Improved analysis of converging shock radiographs

Abstract

We previously reported an experimental platform to induce a spherically-convergent shock in a sample using laser-driven ablation, probed with time-resolved x-ray radiography, and an analysis method to deduce states along the principal shock Hugoniot simultaneously with the x-ray opacity.We have now developed a modified method of analysis that is numerically better-conditioned and faster, and usually provides a better representation of the radiograph with correspondingly lower uncertainties. The previous approach was based on optimizing parameters in a model of the density distribution as a function of radius and time, warped to follow loci such as the shock and the outside of the sample. The converging shock configuration can be described more efficiently in terms of the shocked density and sound speed, expressed as functions of the shock speed Studies of the Hugoniot from various theoretical equations of state (EOS) indicate that, in the typical range of states explored by these experiments, these functions can be described by low-order polynomials. Similarly, few-parameter functions were found suitable for representing the variation of x-ray opacity with shock pressure. This approach was found to perform better in most cases than an alternative method based on parameterization of the EOS.

Shock Hugoniot of diamond from 3 to 80 TPa

“…Low-order polynomials were found adequate for the other fitting functions over the range of the data. More details and comparisons of alternative analysis methods are described elsewhere [16].…”

“…The streak radiograph was analyzed to deduce the radius-time distribution of mass density, represented using smooth functions as described above. The analysis was performed in several different ways to explore the sensitivity [16]. The locus of the shock was represented well by the function r s (t) = α(t c − t) β with parameters α, β, and t c .…”