# Advanced Scheme to Generate MHz, Fully Coherent FEL Pulses at nm Wavelength
## 6 Discussion  
In this paper, we described different seeding schemes that can benefit by employing an oscillator setup to increase the repetition rate of a seeded FEL. We presented an overview of simulations and requirements for its implementation. We developed a simple model to estimate the amplification and modulation process in the modulator. This gave an insight into the design of the resonator in terms of modulator length, resonator requirements, and feasibility of the implementation of this scheme. Then, we focused on simulation results of an HGHG scheme. We showed that there is a number of methods that could be used to dynamically control the power gain in the resonator when the process starts from shot-noise and we compared the performance of a single pass HGHG, a multi-pass HGHG starting with a low repetition rate seed laser and of SASE, which is to be considered as our background.  
Where so far the wavelength range mentioned here could only be reached with an EEHG scheme, the use of a resonator now would make it possible to reach the same wavelength with an HGHG scheme. Alternatively, starting with a shorter wavelength in  
Figure 11: Spectra of final FEL pulse at the same position at the amplifier and with the same electron beam parameters shown at Table 1. The spectral intensity is normalized to the peak intensity calculated at the standard single-pass HGHG simulation. (**a**) SASE. Please notice the extended horizontal axis. The average SASE spectrum over 50 shots is shown with the black line. (**b**) Standard HGHG in a single-pass. (**c**) Oscillator-FEL starting with an external seed laser pulse. (**d**) Oscillator-FEL starting from shot-noise.  
an EEHG scheme, the use of the resonator could push the minimum wavelength beyond the water window and transition metals, making seeding in this important wavelength range possible. These options will be studied in future studies.  
In addition, there are still a number of considerations that need to be addressed as we are moving towards more detailed studies for the realization of this scheme. Even though first stability studies were presented in [22], it is still crucial to study the stability of this scheme over several passes with a non-ideal electron beam, including imperfections and energy chirp effects. In addition, there are other important questions related to its implementation, such as how the repetition rate can be adjusted when experiments need a lower repetition rate, the space constraints to insert mirrors when the longitudinal dispersion required for seeding at short wavelengths is small, the requirements in terms of diagnostics for the recirculating radiation field, and realizing wavelength tunability. These are expected to be addressed in future work.  
Conceptualization, B.F.; data curation, G.P. and F.P.; validation, G.P., B.F. and G.G.; formal analysis, G.P.; writing--Original draft preparation, G.P.; writing--Review and editing, G.P., S.A., B.F., G.G., T.L., F.P., L.S. and J.Z.; project administration, G.P. and G.G. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Impuls- und Vernetzungsfond der Helmholtz-Gemeinschaft e.V. within the CAS-Helmholtz International Laboratory on Free-Electron Laser Science and Technology (CHILFEL), grant number InterLabs-0002.  
Not applicable.  
The authors would like to thank [PERSON] for consultation regarding mirrors in the EUV, [PERSON] for information on kickers, [PERSON] and [PERSON] for useful discussions, and the Maxwell computational resources operated at Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany. Finally the authors thank [PERSON], and [PERSON] for a careful proofreading of the manuscript.  
The authors declare no conflict of interest.