Systematic behavior of spherically converging shocks in the gigabar regime

Spherically-converging shocks at the National Ignition Facility can generate states in the gigabar range, which can be probed by x-ray radiography to give absolute equation of state (EOS) measurements. We have previously used profile-matching to reconstruct Hugoniot states without having to assume the functional form of the EOS, although this approach does not exclude solutions which are not consistent with hydrodynamics and thus the uncertainties on deduced Hugoniot states may be larger than necessary. In principle, profile-matching can be used to deduce isentropes through each Hugoniot point in the converging-shock radiograph, though the experimental data have been too noisy to do this without hydrodynamic constraints. Previous studies dating back to Guderley (1942) have used self-similar solutions of converging shocks in an ideal gas to relate the acceleration to the heat capacity ratio. Hydrodynamic simulations show that flow is only approximately self-similar in the gigabar regime, but the acceleration can be used to constrain and discriminate between EOS. Such solutions test off-Hugoniot states as well as those on the Hugoniot.