Non-linear macroscopic equations for pulse evolution in a high-gain Compton FEL

The non-linear stage of the interaction between electron and light pulses is considered of a high-gain FEL. It is shown that the non-linear oscillations of the radiation intensity can be described analogously to the bouncing motion of a particle in a time-dependent, anharmonic potential. In case the electrons all have the same energy and bunching factor, the potential is constant in the steady state region of the light pulse. In this region, analytical solutions are in good agreement with the full solution. Using the same approximation also in the trailing edge of the light pulse, it is shown that the model provides a surprisingly good description of the physics involved.