Characterization of soft X-ray echo-enabled harmonic generation free-electron laser pulses in the presence of incoherent energy modulations

TL;DR

This paper models how incoherent energy modulations affect the spectral quality of EEHG free-electron laser pulses and validates the model with experimental data, providing insights for optimizing soft X-ray FEL performance.

Contribution

It offers a mathematical model describing the impact of broadband energy modulations on EEHG FEL spectra, supported by experimental validation.

Findings

Energy distortions reduce FEL spectral brightness proportional to harmonic number.

Optimal dispersive section settings enhance spectral stability and brightness.

Model agrees with experimental data from FERMI EEHG FEL in 130-210 eV range.

Abstract

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 agreement with a systematic experimental characterization of the FERMI EEHG FEL 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 reduction of the FEL spectral brightness that is proportional to the EEHG harmonic number. Local maxima of the FEL spectral brightness and of the spectral stability are found for a suitable balance of the dispersive sections' strength and the first seed laser pulse energy. Such characterization provides a benchmark for user experiments and future EEHG implementations designed to reach shorter wavelengths.