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We discuss the design elements of a compact free electron laser device, operating, in an oscillator–amplifier configuration, up to the soft X-ray region. We show that, the source can provide radiation from extreme UV to soft X-ray region, with significantly large output peak and average laser power with undulator lengths not exceeding 7 m.

We study the modifications induced on the longitudinal dynamical behaviour of an e-beam circulating in a Storage-Ring (S.R.) and undergoing a FEL interaction. We discuss the low gain amplifier case and, using the Fokker-Planck equation, evaluate the effect of the FEL interaction on the longitudinal damping time, which is shown to be a function of the detuning parameter and of the intensity itself. We develop a self-consistent model of the S.R. FEL dynamics capable of including saturation, induced energy spread and damping time modifications. The model is shown to be particularly useful to investigate the system evolution and the interplay between the various features causing the saturation of the device.

The kinematic and dynamic properties of a waveguide FEL are described in the small signal small gain approximation in both the homogeneous and inhomogeneous regimes.

We analyze the small signal multimode aspects of the single pass free electron laser and study the operating conditions and the relevant laser parameters.