The electrical conductivity of materials under extremes of temperature and pressure is of crucial importance for a wide variety of phenomena, including planetary modeling, inertial confinement fusion, and pulsed power based dynamic materials experiments. There is a dearth of experimental techniques and data for highly compressed materials, even at known states such as along the principal isentrope and Hugoniot, where many pulsed power experiments occur. We present a method for developing, calibrating, and validating material conductivity models as used in magnetohydrodynamic (MHD) simulations. The difficulty in calibrating a conductivity model is in knowing where the model should be modified. Our method isolates those regions that will have an impact. It also quantitatively prioritizes which regions will have the most beneficial impact. Finally, it tracks the quantitative improvements to the conductivity model during each incremental adjustment. In this paper, we use an experiment on Sandia National Laboratories Z-machine to isentropically launch multiple flyer plates and, with the MHD code ALEGRA and the optimization code DAKOTA, calibrated the conductivity such that we matched an experimental figure of merit to +/-1%.
We report on a new technique for obtaining off-Hugoniot pressure vs. density data for solid metals compressed to extreme pressure by a magnetically driven liner implosion on the Z-machine (Z) at Sandia National Laboratories. In our experiments, the liner comprises inner and outer metal tubes. The inner tube is composed of a sample material (e.g., Ta and Cu) whose compressed state is to be inferred. The outer tube is composed of Al and serves as the current carrying cathode. Another aluminum liner at much larger radius serves as the anode. A shaped current pulse quasi-isentropically compresses the sample as it implodes. The iterative method used to infer pressure vs. density requires two velocity measurements. Photonic Doppler velocimetry probes measure the implosion velocity of the free (inner) surface of the sample material and the explosion velocity of the anode free (outer) surface. These two velocities are used in conjunction with magnetohydrodynamic simulation and mathematical optimization to obtain the current driving the liner implosion, and to infer pressure and density in the sample through maximum compression. This new equation of state calibration technique is illustrated using a simulated experiment with a Cu sample. Monte Carlo uncertainty quantification of synthetic data establishes convergence criteria for experiments. Results are presented from experiments with Al/Ta, Al/Cu, and Al liners. Symmetric liner implosion with quasi-isentropic compression to peak pressure ∼1000 GPa is achieved in all cases. These experiments exhibit unexpectedly softer behavior above 200 GPa, which we conjecture is related to differences in the actual and modeled properties of aluminum.