Recovering particle size distributions in shock compression experiments with Photon Doppler Velocimetry

In shock compression experiments, the free surface of a solid metal sample can eject fast and fine particles. Despite the many diagnostics implemented to measure the mass, size, velocity or temperature of the ejecta, this phenomenon is only partially understood. In this context, Photon Doppler Velocimetry (PDV) has been a valuable optical diagnostic, measuring reliably particles velocities in the single scattering regime. Here we show how, in the context of experiments in gas, PDV allows one to retrieve additional information on the ejecta, e.g., information on the particles' size, even in the presence of strong multiple scattering. We explain what governs ejecta transport in gas and how it can be simulated. To account for multiple scattering of light in these ejecta, we use the Radiative Transfer Equation (RTE) that quantitatively describes PDV spectrograms, and their dependence on the velocity but also size distribution of particles. We simulate spectrograms by solving the RTE numerically on hydrodynamic ejecta simulations. Finally, by comparing simulated and experimental spectrograms, we recover particle size information from a diagnostic initially designed for velocity measurements. This work demonstrates an unprecedented level of constraint on the ejecta description.