FEL mode propagation at saturation

We consider the propagation of an electromagnetic wave generated by an FEL after saturation has occurred. Two regimes are considered: one in which the incident wave amplitude is much greater than the wave amplitude generated by the beam, and the other in which the opposite is true. In neither case is there refractive optical guiding. We allow for velocity detuning and wiggler tapering, and calculate the taper design for maintaining synchronism.