Fig. 1. Schematic layout of the bunching enhanced scheme for coherent harmonic generation with the DS-M-DS configurations. The dispersion Sec. I and dispersion Sec. II, indicated by the dashed boxes, need to be designed specifically for a given e beam.

Fig. 2. Schematic of standard CHG and bunching enhanced CHG schemes: (a) and (c) x–z–p phase-space distributions of the e beam at the exit of the modulator in the standard CHG and bunching enhanced CHG schemes, respectively; (b) and (d) x–z–p phase-space distributions of the e beam at the entrance of the radiator in the standard CHG and bunching enhanced CHG schemes, respectively. The initial horizontal size and energy spread of the e beam are assumed to be 1 µm and 0.1%, respectively. The coupling coefficient R₁₆ induced by DS-I is 2 cm, and the amplitude of energy modulation is A = 3. The corresponding coupling coefficients induced by DS-II are R₅₁ = 2.2 × 10⁻⁴ and R₅₆ = −4.7 × 10⁻⁵ m.

Fig. 3. PIC simulation results for LWFA. (a) Density profile used in the simulation and corresponding evolution of the energy spectrum dQ/dE of the e beam as a function of the longitudinal positions, where Q and E are the beam charge and energy, respectively. (b) Normalized emittance in the horizontal (black) and vertical (red) directions, beam current (blue), and relative energy spreads (RES) over slices. Each slice has a length of 31.25 nm, which is chosen as the grid size in the PIC simulation.

Fig. 4. Phase merging with the normal dispersion scheme. (a) Evolution of the Twiss parameters β_x and β_y and horizontal dispersion D_x along the beamline and the corresponding schematic layout of the beamline, with quadrupoles, dipoles, and undulators represented by red, blue, and green squares, respectively. (b) and (c) Longitudinal phase-space snapshots of the e beam at the exit of the modulator and the entrance of the radiator, respectively. (d) Normalized emittances in the horizontal (black) and vertical (red) directions, beam current (blue), and relative energy spread (RES, green) over slices. (e) Corresponding bunching factors for the phase merging (PM, red) and without phase merging (w/o PM, blue) situations, respectively.

Fig. 5. Phase merging with the angular dispersion scheme. (a) Evolution of the Twiss parameters β_x and β_y and horizontal dispersion D_x along the beamline and the corresponding schematic layout of the beamline, with the quadrupoles, dipoles, and undulators represented by red, blue and green squares, respectively. (b) and (c) Longitudinal phase-space snapshots of the e beam at the exit of the modulator and the entrance of the radiator, respectively. (d) Normalized emittances in the horizontal (black) and vertical (red) directions, beam current (blue), and relative energy spreads (RES, green) over slices. (e) Corresponding bunching factors for the phase merging (PM, red) and without phase merging (w/o PM, blue) situations, respectively.

Fig. 6. Phase merging with the angular modulation and dispersion scheme. (a) Evolution of the Twiss parameters β_x and β_y and horizontal dispersion D_x along the beamline and the corresponding schematic layout of the beamline, with the quadrupoles, dipoles, and undulators represented by red, blue and green squares, respectively. (b) and (c) Longitudinal phase-space snapshots of the e beam at the exit of the modulator and the entrance of the radiator, respectively. (d) Normalized emittances in the horizontal (black) and vertical (red) directions, beam current (blue), and relative energy spreads (RES, green) over slices. (e) Corresponding bunching factors for the phase merging (PM, red) and without phase merging (w/o PM, blue) situations, respectively.

Fig. 7. Radiation properties of phase merging scheme with angular dispersion. (a) Radiation energy along the periods of the radiator and corresponding transverse profile of radiation at the exit of the radiator. (b) Power profile of radiation for various periods of the radiator. (c) Spectrum at the exit of the radiator.

Fig. 8. Tolerances of the presented angular dispersion scheme with regard to energy fluctuations and pointing jitter. (a) Peak current, (b) bunching factor for the tenth harmonic, and (c) relative pulse energy as functions of energy fluctuations and pointing jitter at the beamline entrance (the exit of the plasma).