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The time evolution of the electron density and the resulting time dependenceof X-ray diffraction peak intensity in a crystal irradiated by highly intensefemtosecond pulses of an XFEL is investigated theoretically on the basis ofrate equations for bound electrons and the Boltzmann equation for the kineticsof the unbound electron gas that plays an essential role in the time evolutionof the electron density of a crystal. The photoionization, Auger process,electron-impact ionization, electron--electron scattering, and three-bodyrecombination have been implemented in the system of rate equations. Analgorithm for the numerical solution of the rate equations was simplified byincorporating analytical expressions for the cross sections of all the electronconfigurations in ions within the framework of the effective charge model.Using this approach we evaluate the time dependence of the inner shellpopulation and electronic kinetic energy during the time of XFEL pulsepropagation through the crystal for photon energies between 3 and 12 keV and apulse width of 40 fs considering a flux of 10^12 ph/pulse (focusing on a spotsize of ~ 1 mum^2, this flux corresponds to a fluence ranging between 0.6 and1.6 mJ/mum^2). The time evolution of the atomic scattering factor and itsfluctuation is numerically analyzed for the case of a Silicon crystal takinginto account the decrease of the bound electron density during the pulsepropagation. The time integrated intensity drops dramatically if the fluence ofthe XFEL pulse exceeds 1.6 mJ/mum^2.

Time dependence of X-ray diffraction intensity of a crystal induced by an intense femtosecond X-ray pulse