## 3 New Operation Modes  
The variable gap undulators not only allow fast wavelength scans but also enable novel operation modes, such as advanced tapering schemes, frequency doubling, two-color operation, and harmonic lasing self-seeding. With optimized undulator tapering, photon pulse energies up to 1 mJ have been demonstrated at FLASH2 [8]. A particularly interesting option in this respect is reverse tapering [9; 10]. In combination with a harmonic afterburner for circular polarization currently under design this should in the future allow experiments with variable polarization at photon energies beyond the water window at FLASH2. Tuning the FLASH2 undulators individually it is also possible to push the photon energy range of FLASH beyond the current limit of 300 eV in the fundamental. Setting the first part of the undulator section to twice the final wavelength in a frequency doubling scheme it has been shown that the photon energy range of FLASH2 can be extended up to 400 eV with stable pulse energies of a few uJ, significantly higher than what has been achieved when the full undulator section is set to the final wavelength at the same electron energy [11]. Another interesting option is harmonic lasing self-seeding (HlSS) which had been proposed a while ago [12] as a method to reach higher photon energies with increased brightness. With FLASH2, HlSS was recently demonstrated for the first time experimentally and the theoretical predictions were confirmed [13]. In the following some results for the different schemes will be presented. Harmonic lasing self-seeding (HlSS), while proposed some time ago, could never be tested at FLASH1 with its fixed gap undulators. HlSS requires the setting of the first part of the undulator section to a sub-harmonic (\(h\lambda\)) of the final wavelength which is schematically shown in Figure 6. As can be seen in Figure 7, saturation is reached earlier with HlSS than with conventional SASE. This is clear from the higher power and the reduction in fluctuations when saturation is reached. More importantly, the bandwidth is also reduced and therefore the brightness is higher, as shown in Figure 8. Due to the limitations of FLASH2, which was originally not built with this concept in mind, one can only go to the second or third harmonic of the wavelength selected for the first part of the undulator,  
Figure 5: Photon spotsize for 50 (**left**), 85 (**middle**) and 150 nm (**right**) wavelength, 15 m downstream of the undulator with automatic optics adjustment in the undulator switched on. Without adjustment, the undulators cannot be closed to produce wavelengths longer than 85 nm because of beam loss. but in principle, higher harmonics could be considered when an FEL line is specifically designed for efficient use of the HLSS scheme. Figure 6: Conceptual scheme of a harmonic lasing self-seeded (HLSS) FEL. Figure 7: Growth of pulse energy (**a**) and fluctuations (**b**) along the undulator for SASE (black) and HLSS (blue). In the HLSS experiment the first four undulators were set to 33 nm and the next six undulators to 11 nm, while in the SASE case all ten undulators modules were set to 11 nm. The wavelength limits can be pushed at FLASH2 by tuning the undulator sections individually as shown in the frequency doubler scheme in Figure 9. Given the maximum electron beam energy of FLASH of 1.25 GeV, radiation in the water window at 4 nm can only be reached with the present FLASH2 undulator design and normal SASE operation with all undulators set to the same wavelength using the complete undulator length. Going to shorter wavelengths, the SASE intensity drops fast, because saturation is no longer reached. In addition, the SASE fluctuations increase for the same reason. Compared to this, the radiation intensity is clearly higher than it would be without a frequency doubler scheme, as can be seen in Figure 10. In the experiment, first the fundamental at frequency \(\omega\) is tuned for maximum SASE gain in the uniform undulator.