Abstract
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%.
Highlights
The Z-machine (Z) at Sandia National Laboratories (SNL) is one of the premier current sources in the world for magnetically driven, high-pressure dynamic materials and inertial confinement fusion (ICF) experiments.1 A wide range of different experiments are performed on Z, all of which are energized by delivering current (%10–30 MA) to an ensemble of metallic conductors on a time scale %100–1000 ns.2–13 Magnetic energy is converted into kinetic energy of conductor motion, and into thermal energy via Joule heating of conducting materials by nonlinear magnetic diffusion
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 þ/À1%
We have demonstrated the feasibility of determining the electrical conductivity of compressed metals in a range of density and temperature using measured flyer plate velocities in combination with DFT calculations, MHD simulation, and mathematical optimization
Summary
The Z-machine (Z) at Sandia National Laboratories (SNL) is one of the premier current sources in the world for magnetically driven, high-pressure dynamic materials and inertial confinement fusion (ICF) experiments. A wide range of different experiments are performed on Z, all of which are energized by delivering current (%10–30 MA) to an ensemble of metallic conductors (the load) on a time scale %100–1000 ns. Magnetic energy is converted into kinetic energy of conductor motion, and into thermal energy via Joule heating of conducting materials by nonlinear magnetic diffusion. A significant progress has been made using DFT (Density Functional Theory) based ab initio calculations to produce accurate models of EOS and electrical conductivity.. A significant progress has been made using DFT (Density Functional Theory) based ab initio calculations to produce accurate models of EOS and electrical conductivity.14–17 These models must still be validated through experiments. The focus of this work is on using a combination of experimentation, MHD simulation, empirical models, and ab initio calculations to produce an accurate, calibrated model of electrical conductivity for copper (Cu). For example, the Ziman model in conjunction with average atom models like Inferno is more accurate than the semi-empirical models, but are subject to large variations in their answers based on which potentials and assumptions are chosen At high temperatures, these codes are often quite adequate (Grinenko et al.32), but in the compressed solid at modest temperature (several thousand Kelvin) they are less reliable. We used a sensitivity study to determine which sections of the model needed modification and, through an iterative process, corrected the model such that the simulations more accurately represent the experiments
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