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Abstract
X-ray devices are far superior to optical ones for providing nanometre spatial and
attosecond temporal resolutions. Such resolution is indispensable in biology, medicine,
physics, material sciences, and their applications. A bright ultrafast coherent X-ray
source is highly desirable, for example, for the diffractive imaging of individual
large molecules, viruses, or cells. Here we demonstrate experimentally a new compact
X-ray source involving high-order harmonics produced by a relativistic-irradiance
femtosecond laser in a gas target. In our first implementation using a 9 Terawatt
laser, coherent soft X-rays are emitted with a comb-like spectrum reaching the 'water
window' range. The generation mechanism is robust being based on phenomena inherent
in relativistic laser plasmas: self-focusing, nonlinear wave generation accompanied
by electron density singularities, and collective radiation by a compact electric
charge. The formation of singularities (electron density spikes) is described by the
elegant mathematical catastrophe theory, which explains sudden changes in various
complex systems, from physics to social sciences. The new X-ray source has advantageous
scalings, as the maximum harmonic order is proportional to the cube of the laser amplitude
enhanced by relativistic self-focusing in plasma. This allows straightforward extension
of the coherent X-ray generation to the keV and tens of keV spectral regions. The
implemented X-ray source is remarkably easily accessible: the requirements for the
laser can be met in a university-scale laboratory, the gas jet is a replenishable
debris-free target, and the harmonics emanate directly from the gas jet without additional
devices. Our results open the way to a compact coherent ultrashort brilliant X-ray
source with single shot and high-repetition rate capabilities, suitable for numerous
applications and diagnostics in many research fields.