Multiple scattering of light in shock compression experiments.

Photon Doppler Velocimetry (PDV) is ubiquitous to characterize ejecta in shock physics experiments. It’s cornerstone is the single backscattering regime hypothesis in which v = l/2f, with v velocity of the particles, l wavelength and f frequency. Nonetheless, experimental and numerical works have shown the presence of multiple scattering in this kind of medium.

In order to account for multiple scattering, we create a framework where, considering the time scales at stake, we prove that the spectrogram is proportional to the scattered specific intensity I(r, u, t, w). This radiometric quantity can be interpreted as a radiative flux at position r, in direction u, at time t and frequency w. It obeys the Radiative Transfer Equation (RTE), which includes multiple scattering, that we generalize to take into account the Doppler shift.

This theoretical work is backed by a Monte-Carlo numerical scheme that allows to solve the RTE. We present the corresponding simulations that include both functionalities previously seen and novel features. We introduce position dependant scattering cross sections, Mie phase functions but also correlated velocity and size particle distributions. This allows for a precise description of the ejecta cloud and therefore higher simulated spectrogram fidelity.