Application of multiple scattering theory to Doppler velocimetry of ejecta from shock-loaded samples

Abstract

We address the actual problem of retrieving the physical parameters of ejecta from data of heterodyne Doppler velocimetry. Under the assumption that ejected particles are randomly spaced and their number within the probed volume is great, the noise-free component of the power spectrum of heterodyne beats is shown to be expressed in terms of a solution to the transport equation for the field correlation function which accounts for multiple scattering and absorption of the probing beam in the ejecta cloud. This provides a means for theoretical modeling of experimental Doppler data. The ejecta cloud is considered as a plane layer of particles moving in the air away from the free-surface of the shock-loaded sample. The spatial profile of the scattering coefficient and the cloud thickness are related directly to the distribution of ejected particles over velocities and coordinates. The slowing-down of ejected particles in the air leads to an ambiguous relation between the velocity of particles and their position, resulting in essential complication of the particle distribution. Using a multi-group description of the ejecta cloud, we reduce the transport equation to a system of linked Milne-like equations. The system is solved numerically with the discrete ordinate code. Varying the values of the cloud optical thickness and the parameters of the particle distribution over sizes and initial velocities, we fit the calculated spectrum to the time-resolved data of heterodyne Doppler measurements. Such an approach enables retrieving the primary ejecta characteristics (the total ejected mass, the density-velocity profile and the size distribution of ejected particles) directly from heterodyne experiments. Application of the proposed method to the velocimetry data on ejecta is presented.