Stimulated X-ray Raman scattering in Free Electron Lasers with   incoherent spectrum
  The single-pulse spectrum of self-amplified spontaneous emission (SASE) free electron lasers (FELs) is characterized by random fluctuations in frequency. The typical spectrum bandwidth for a hard x-ray FEL is in the range of 10-20 eV and is comparable with the distance between energy levels of valence electrons in atoms an molecules. We calculate the rate of transitions in a quantum three-level system with the energy difference of several eV caused by such radiation and show that for x-ray intensities in the range of $10^{20}$ W/cm$^2$ the probability of the transition over the duration of the x-ray pulse is large. We argue that this effect can be used to modify the spectrum of a SASE FEL potentially making it more narrow. 
Gennady Stupakov and Max Zolotorev
physics.acc-ph