Abstract
The system of the nonlinear non-stationary equations describing spatial-temporal dynamics of the amplitudes of an ondulator radiation and a space-charge wave of a relativistic electron beam in the resonator is obtained. A free electron laser resonator with longitudinal electrostatic wiggler is considered. In the linear approximation, the threshold conditions of lasing for Raman and Compton regimes under excitation of forward and backward electromagnetic wave are achieved. In the various physical situations, the variation of the minimum length of the resonator with the amplitude of wiggler, density of electron beam, and with the reflection coefficients of resonator's mirrors is investigated.
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