  A model of a Free Electron Laser operating with an elliptically polarised
undulator is presented. The equations describing the FEL interaction, including
resonant harmonic radiation fields, are averaged over an undulator period and
generate a generalised Bessel function scaling factor, similar to that of
planar undulator FEL theory. Comparison between simulations of the averaged
model with those of an unaveraged model show very good agreement in the linear
regime. Two unexpected results were found. Firstly, an increased coupling to
harmonics for elliptical rather than planar polarisarised undulators. Secondly,
and thought to be unrelated to the undulator polarisation, a signficantly
different evolution between the averaged and unaveraged simulations of the
harmonic radiation evolution approaching FEL saturation.
