CHAPTER 20:Photoionisation Inner-shell X-ray Lasers

The unprecedented intensities achievable with X-ray free electron lasers (XFELs) open new opportunities to expand quantum and nonlinear optical processes to the X-ray domain. The most prominent manifestation of quantum optics is the laser, and the first X-ray laser (XRL) concept was published in 1967. It is based on the creation of a population inversion in an atomic system following rapid photoionisation of the inner-most electronic shell. The source has to be intense enough, so that inner-shell ionisation rates become comparable to the core-hole lifetime. This became possible with the dawn of XFELs, and here we give an overview, focusing on a Kα neon XRL. Such XRL pulses can be transform limited and are among the shortest, coherent and brightest X-ray pulses obtained in the laboratory. Operating the XRL at the onset of the exponential gain region can also result in spectral gain-narrowing with emission features narrower than the natural lifetime broadening. Applications will be discussed in the frame of X-ray emission spectroscopy of molecular gas targets and an extensive outlook will give a glance on recent and future developments in the field, in particular the extension of stimulated hard X-ray emission spectroscopy to the liquid and solid phase.