European XFEL Produces 10-TW Attosecond Soft-X-Ray Pulses

Attosecond x-ray pulses are intended to probe electron motion in atoms, molecules, and solids on its native timescale, but reaching this regime with high peak power is difficult. Table-top attosecond sources provide short pulses at moderate intensity; free-electron lasers can raise pulse energy, yet their pulse structure and duration must be characterized indirectly. This European XFEL experiment reports soft-x-ray pulses of roughly 100 as with peak power on the order of 10 TW, using a compressed high-current electron bunch.

Core Contribution

The paper combines five stages of electron-bunch compression with high-energy operation of a soft-x-ray undulator. The purpose is direct: produce ultrahigh peak current before the bunch enters the undulator, then use the resulting self-amplified spontaneous-emission process to generate unusually short, intense pulses. The authors frame the result as an extension of the accessible parameter range for attosecond x-ray science, because the reported pulses pair attosecond duration with millijoule-scale pulse energy.

The important qualification is that the paper does not directly recover the full temporal electric-field profile for each event. Its duration estimate is inferred from single-mode spectra under an assumption about the time-bandwidth product. That makes the reported pulse class compelling experimental evidence, but it also makes the phase assumption central to the headline duration and power estimate.

Technical Approach

The European XFEL layout contains five compression stages, indicated in the paper's facility schematic. Compression raises the electron-bunch peak current, while the high electron energy allows operation of the soft-x-ray undulator in the regime used here. Simulations of the longitudinal phase space trace the bunch after the arc, after the undulator with lasing suppressed, and with lasing enabled. The latter includes a localized distortion in the lasing region; the accompanying current and FEL-power profiles connect that part of the bunch to the emitted pulse.

For isolated single-mode events, the authors estimate duration from the measured FWHM photon-energy bandwidth $\Delta E$ using a Gaussian pulse model:

where $R$ is the ratio of the pulse time-bandwidth product to its transform-limited value. A transform-limited pulse has $R=1$. The paper adopts the range $1\leq R\leq2$, citing temporal-domain measurements of comparable high-gain FEL pulses that found time-bandwidth products generally between one and two, with values near one most common. At an 18-eV bandwidth, $R=1$ corresponds to approximately 100 as.

Results and Analysis

The spectral data span three runs. The paper plots FWHM bandwidth against pulse energy for single-mode events and overlays curves corresponding to 10-TW peak power for $R=1$ and $R=2$. This is the key empirical comparison: rather than treating high pulse energy alone as evidence of high power, the analysis tests whether each event’s energy-bandwidth combination is compatible with a 10-TW pulse under the stated duration model.

Figure 4 reports that 57% of displayed events lie above the $R=1$ 10-TW line and 6% lie above the $R=2$ line. The authors interpret these fractions as strong evidence for attosecond pulses with peak powers on the order of 10 TW. That reading is supported by a substantial collection of measured single-mode spectra across runs, and the European XFEL repetition rate allows data sets to be accumulated quickly. Still, the result is best understood as a spectrally constrained duration-and-power inference, not a direct single-shot temporal measurement.

Figure 4 also shows considerable event-to-event scatter in bandwidth and energy, consistent with the shot-to-shot fluctuations intrinsic to SASE operation. For applications needing the shortest and strongest pulses, the paper proposes selecting events with nondestructive pulse-energy measurements and spectral diagnostics. That is practical at a facility delivering up to tens of thousands of pulses per second, but it shifts part of the value from deterministic pulse production to post-selection of favorable shots.

The experiment therefore establishes a high-power attosecond operating point at a soft-x-ray FEL. Its significance is clearest for experiments where pulse energy and temporal resolution must coexist, including nonlinear x-ray studies and measurements of strongly driven electron dynamics. The evidence supports the reported regime under the stated Gaussian-pulse and time-bandwidth assumptions; direct temporal characterization would reduce the remaining ambiguity.