Fig. 1. SASE FEL scheme using the PU with the beam from the LWFA. The transverse distribution of the beam (a) without and (c) with the transverse dispersion. (b), (d) Corresponding angular profiles of the radiation power.

Fig. 2. (a) Radiation power along the PU around 30 nm; (b) single-shot spectra of an SASE FEL; (c), (d) corresponding transverse angular profiles of the radiation power obtained by beam without and with the horizontal dispersion.

Fig. 3. (a) Radiation power along the PU around 3.9 nm; (b) single-shot spectra of the SASE FEL; (c), (d) corresponding transverse angular profiles of the radiation power obtained by beam without and with the horizontal dispersion.

Fig. 4. SASE FEL (a) radiation power, (b) bandwidth and (c) transverse mode parameter at 30 nm at the exit of the undulator with different dispersions of the beam in the PU (blue) and TGU (red) schemes.

Fig. 5. Negative imaginary part of the FEL growth rate (in units of ) as a function of the horizontal position (in units of ) for both the PU and TGU schemes in the fundamental mode ( cm).

Fig. 6. (a) SASE FEL power with different halfwidths of the slit at the entrance of the undulator in the PU scheme. (b)–(e) Horizontal distribution of the radiation with different halfwidths of the slit in the PU scheme. The halfwidths of the slit are , , and , respectively. The horizontal dispersion is 2.5 cm.

Table 1. beam and undulator parameters used in our study for EUV and soft X-ray FELs.