Figure 1

Self-similar shape of a superradiant pulse along the $\zeta$ coordinate in the $e$-bunch frame at the end of the SPARC amplifier [Perseo simulation [29] with the parameters in Table , case (B)]. Insertion: Longitudinal phase space and bunching coefficients $|b_n{|}^2$ for the first 5 harmonics in the front side of the pulse (highlighted region).Reuse & Permissions

Figure 2

Single shot spectra-spatial measurements carried out varying the seed energy $E_s$: (a) $E_s=1.2\pm 0.4\mathrm{nJ}$, (b) $E_s=0.25\pm 0.06\mu \mathrm{J}$, and (c) $E_s=2.0\pm 0.5\mu \mathrm{J}$. The electron beam characteristics correspond to case (A) in Table . The vertical axis represents the vertical position on the input spectrometer slit (6.5 mm). Spectra were obtained by means of an in-vacuum spectrometer [30] (normal incidence grating imaging the variable entrance slit on an UV grade CCD camera, Versarray, 1300B-Princeton Instruments). The color intensity (lower left color bar) is expressed in [$(\mathrm{nJ}/\mathrm{mm})/\mathrm{nm}$]. A cleaning procedure is applied to the images to remove the background noise. The signal to noise ratio ($s/n$) prior to cleaning is reported on each plot. The average pulse energy $⟨E⟩$ and rms energy fluctuations ${\sigma }_E$ in the three conditions are given by (a) $⟨E⟩=3.6\pm 2.1\mu \mathrm{J}$, (b) $⟨E⟩=7.2\pm 2.0\mu \mathrm{J}$, and (c) $⟨E⟩=6.5\pm 1.3\mu \mathrm{J}$. The displayed spectra pulse energies are (a) $E=5.3\mu \mathrm{J}$, (b) $E=8.0\mu \mathrm{J}$, and (c) $E=8.4\mu \mathrm{J}$.Reuse & Permissions

Figure 3

Same as in Fig. 2, the spectra of the harmonics from the 1st to the 11th. Beam data of Table , case (B). Spectra from the 7th to the 11th harmonics have been acquired, interposing an Al filter to improve the $s/n$ ratio (upper left corner in each image).Reuse & Permissions

Figure 4

(a) Genesis 1.3 [31] data post processed through a procedure resembling the slit, grating, and CCD of the spectra detection system. The simulation done with the parameters in Table , case (B). The pulse energy is $E=18\mu \mathrm{J}$, to be compared with the value observed in the experiment ($E=20\mu \mathrm{J}\pm 6\mu \mathrm{J}$). (b) Same data as in (a), but with the addition of a pedestal in the laser seed with an intensity ${10}^{-5}$ smaller than the main pulse.Reuse & Permissions

Figure 5

Relative rms. bandwidth vs harmonic order for spectra in Fig. 3 (black stars), Genesis 1.3 simulation (blue rhombus), and Perseo simulation (red rhombus with error bars). The latter is the result of averaging over 100 simulations where a jitter in the beam energy as given in Table  (A) has been included.Reuse & Permissions

Figure 6

Experimental and simulated energy vs harmonics number. Error bars for the experimental data (black stars) represent rms fluctuation combined with error propagation of the calibration factors. Simulations data by PERSEO (at the left of the exp. data) and GENESIS 1.3 (at the right) are the result of averaging over 100 simulations with an rms jitter in the beam energy of 0.27 MeV [Table  case (A)]. The curves represent the predictions of the model in [27] (a) and normalized to the measured energy at the fundamental (b).Reuse & Permissions