Retrieving Transport Properties from Multiscale Flows using X-ray Photon Correlation Spectroscopy (XPCS)

Complex multiscale flows associated with instabilities and turbulence are commonly induced under high energy density (HED) conditions, but accurate measurement of their transport properties has been challenging. X-ray photon correlation spectroscopy (XPCS) with coherent X-ray sources can, in principle, probe material dynamics to infer transport properties using time autocorrelation of density fluctuations. Here we develop a theoretical framework for utilizing XPCS to study material diffusivity in multiscale flows. We extend single-scale shear flow theories to broadband flows using a multiscale analysis that captures shear and diffusion dynamics. We demonstrate the versatility of the method over several orders of magnitude in timescale using sequential-pulse XPCS and X-ray speckle visibility spectroscopy (XSVS). Our framework enables the concurrent measurements of diffusivity and characteristic shear velocities in multiscale flows, which establishes the theoretical foundation for XPCS as a promising diagnostic for HED systems.