Free electron lasers operating with variably polarization undulators

We discuss the properties of Free Electron Lasers (FEL) operating with variably polarizing undulators. We study the characteristics of the electron motion in this type of undulators and analyze the spectral properties of the emitted radiation. We also derive general expressions for the small signal gain coefficient and for the saturation intensity. Finally, we explore the characteristics of FEL operation in the hypothesis of Optical-Klystron configuration with particular reference to devices exploiting undulators with opposite polarizations. Regarding this last point, we show that interference may produce undesidered effects which may reduce rather than increase the small signal gain.