Fig. 1. (a) Schematic of plasma-based XFEL photon energy improvement setup (not to scale). A witness beam is accelerated in a nonlinear plasma wake excited by a driver beam. The nearly energy-doubled witness beam and the energy-depleted driver are captured by a magnet quadrupole triplet (QT1) after the plasma. A collimator and a magnetic chicane are used to dump the driver. The witness beam then propagates through another magnet quadrupole triplet (QT2) into a magnetic undulator and radiates high-energy photons. (b) Electron density n_e of the plasma and the beams in the ξ–x plane and on-axis accelerating field E_z (black line) from PIC simulations, where ξ = z − ct. (c) Saturated radiation spectra from the same undulator with and without the afterburner.

Fig. 2. (a) On-axis accelerating field (top) and predicted relative slice energy spread (bottom) along the witness beam for five different cases. ξ_w is the center of the witness beam. The dashed line represents the growth rate ρ. (b) Useable fraction of witness beam η when its delay and peak current are varied. Note that the witness beam charge is kept constant by adjusting its duration.

Fig. 3. (a) Longitudinal phase space of driver beam (blue dots) and witness beam (orange dots) at the end of the PBA. The black dashed line indicates the initial energy of 8 GeV. The inset is an enlarged view of the longitudinal phase space. (b) Slice current I (blue line), relative energy spread (green dashed line), and normalized emittance ɛ_n (black solid and red dotted lines) of the witness bunch at the end of the PBA. The blue shaded area indicates the part whose slice energy spread is smaller than ρ.

Fig. 4. (a) The shaded area shows the evolution of the horizontal envelope of the driver, with the boundaries representing the positions at half of the peak density. The lines show the centroid of the witness beam (purple line) and the β function of the witness electrons near the central energy W_c (black lines). The driver beam is blocked by a collimator at z_l = 2 m and a beam dump (gray shaded block). The magnetic lattice of the beam transport line is indicated by the blocks at the bottom. (b) Slice current I, relative energy spread δ_W, normalized emittance ɛ_n, and β function of the witness bunch at the end of the beam transport line. The blue shaded area corresponds to the part whose slice energy spread is smaller than ρ.

Fig. 5. (a) Radiation peak power along the undulator in three cases: without SUR and without the tapered undulator (blue dashed line), with SUR but without the tapered undulator (yellow line) and with both SUR and the tapered undulator (orange line). The narrow shaded area corresponds to one standard deviation based on ten SASE averaged runs. (b)–(d) Time-domain, spectral-domain and Wigner-Ville distributions of one representative radiation pulse at z_u = 120 m for the case with both SUR and the tapered undulator. A Gaussian fit of the spectrum is shown by the red dashed line in (b).

Fig. 6. Emittance growth and corresponding 3D FEL growth rate reduction caused by hosing instability for different initial x-direction offsets.