  The principal Hugoniot of carbon, initially diamond, was measured from 3 to
80 TPa (30 to 800 million atmospheres), the highest pressure ever achieved,
using radiography of spherically-converging shocks. The shocks were generated
by ablation of a plastic coating by soft x-rays in a laser-heated hohlraum at
the National Ignition Facility (NIF). Experiments were performed with low and
high drive powers, spanning different but overlapping pressure ranges. The
radius-time history of the shock, and the profile of mass density behind, were
determined by profile-matching from a time-resolved x-ray radiograph across the
diameter of the sphere. Above ~50 TPa, the heating induced by the shock was
great enough to ionize a significant fraction of K-shell electrons, reducing
the opacity to the 10.2 keV probe x-rays. The opacity and mass density were
deduced simultaneously using the constraint that the total mass of the sample
was constant. The Hugoniot and opacity were consistent with density functional
theory calculations of the electronic states and equation of state (EOS), and
varied significantly from theoretical Hugoniots based on Thomas-Fermi theory.
Theoretical models used to predict the compressibility of diamond ablator
experiments at the NIF, producing the highest neutron yields so far from
inertial confinement fusion experiments, are qualitatively consistent with our
EOS measurements but appear to overpredict the compressibility slightly. These
measurements help to evaluate theoretical techniques and constrain wide-range
EOS models applicable to white dwarf stars, which are the ultimate evolutionary
form of at least 97% of stars in the galaxy.
