  To facilitate the treatment of electromagnetic effects in applications such
as dynamically perturbed vortons, this work employs a covariantly formulated
string-source Green measure to obtain a coherent relativistic scheme for
describing the self interaction of electromagnetic currents in string models of
a very general kind, at leading order in the relevant field gradients, using a
regularised gradient operator given by $\hat\nabla_\nu=$ $\bar\nabla_\nu
+{1\over 2} K_\nu$ where $\bar\nabla_\nu$ is the usual tangential gradient
operator and $K_\nu$ is the extrinsic curvature vector.
