  Electromagnetic radiation in the soft x-ray spectral range ($1-100~\rm{nm}$
wavelengths or $0.01-1~\rm{keV}$ photon energies) is rapidly gaining importance
in both fundamental research and industrial applications. At present the degree
of coherence and the average photon flux required by advanced applications is
only available at large-scale synchrotron facilities and Free Electron Lasers
(FELs), severely limiting the range of applications. We propose a fully
coherent soft x-ray source, based on Inverse Compton Scattering (ICS) of
electron bunches created by photoionization of a laser-cooled and trapped
atomic gas. By combining spatial modulation of the photoionization process with
radiofrequency bunch compression techniques, micro-bunching at soft x-ray
wavelengths and thus coherent amplification can be realised, resulting in a
soft x-ray table-top Compton light source.
