## 2 FERMI Overview  
FERMI is located at the Elettra laboratory in Trieste. The FEL facility covers the VUV to soft X-ray photon energy range with two FELs, FEL-1 and FEL-2 both based on the High Gain Harmonic Generation seeded mode (HGHG) [14]. The HGHG scheme consists in preparing the electron beam phase space in a first undulator, called modulator in Figure 1, where the interaction with an external laser, the seed, induces a controlled and periodic modulation in the electron beam longitudinal energy distribution.  
Figure 1: Sketch of the High Gain Harmonic Generation (HGHG) free electron laser (FEL) configuration. Seed laser pulse and electron beam are superimposed in a first undulator indicated as modulator. The FEL interaction induces an electron energy modulation with the periodicity of the seed wavelength. The dispersive section converts this energy modulation into a density modulation containing higher order Fourier components of the original modulation. One of these components is finally amplified in the radiator.  
The beam propagates through a \"dispersive section\", a magnetic device introducing a strong correlation between the electron energy and the path length. This dispersive section converts the energy modulation into a density modulation, which is characterized by higher order harmonic components and retains the phase properties of the seed. The \"density\" modulated beam is then injected into a long FEL amplifier, similar to the one adopted in SASE FELs. The amplification process is initially enhanced by the presence of the modulation. The modulation depth is calibrated by tuning the seed intensity, in order to reach FEL saturation and efficient energy extraction at the end of the amplifier.  
The HGHG cascade scheme is implemented in FERMI FEL-1, to generate fully coherent radiation pulses in the VUV spectral range [15]. The seed signal, continuously tunable, typically in the range 230-260 nm, is obtained from a sequence of nonlinear harmonic generation and mixing conversion processes from an optical parametric amplifier. The radiation resulting from conversion in the FEL up to the 13 th harmonic is routinely delivered to user experiments [16].  
The amplitude of the energy modulation necessary to initiate the HGHG process grows with the order of the harmonic conversion. The induced energy dispersion has a detrimental effect on the high gain amplification in the final radiator, for this reason the design of FEL-1 relied on harmonic conversions up to harmonic 13. During the last years of operations, we have demonstrated the ability to operate the FEL at even higher harmonic orders with reduced performances, e.g., up to the 20 th harmonic, but substantially higher orders can be reached with a double stage HGHG cascade, where the harmonic conversion is repeated twice. The double conversion is done with the fresh bunch injection technique [17; 18] on FERMI FEL-2 [19], shown in Figure 2. The FEL is composed by a first stage, analogous to FEL-1 (see Figure 1), followed by a delay line, a magnetic chicane slowing down the electron beam with respect to the light pulse generated in the first stage. The light pulse from the first stage is shifted to a longitudinal portion of the beam unperturbed by the seed in the first stage. In this way the light from the first stage functions as a short wavelength seed for the second stage. This scheme was implemented for the first time on FERMI FEL-2 and was used to demonstrate the seeded FEL coherent emission in the soft-X rays, up to harmonic orders of 65, and more [19].