## 3 Echo Enabled Harmonic Generation Seeding  
One of the key features of the FLASH2020+ project is to introduce external seeding schemes in the FLASH1 beamline in parallel with the SASE operation at FLASH2. While the basic principle is being proved by experiments using the presently installed Xseed setup [56], full capabilities of seeding supporting user operations in FLASH require a complete redesign of FLASH1. New undulators, which take advantage of the increased beam energy (see Section 2.2) are being designed to keep the present coverage over the spectral range down to 4 nm even with external seeding. Moreover, the new scheme will also provide flexibility to control the FEL polarization using APPLE-III undulators for the final radiator of the new beamline. Recent results have shown that Echo Enabled Harmonic Generation (EEHG) [80] can be used efficiently to produce highly coherent soft X-ray FEL pulses [81]. The EEHG scheme planned at FLASH uses two UV laser beams, seed laser 1 and seed laser 2 (Figure 3) [41]. Figure 2: Microbunching gain after the first and second bunch compression stage for (**a**) the FLASH2020+ linac, (**b**) FERMI in usual configuration featuring only a single bunch compression stage, (**c**) FERMI in double compression scheme. Simulation results were obtained from a dedicated non-linear Vlasov solver [71], while the analytical results are based on a linear perturbation theory. To avoid a change of electron beam energy to modify the FEL radiation wavelength, as is the case for the present fixed-gap undulator system, the new APPLE-III radiators will allow a remote adjustment of the K-parameter in each radiator segment. However, given the limited tuning capabilities of the short period APPLE-III radiators, a minimum of three beam energies are required to cover the whole anticipated spectral range (Table 3). External seeding is completed with two modulators (Table 4) and three chicanes (Table 5) making the electron beam's interaction with external lasers possible and allowing the necessary manipulation of the electron beam phase space. Two planar long period undulators will be used for resonant interaction of the beam with two UV seed lasers. Details on the laser systems and the laser beam injection chicanes are reported in the next section. Compared to the existing seeding facilities [6, 82], FLASH will, for the first time, implement seeding at a MHz repetition rates. To succeed, some of the seed laser parameters typically used elsewhere must be significantly modified (Table 3). As described in the next section, the two seed lasers will have a central wavelength of around 300 nm and 343 nm. Therefore, it is necessary to operate EEHG at the 75 th harmonic for reaching the shortest wavelength (4 nm). Theoretical predictions show that a high degree of bunching \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **Modulator** & **Radiator** & **Units** \\ \hline Period & 80 & 33 & mm \\ Length & 2.4 & 2.4 & m \\ Type & Planar & APPLE III & \\ Number & 2 & 11 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Seeding undulator parameters. Figure 3: Layout of the seeding beamline (side view). Seed laser 1 (Seed1) is injected using the in coupling chicane (R56_0), while seed laser 2 (Seed2) uses the overshearing chicane (R56_1). Bunching chicane (R56_2) is used to convert the energy modulation produced by the two lasers in the two modulators (Mod1,2) into bunching before the beam enters the final radiator (Rad1,...). \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Parameter** & **Short** & **Intermediate** & **Long** & **Units** \\  & **Wavelengths** & **Wavelengths** & **Wavelengths** & **Units** \\ \hline FEL wavelength & 4–15 & 10–40 & 30–60 & nm \\ e-beam energy & 1.35 & 0.95 & 0.75 & GeV \\ Peak current & 500 & 500 & 500 & A \\ Slice energy spread & 150 & 150 & 150 & keV \\ Energy chirp & 15 & 15 & 15 & MeV/ps \\ Seeding scheme & EEHG & EEHG/HGHG & HGHG & \\ \hline \hline \end{tabular}
\end{table}