Many scientific disciplines ranging from physics, chemistry and biology to material sciences, geophysics and medical diagnostics need a powerful X-ray source with pulse lengths in the femtosecond ...range 1-4. This would allow, for example, time-resolved observation of chemical reactions with atomic resolution. Such radiation of extreme intensity, and tunable over a wide range of wavelengths, can be accomplished using high-gain free-electron lasers (FEL) 5-10. Here we present results of the first successful operation of an FEL at a wavelength of 32 nm, with ultra-short pulses (25 fs FWHM), a peak power at the Gigawatt level, and a high degree of transverse and longitudinal coherence. The experimental data are in full agreement with theory. This is the shortest wavelength achieved with an FEL to date and an important milestone towards a user facility designed for wavelengths down to 6 nm. With a peak brilliance exceeding the state-of-the-art of synchrotron radiation sources 4 by seven orders of magnitude, this device opens a new field of experiments, and it paves the way towards sources with even shorter wavelengths, such as the Linac Coherent Light Source 3 at Stanford, USA, and the European X-ray Free Electron Laser Facility 4 in Hamburg, Germany.
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