Multiple scattering of light in shock compression experiments

Photon Doppler Velocimetry (PDV) is ubiquitous to characterize ejecta in shock physics experiments. This technique accurately measures particle velocity thanks to the induced Doppler shift, assuming light is scattered once. Nonetheless, exper-imental and numerical works have shown the presence of multiple scattering in shock ejecta. In order to account for multiple scattering, we develop a theoretical framework where, considering the time scales at stake, we prove that the PDV spectrogram is linked to the specific intensity of the scattered field. This specific intensity is shown to obey a Radiative Transfer Equation (RTE), which includes multiple scattering, that we generalize to take into account both Doppler shifts and statistical inhomogeneities of the ejecta in particle velocity, number density and size. We numerically solve this RTE for a realistic ejecta to compute spectrograms at different wavelengths. First, this study proves the presence of the multiple scattering regime at all studied wavelengths. Second, we show that the evolution of spectrograms on wavelength is mostly due to differences in absorption.