Classical theory of saturation effects in a free-electron laser

Classical equations of electron motion in a free-electron laser are studied in the case when the electromagnetic field does not meet the conditions of validity of the small-signal approximation. Asymptotic expressions in a strong field are derived for the energy emitted by an electron and for the gain. A comparison is made of the results of classical and quantum calculations. It is shown that averaging of measured physical values over the phase of the classical electron motion makes it possible to achieve identical results within the limits of both classical and quantum-mechanical approaches.