Penumbral Imaging of micrometer size plasma hot spots at shock stagnation in Gbar EOS experiments on the National Ignition Facility*

We have developed an experimental platform for absolute equation of state (EOS) measurements up to Gbar pressures on the National Ignition Facility (NIF). We use a symmetry-tuned hohlraum drive to launch a spherical shock wave into a solid CH sphere. Streaked Radiography is the primary diagnostic to measure the density change at the shock front as the pressure increases towards smaller radii. At shock~stagnation in the center of the capsule, we observe short and bright x-ray self emission from high density (50 g/cm$^3$) plasma at 1 keV. Here, we present results obtained with penumbral imaging, carried out to characterize the size of the hot spot emission. A detailed understanding of this size and~emission strength allows for benchmarking radiation-hydro simulations in a regime that is not accessible to radiography. The application of penumbral imaging extends existing NIF diagnostic capabilities to higher spatial resolution (currently 10 $\mu$m to 1 $\mu$m) and higher sensitivity. At peak emission we find the hot spot radius to be as small as 5.8 $+$/- 1 $\mu$m, corresponding to a convergence ratio of 200.