Figure 1

Schematic configuration of the spectrometer. The spectrometer consists of an ultraprecisely figured elliptical mirror, an analyzer silicon (555) crystal, and a MPCCD detector. The elliptical mirror was coated with rhodium. The grazing incident angle was 2.7 mrad, the length of the mirror was 100 mm, and the focal length was 85 mm. The mirror enlarged the divergence angle of the x-ray beam to 2.5 mrad along the dispersion direction of the spectrometer. The silicon crystal with a Bragg angle of 81.3 deg for 10-keV x rays was located at 0.6 m from the elliptical mirror. The MPCCD detector, with a pixel size of $50\times 50\mu {\mathrm{m}}^2$, was set at 3.6 m from the silicon crystal. These components are set in the horizontal plane ($\pi$ polarization). The resultant spectral resolution and range were 20 meV and 4.2 eV, respectively.Reuse & Permissions

Figure 2

Measured single-shot spectra of XFEL for (a) compression condition 1, (b) compression condition 2, and (c) compression condition 3. The horizontal axis indicates relative photon energy from the central value of $E=9997\mathrm{eV}$. The weighted-average width $\delta$ of the spikes was determined to be (a) ${\delta }_1=110\mathrm{meV}$, (b) ${\delta }_2=290\mathrm{meV}$, and (c) ${\delta }_3=600\mathrm{meV}$ in FWHM. (d)–(f) Simulated spectra with the average spike widths that are the same as those in (a)–(c), respectively. In the simulation, we used the energy chirps of the electron-beam $(\Delta E/E)/dt=(d)2\times {10}^{-5}{\mathrm{fs}}^{-1}$, (e) $4\times {10}^{-5}{\mathrm{fs}}^{-1}$, and (f) $8\times {10}^{-5}{\mathrm{fs}}^{-1}$ for conditions 1, 2, and 3, respectively.Reuse & Permissions

Figure 3

Dependence of the simulated spike width on electron energy chirp. The bunch duration of the electron beam was fixed at 19 fs. The spike widths were obtained from the simulated spectra by fitting multiple Gaussian distributions, which is the same method as applied to the experimental data analysis.Reuse & Permissions

Figure 4

(a)–(c) Simulated temporal profiles of XFEL pulses that correspond to the energy spectra in Figs. 2d, 2e, 2f. The pulse durations were (a) $\Delta T_1=31\mathrm{fs}$, (b) $\Delta T_2=8.9\mathrm{fs}$, and (c) $\Delta T_3=4.5\mathrm{fs}$.Reuse & Permissions

Figure 5

XFEL pulse duration as functions of spike widths for several electron energy chirps. Experimental results are shown by the red region (condition 1), the blue region (2), and the green region (3). The pulse durations were determined to be $34^{+13}{}_{-7}\mathrm{fs}$, $9.7^{+2.3}{}_{-1.2}\mathrm{fs}$, and $5.1^{+0.8}{}_{-0.5}\mathrm{fs}$, respectively.Reuse & Permissions