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Physical review accelerators and beams 24(8), 080702 (2021). doi:10.1103/PhysRevAccelBeams.24.080702, Echo-enabled harmonic generation free-electron lasers (EEHG FELs)are promising candidates to produce fully coherent soft x-ray pulses by virtue of efficient high harmonic frequency up-conversion from UV lasers.The ultimate spectral limit of EEHG, however, remains unclear, because of the broadening and distortions induced in the output spectrum by residual broadband energy modulations in the electron beam. We present a mathematical description of the impact of incoherent(broadband) energy modulations on the bunching spectrum produced by the microbunching instability through both the accelerator and the EEHG line. The model is in agreementwith a systematic experimental characterization of the FERMI EEHGFEL in the photon energy range $130-210$ eV. We find that amplification of electron beam energy distortions primarily in the EEHG dispersive sections explains an observed reductionof the FEL spectral brightness that is proportional to the EEHGharmonic number. Local maxima of the FEL spectral brightness and of the spectralstability are found for a suitable balance of the dispersive sections'strength and the first seed laser pulse energy. Such characterizationprovides a benchmark for user experiments and future EEHG implementations designed to reach shorter wavelengths., Published by American Physical Society, College Park, MD

International audience; Extension of stable longitudinal coherence from vacuum ultraviolet to x rays is highly sought after in the free-electron laser (FEL) community, but it is often prevented by bandwidth broadening originated in the electron beam microbunching instability. We demonstrate that a proper tuning of the linear optics before the beam enters the undulator mitigates the microbunching-induced sideband instability. The experiment was conducted at the Fermi FEL operated in echo-enabled harmonic generation mode, where the spectral brightness at 7 nm wavelength was doubled. The FEL performance is compared to nonoptimized optics solutions and characterized in terms of peak intensity and spectral bandwidth shot-to-shot stability. The technique has straightforward implementation, because it uses quadrupole magnets routinely adopted for beam transport, and it applies to any FEL architecture, so paving the way to the production of high-intensity Fourier-transform limited x-ray pulses in existing and planned FEL facilities.

In storage rings, when the number of electrons in a bunch exceeds a threshold value, microstructures appear spontaneously in the bunch. Experimental observations of these microstructures and their evolution are indirect to obtain. In practice, most information is obtained from the terahertz coherent synchrotron radiation (THz CSR), since microstructures in the millimeter range radiate THz CSR. Here we show, thanks to a simple analytical formula associated to numerical simulations, that a frequency component in the THz CSR signal permits one to obtain information about the structure of the electron bunch longitudinal phase space during the microbunching instability. The proposed formula permits one also to link experimental information together, in particular the bunch length and the THz CSR spectrum.