  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 full 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 full 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
29.16%.
