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

TL;DR

This paper models the time-dependent changes in X-ray diffraction intensity of a crystal under intense femtosecond XFEL pulses, revealing significant intensity drops at high fluences due to electron density depletion.

Contribution

It introduces a theoretical framework combining rate equations and Boltzmann kinetics to analyze electron dynamics and diffraction intensity during XFEL irradiation.

Findings

Intensity drops sharply above 1.6 mJ/μm^2 fluence.

Time evolution of electron density affects diffraction peak intensity.

Model applicable to silicon crystals at photon energies 3-12 keV.

Abstract

The time evolution of the electron density and the resulting time dependence of X-ray diffraction peak intensity in a crystal irradiated by highly intense femtosecond pulses of an XFEL is investigated theoretically on the basis of rate equations for bound electrons and the Boltzmann equation for the kinetics of the unbound electron gas that plays an essential role in the time evolution of the electron density of a crystal. The photoionization, Auger process, electron-impact ionization, electron--electron scattering, and three-body recombination have been implemented in the system of rate equations. An algorithm for the numerical solution of the rate equations was simplified by incorporating analytical expressions for the cross sections of all the electron configurations in ions within the framework of the effective charge model. Using this approach we evaluate the time dependence of the inner shell population and electronic kinetic energy during the time of XFEL pulse propagation through the crystal for photon energies between 3 and 12 keV and a pulse width of 40 fs considering a flux of 10^12 ph/pulse (focusing on a spot size of ~ 1 mum^2, this flux corresponds to a fluence ranging between 0.6 and 1.6 mJ/mum^2). The time evolution of the atomic scattering factor and its fluctuation is numerically analyzed for the case of a Silicon crystal taking into account the decrease of the bound electron density during the pulse propagation. The time integrated intensity drops dramatically if the fluence of the XFEL pulse exceeds 1.6 mJ/mum^2.