FEL Generation of Extreme Ultraviolet Coherent Radiation: Theoretical Aspects

The main features of the interaction between free-electrons and electromagnetic (e.m.) waves have been deeply investigated in these last years, in connection with FEL dynamics. The first approach to the FEL topics was done in a quantum mechanical framework. In spite of this fact, the most interesting results were obtained by using completely classical approaches. This kind of treatment, which is well justified for the up to now developed FEL sources (infrared and visible radiation), can become no more adequate in the extreme UV spectral region. In this paper the validity limits of the classical approach are investigated. It is found that low electron energy operation with small wavelength pump wave may require the quantization of the electron motion, while the high energy and long pass undulator devices can be treated satisfactorily with classical mechanics. Furthermore, the coherence properties of the emitted radiation are studied. For these topics too, the classical or quantum character of the electron motion plays a crucial role. In particular, it is possible to show that, when a "semi-classical" treatment can be done (i.e., quantized radiation and classical electron) the e.m. field coherent states preserved by the FEL interaction are the same as the ones of standard lasers, i.e. the harmonic oscillator coherent states (Glauber states). Finally, the very short wavelength FEL operation is investigated by accounting for the limitation coming from electron beam energy spread and emittance. It comes out that recirculated FEL devices (i.e., Storage Ring FELs) may have, under this point of view, performances better than the single pass ones.