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.

Resonant oscillators with stable frequencies and large quality factors help us to keep track of time with high precision. Examples range from quartz crystal oscillators in wristwatches to atomic oscillators in atomic clocks, which are, at present, our most precise time measurement devices¹. The search for more stable and convenient reference oscillators is continuing^2–6. Nuclear oscillators are better than atomic oscillators because of their naturally higher quality factors and higher resilience against external perturbations^7–9. One of the most promising cases is an ultra-narrow nuclear resonance transition in ⁴⁵Sc between the ground state and the 12.4-keV isomeric state with a long lifetime of 0.47 s (ref. ¹⁰). The scientific potential of ⁴⁵Sc was realized long ago, but applications require ⁴⁵Sc resonant excitation, which in turn requires accelerator-driven, high-brightness X-ray sources¹¹ that have become available only recently. Here we report on resonant X-ray excitation of the ⁴⁵Sc isomeric state by irradiation of Sc-metal foil with 12.4-keV photon pulses from a state-of-the-art X-ray free-electron laser and subsequent detection of nuclear decay products. Simultaneously, the transition energy was determined as $${\mathrm{12,389.59}}_{+0.12\left({\rm{syst}}\right)}^{\pm 0.15\left({\rm{stat}}\right)}\,{\rm{eV}}$$12,389.59 + 0.12 syst ± 0.15 stat eV with an uncertainty that is two orders of magnitude smaller than the previously known values. These advancements enable the application of this isomer in extreme metrology, nuclear clock technology, ultra-high-precision spectroscopy and similar applications.

Two-color high intensity x-ray free-electron lasers (FELs) provide powerful tools for probing ultrafast dynamic systems. A novel concept of realizing fresh-slice two-color lasing through slice-dependent transverse mismatch has been proposed by one of the authors [Y. Chao, SLAC Report No. SLAC-PUB-16935, 2016]. In this paper we present a feasible example following this concept based on the Linac Coherent Light Source parameters. Time-dependent mismatch along the bunch is generated by a passive dechirper module and controlled by downstream matching sections, enabling FEL lasing at different wavelength with a split undulator configuration. Simulations for soft x-ray FELs show that tens of gigawatts pulses with femtosecond duration can be generated.

We demonstrated selective slice-dependent lasing by controlling the matching to the undulator of different slices within an electron bunch. The slice-dependent mismatch was realized through quadrupole wakefield generated in a corrugated structure. A deterministic procedure based on empirical beam transport and phase space information is used to match selected slices by turns to lase in the undulator while keeping all other slices from lasing, thus staying fresh. Measurements of time-resolved electron bunch energy loss by a transverse deflecting cavity confirmed the predicted behavior.

Microbunching instability (MBI) has been one of the most challenging issues in designs of high-brightness beam transport lines for single-pass or recirculating accelerators. Although the intrabeam scattering (IBS) has long been studied in lepton or hadron storage rings as a slow diffusion process or in high-intensity proton linear accelerators as one mechanism for the beam halo, the effects of IBS on single-pass or recirculating electron accelerators have drawn attention only in the recent two decades due to emergence of linac-based or energy-recovery-linac-based fourth-generation light sources, which require high-quality electron beams during the beam transport. In this paper we develop a theoretical formulation of microbunching instability in the presence of IBS for single-pass or recirculation accelerators. To quantify MBI with inclusion of IBS, we start from the Vlasov-Fokker-Planck (VFP) equation, combining both collective interactions and incoherent IBS effects. The linearized VFP equation and the corresponding friction and diffusion coefficients are derived. The evolutions of the resultant density and energy modulations are formulated as a set of coupled integral equations. The theoretical formulation is then applied to a recirculating beamline design. The results from the semianalytical calculation are compared and show good agreement with massive particle tracking simulations.