Optimization and stability analysis of the cascaded EEHG-HGHG free-electron laser

X-ray free-electron lasers (XFELs) are powerful tools to explore and study nature for achieving remarkable advances. Generally, seeded FELs are ideal sources for supplying fully coherent soft x-ray pulses. Benefiting from the high-frequency up-conversion efficiency, the cascading configuration with echo-enabled harmonic generation (EEHG) and high-gain harmonic generation (HGHG) holds promising prospects for generating fully coherent radiation at 1 nm wavelength. In this paper, we design and optimize EEHG-HGHG configuration using parameters of Shanghai High-Repetition-Rate XFEL and Extreme Light Facility. In addition, we systematically analyze the effect of relative timing jitter on the output FEL performance based on various start-to-end electron beams. The intensive numerical simulations show that the cascaded EEHG-HGHG scheme can achieve 1 nm FEL pulses with peak power up to 15 GW. Further sensitivity analysis indicates that the relative timing jitter between the electron beam and seed laser has a significant impact on the FEL performance. The RMS timing jitter of 3 fs can lead to the final output pulse energy fluctuations of 29%.