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We developed a single-shot X-ray spectrometer for wide-range high-resolution measurements of Self-Amplified Spontaneous Emission (SASE) X-ray Free Electron Laser (XFEL) pulses. The spectrometer consists of a multi-layer elliptical mirror for producing a large divergence of 22 mrad around 9070 eV and a silicon (553) analyzer crystal. We achieved a wide energy range of 55 eV with a fine spectral resolution of 80 meV, which enabled the observation of a whole SASE-XFEL spectrum with fully-resolved spike structures. We found that a SASE-XFEL pulse has around 60 longitudinal modes with a pulse duration of 7.7 ± 1.1 fs

Measurement of the X-ray Spectrum of a Free Electron Laser with a Wide-Range High-Resolution Single-Shot Spectrometer