  A new three dimensional model of the FEL is presented. A system of scaled,
coupled Maxwell Lorentz equations are derived in the paraxial limit. A minimal
number of limiting assumptions are made and the equations are not averaged in
the longitudinal direction of common radiation/ electron beam propagation,
allowing the effects of coherent spontaneous emission and non-localised
electron propagation to be modelled. The equations are solved numerically using
a parallel Fourier split-step method.
