## 3 Setup and Results
After a first chicane delay optimization, which gave about a factor four increase in FEL output energy, we set the undulator segments into an alternating pattern configuration, taking care of obtaining a similar output from each separate color and keeping the output pulse energy level around a few tens of microjoules, to ensure that we were still in the linear regime. Later on, the configuration was tweaked a few times to optimize the output at \(\omega_{FM}\) and to minimize the background colors at \(\omega_{1,2}\). Figure 1 actually refers to an intermediate configuration. At this point, calibrating the XGM for the difference frequency gives an unphysical background value from the colors at \(\omega_{1}\) and \(\omega_{2}\), but further closing a few segments (up to six) at the end of the undulator to the frequency difference \(\omega_{2}-\omega_{1}\) (while keeping at least two segments detuned after segment 16 to create longitudinal dispersion), yields a variation in the XGM signal that corresponds directly to the pulse energy of the mixed frequency. Once the mixed frequency signal is found, one can follow up optimizing the configuration used and, subsequently, characterizing the output signal. In Table 1, we report up to 4.5 mJ with six radiator segments tuned at 600 eV. The segments in the radiator were tapered to an empirically found optimum valid for the six radiators. The XGM value of 4 mJ with one radiator segment closed was below the measurement uncertainty. Visually, it reared the background contribution of the two frequencies \(\omega_{1,2}\) and since the XGM was set for \(\omega_{FM}\) does not have physical meaning. The backgrounds from each of the two colors \(\omega_{1,2}\) were measured in the optimized configuration by detuning all other segments, and were found in the noise level (a few microjoules), which we ascertained separately by imparting a transverse kick to the electron trajectory prior to the entrance to SASE3. During the optimization, we were able to reduce the contribution of the two colors of about a factor ten (from the few tens of microjoules reported above), while providing an optimal bunching level at \(\omega_{FM}\). In this respect, tuning the longitudinal dispersion by adjusting the \(K\) value of the segments out of resonance before the final radiator easily led to important changes during the tuning process (without performing a systematic study, we found a factor two improvement with four radiator segments). Note that the background level decreased substantially in time as we performed the various experiments. During the very first experiment, Exp. 1 (see Table 1), we imaged [11] the transverse FEL radiation pulse distribution with the help of a scintillator with the radiator segments detuned (left plot in Figure 2) or at resonance with the mixed frequency (right plot in Figure 2). The appearance of the freqeuncy mixed signal, with a slight pointing difference with respect to the background from the two initial colors at 1200 eV and 700 eV is evident. The estimated angular divergence at 500 eV is in the order of 20 \(\upmu\)rad. An important feature of the frequency mixed mode is that, despite the more involved setting procedure, it is easily tuneable in output photon energy. We showed this during the fourth experiment, by scanning the final photon energy from 504 eV to 604 eV in steps of 20 eV. This was done by adjusting the K parameter of the final radiator (and hence \(\omega_{FM}\)) and that of the color with highest photon energy, \(\omega_{2}\). The scan was performed with four radiator segments tuned at resonance and without adjusting any other parameter. It took about four minutes to perform this scan manually and it could be easily automatized. Results are shown in Figure 3, which shows an average output pulse energy stability within about 200 \(\upmu\)J. Another important characteristic to be studied is the amplification bandwidth around the nominal output frequency \(\omega_{FM}\).