First, a method is given for deriving the parameters of a set of ideal current loops that will serve as sources for the field of a PPM-focused TWT, then the magnetic vector potentials are derived from the loop parameters. The axial and radial fields at any point are then obtained by nine-point interpolation and differencing of the potential matrix. The method is free from any paraxial approximations.