Unaveraged three-dimensional modelling of the FEL

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.