Time-dependent X-ray Bragg diffraction

The theory of time-dependent X-ray Bragg diffraction by crystals is developed on the basis of the Green-function (point-source) formalism. A general case of incident radiation partially coherent in time and space is considered. The time-delay effect of the diffracted radiation is described when the ultrashort time duration incident pulse strikes the crystal surface. The problem in question is closely connected with the effect of time delay in the resonance scattering of synchrotron radiation by nuclei in a crystal. It is found that, for the case where the incident wave is plane (or is an incoherent superposition of plane waves) and the time-dependent pulse is a pseudo δ function in time, the instantaneous crystal reflectivity is a smooth temporal function and tends to the value corresponding to the integrated reflectivity calculated by means of the conventional dynamical–kinematical X-ray diffraction theory. If the incident X-ray pulse profile is a pseudo 6 function in both time and space, the temporal crystal response has the same functional dependence as the spatial distribution of the diffracted intensity under the condition of conventional Bragg diffraction of the X-ray beam with lateral width < t_oc, where the time delay t_o is equal to Λ/2πc and (μ_oC)⁻¹ in the cases of dynamical and kinematical X-ray scattering within a crystal, respectively (Λ is the X-ray extinction length, μ_o is the linear absorption coefficient and c is the velocity of light in vacuum).