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 delta 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 delta 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(o)c, where the time delay t(o) is equal to Lambda/2 pi c and (mu(o)c)(-1) in the cases of dynamical and kinematical X-ray scattering within a crystal respectively (Lambda is the X-ray extinction length, mu(o), is the linear absorption coefficient and c is the velocity of light in vacuum).