Fig. 1. Schematic layout of the proposed method (a) and the design of the chirped frequency-beating seed laser system (b). The movement direction of the movable platform is indicated by black bidirectional arrows.

Fig. 2. Schematic diagram of the chirped frequency-beating laser.

Fig. 3. Wigner distribution of an XFC.

Fig. 4. Repetition frequency with respect to and the linear chirp rate .

Fig. 5. Schematic diagram of the Wigner distribution (a) and envelope (b) of the frequency-beating laser.

Fig. 6. Longitudinal phase space evolution. Schematic of the phase space of electron beams in the scheme: after Modulator 1 (a), after Chicane 1 (b) and after Chicane 2 (c), (d).

Fig. 7. Bunching optimization of EEHG for = 3 and = 4 (a) and the initial bunching factor distribution of the electron beam (b).

Fig. 8. Radiation performance of the proposed method. Spectra (a) and saturation power distributions (b) of the XFC.

Fig. 9. Radiation spectrum when the time delay is 5.50 ps rather than the optimized value of 4.91 ps.

Fig. 10. Power and spectrum distributions of the XFCs when N = 2 and N = 1/2.

Fig. 11. Spectra of the XFCs when an initial 30 fs laser is used.

Fig. 12. XFC radiation spectra with the relative time delay deviating from the optimized value of 4.91 ps for = 1.