With intensities 10(8)-10(10) times greater than other laboratory sources, X-ray free-electron lasers are currently opening up new frontiers across many areas of science. In this Review we describe how these unconventional lasers work, discuss the range of new sources being developed worldwide, and consider how such X-ray sources may develop over the coming years

A technique is proposed to generate attosecond pulse trains of radiation from a Free-Electron Laser amplifier. The optics-free technique synthesises a comb of longitudinal modes by applying a series of spatio-temporal shifts between the co-propagating radiation and electron bunch in the FEL. The modes may be phase-locked by modulating the electron beam energy at the mode spacing frequency. Three-dimensional simulations demonstrate the generation of a train of 400 as pulses at giga-watt power levels evenly spaced by 2.5 fs at a wavelength of 124Å. In the X-ray at wavelength 1.5Å, trains of 23 as pulses evenly spaced by 150 as and of peak power up to 6 GW are predicted.

This review is focused on free-electron lasers (FELs) in the hard to soft x-ray regime. The aim is to provide newcomers to the area with insights into: the basic physics of FELs, the qualities of the radiation they produce, the challenges of transmitting that radiation to end users and the diversity of current scientific applications. Initial consideration is given to FEL theory in order to provide the foundation for discussion of FEL output properties and the technical challenges of short-wavelength FELs. This is followed by an overview of existing x-ray FEL facilities, future facilities and FEL frontiers. To provide a context for information in the above sections, a detailed comparison of the photon pulse characteristics of FEL sources with those of other sources of high brightness x-rays is made. A brief summary of FEL beamline design and photon diagnostics then precedes an overview of FEL scientific applications. Recent highlights are covered in sections on structural biology, atomic and molecular physics, photochemistry, non-linear spectroscopy, shock physics, solid density plasmas. A short industrial perspective is also included to emphasise potential in this area.