Ångstrom and attosecond are the fundamental spatiotemporal scales for electron dynamics in various materials. Although attosecond pulses with wavelengths comparable to the atomic scales are expected to be a key tool in advancing attosecond science, producing high-power hard X-ray attosecond pulses at ångstrom wavelengths remains a formidable challenge. Here, we report the generation of terawatt-scale attosecond hard X-ray pulses using a free-electron laser in a special operation mode. We achieved 9 keV single-spike X-ray pulses with a mean pulse energy of around 180 μJ, exceeding previous reports by more than an order of magnitude, and an estimated average pulse duration of 200 as at full-width at half-maximum. Exploiting the unique capability of the European XFEL, which can deliver ten pulse trains per second with each containing hundreds of pulses at megahertz repetition rates, this study demonstrates the generation of attosecond X-ray pulses at a 2.25 MHz repetition rate. These intense high-repetition-rate attosecond X-ray pulses present transformative prospects for structural and electronic damage-free X-ray measurements and attosecond time-resolved X-ray methodologies, heralding a new era in ultrafast X-ray science.

High-resolution X-ray spectroscopy in the sub-nanosecond to femtosecond time range requires ultrashort X-ray pulses and a spectral X-ray flux considerably larger than that presently available. X-ray free-electron laser (XFEL) radiation from hard X-ray self-seeding (HXRSS) setups has been demonstrated in the past and offers the necessary peak flux properties. So far, these systems could not provide high repetition rates enabling a high average flux. We report the results for a cascaded HXRSS system installed at the European XFEL, currently the only operating high-repetition-rate hard X-ray XFEL facility worldwide. A high repetition rate, combined with HXRSS, allows the generation of millijoule-level pulses in the photon energy range of 6–14 keV with a bandwidth of around 1 eV (corresponding to about 1 mJ eV^–1 peak spectral density) at the rate of ten trains per second, each train including hundreds of pulses arriving at a megahertz repetition rate. At 2.25 MHz repetition rate and photon energies in the 6–7 keV range, we observed and characterized the heat-load effects on the HXRSS crystals, substantially altering the spectra of subsequent X-ray pulses. We demonstrated that our cascaded self-seeding scheme reduces this detrimental effect to below the detection level. This opens up exciting new possibilities in a wide range of scientific fields employing ultrafast X-ray spectroscopy, scattering and imaging techniques.

The European X-ray Free-Electron Laser Facility in Germany delivers x-ray pulses with femtosecond pulse duration at a repetition rate of up to 4.5 MHz. The free-electron laser radiation is created by the self-amplified spontaneous emission (SASE) process, whose stochastic nature gives rise to shot-to-shot fluctuations in most beam properties, including spectrum, pulse energy, spatial profile, wavefront, and temporal profile. Each spectrum consisting of many spikes varies in width and amplitude that appear differently within the envelope of the SASE spectrum. In order to measure and study the SASE spectrum, the HIgh REsolution hard X-ray single-shot (HIREX) spectrometer was installed in the photon tunnel of the SASE1 undulator beamline. It is based on diamond gratings, bent crystals as a dispersive element, and a MHz-repetition-rate strip detector. It covers a photon energy range of 3 keV–25 keV and a bandwidth of 0.5% of the SASE beam. The SASE spikes are resolved with 0.15 eV separation using the Si 440 reflection, providing a resolving power of 60 000 at a photon energy of 9.3 keV. The measured SASE bandwidth is 25 eV. In this paper, we discuss the design specifications, installation, and commissioning of the HIREX spectrometer. The spectral results using Si (110), Si (111), and C (110) crystals are presented.

The emerging concept of `beam by design' in free-electron laser (FEL) accelerator physics aims for accurate manipulation of the electron beam to tailor spectral and temporal properties of the radiation for specific experimental purposes, such as X-ray pump/X-ray probe and multiple wavelength experiments. `Beam by design' requires fast, efficient, and detailed feedback on the spectral and temporal properties of the generated X-ray radiation. Here a simple and cost-efficient method to extract information on the longitudinal Wigner distribution function of emitted FEL pulses is proposed. The method requires only an ensemble of measured FEL spectra and is rather robust with respect to accelerator fluctuations. The method is applied to both the simulated SASE spectra with known radiation properties as well as to the SASE spectra measured at the European XFEL revealing underlying non-linear chirp of the generated radiation. In the Appendices an intuitive understanding of time–frequency representations of chirped SASE radiation is provided.

The invention of the laser transformed optics by providing intense, coherent light in the visible region, but extending this concept to X-rays has been hindered by a lack of suitable gain media and mirrors. Current hard X-ray free-electron laser (XFEL) facilities ^1–5 overcome this by amplifying shot noise from a high-peak-current electron bunch via self-amplified spontaneous emission ⁶ in a single pass through long undulators, delivering very high brightness but with a noisy, multi-spiked temporal and spectral profile. Cavity-based XFELs (CBXFELs) ^7–9 were proposed to close this gap by recirculating spectrally filtered X-ray pulses in a Bragg-reflecting cavity synchronized to a high-repetition-rate electron beam. Here we show lasing with multi-pass gain at 6.952 keV in a 132.8-m round-trip diamond-based Bragg cavity ¹⁰ at the European XFEL, matched to the 2.23-MHz bunch spacing of the superconducting accelerator ⁵ . Under stringent length and angular stability requirements, a ring-up in the cavity across successive bunches was observed, producing spectrally pure, microjoule-level pulses. This establishes the feasibility of CBXFELs in an accelerator environment and validates diamond Bragg optics for X-ray resonators. The demonstrated spectral purity opens a path to next-generation X-ray science, which demands highly coherent, stable sources.