Free-electron laser with resonant pumping

We find the boundaries of regular and chaotic dynamics zones around the magnetoresonance for a hybrid planar free-electron laser amplifier. For the zones of regular dynamics the maximal magnetoresonant gain is calculated analytically and is shown to be in a good agreement with non-linear numerical simulations. It is also analytically demonstrated that in the vicinity of magnetoresonance the gain is independent of the spatial amplitude of undulator magnetic field. Moreover, we find that in the zone of regular dynamics above the magnetoresonance the efficiency of amplification achieves its maximal value and is less prone to the influence of space-charge effects.