The goal of our project was to develop a new experimental approach to enable the measurement of the insulator-to-metal transition in warm dense fluid helium for modeling the interiors of giant planets and dwarf stars. We significantly improved Lawrence Livermore National Laboratory's capabilities in laser-driven shock-compression experiments using pre-compressed samples, including the preparation of diamond anvil cell targets. Other improvements included enhanced data quality at the Omega 60 and Omega EP laser facilities at the University of Rochester's Laboratory for Laser Energetics. These advances allowed us to collect high-quality data that will be used to benchmark advanced quantum models for condensed matter. The new experimental capabilities pave the way for the development of novel measurement techniques that could be fielded on the National Ignition Facility in the near future.
Despite the considerable efforts of researchers in the fields of condensed matter physics, astrophysics, plasma physics, high-energy-density (HED) science, and inertial confinement fusion research, the equation of state and the transport properties of low-Z systems are poorly understood (Graziani et al. 2014, McMahon et al. 2012). An accurate description of the transition from the condensed-matter regime to the warm-dense-matter regime is particularly difficult, yet it is critical to improving our understanding of planetary and stellar formation and evolution. In the wake of the tremendous amount of data collected by NASA's Juno and Cassini probes at Jupiter and Saturn, the need increases for accurate models of the physical and chemical properties of gas-giant constituents such as hydrogen isotopes, helium, and their mixtures (Dougherty et al. 2018, Guillot et al. 2018).
There has been significant progress recently toward a better understanding of the insulator-to-metal transition in dense fluid hydrogen (Brygoo et al. 2015, Celliers et al. 2018, Loubeyre et al. 2012). However, the relationship of the molecular dissociation to the metalization and ionization processes must be described before we can understand the roles of density and temperature in that transition. Because helium does not form molecules, understanding the microscopic mechanisms underpinning its transition from an insulator to a warm dense metal should be more straightforward. Helium therefore constitutes an excellent testbed for advanced numerical and theoretical methods for warm dense low-Z system physics (Stixrude and Jeanloz, 2008). Unfortunately, large discrepancies still exist between the scarce existing experimental data and state-of-the-art simulation results (Celliers et al. 2010, Eggert et al. 2008, Preising et al. 2018, Soubiran et al. 2012).
The objectives of our project were to improve technical capabilities in laser-driven dynamic compression experiments and to use the new platforms to document the influence of high density and temperature on the insulator-to-metal transition in dense fluid helium. In the course of the project, we identified the need to develop an integrated CH-polymer plasma-deposition setup to deposit high-quality thick films of polyimide to serve as an ablator material.
Our two-step approach was to combine static compression with shock compression (Jeanloz et al. 2007, Loubeyre et al. 2004). The first step was to tune the initial density of the sample of interest by applying extreme pressure (tens of thousands of kilobars) using diamond anvil cells (DACs) (see the figure).
In the second step, powerful laser beams were tightly focused on the diamond opening to vaporize the polymer plasma ablator material and launch strong shock waves into the DAC. These shock waves applied megabar-scale pressures to the sample for a few nanoseconds, also heating it to several tens of thousands of degrees kelvin. Tuning the initial density enabled us to achieve specific shock-compression states at higher densities and lower temperatures for a given pressure when compared to cryogenic liquid or gas samples (Celliers et al. 2010, Eggert et al. 2008, Millot et al. 2018). We used ultrafast velocimetry to measure the shock-velocity history during its transit through the pre-compressed sample (Celliers et al. 2004) and correlated the shock-velocity measurements with simultaneous thermal-emission measurements using a streaked optical pyrometry (SOP) instrument (Miller 2013, Millot et al. 2018).
Recording the shock velocity and the associated thermal emission during the shock transit through a tiny quartz plate compressed together with the sample allowed us to determine the compressibility and shock temperature of the sample and to characterize its optical refractive index (Brygoo et al. 2015, Millot et al. 2018). Because the optical properties can be determined from quantum simulations such as density-functional-theory-based molecular dynamics (Stixrude and Jeanloz 2008), our measurements provided stringent tests for these complex numerical methods.
Our work developing a new experimental approach to enable measurement of the insulator-to-metal transition supports both the NNSA goal of managing issues related to stockpile stewardship and Lawrence Livermore National Laboratory's mission focus area of stockpile stewardship science. It also enhances the Laboratory's core competencies in HED science, as well as lasers and optical science and technology by the development of novel measurement techniques that could be fielded on the National Ignition Facility.
During this project we were able to collect high-quality data at unique extreme conditions that will reinforce the Laboratory's leadership position in the field of HED science. This project is a good example of the continued innovation in experimental methods that are needed to benchmark new numerical and theoretical approaches to modeling quantum condensed matter, a critical need for the Laboratory's mission.
We successfully developed new capabilities to enable new measurement techniques in dynamic compression science. Further analysis will be needed to fully exploit our data and publish our findings in peer-reviewed publications. Nevertheless, preliminary analysis indicates that we will be able to extract quantitative measurements of the absorption coefficient of shock-compressed helium at higher pressure–density conditions than in our previous studies. In particular, we should be able to revise the experimentally derived dependence of the electronic band gap with the temperature and density proposed in Celliers et al. (2010). This is particularly important because predicting the electronic structure of non-metallic material has historically been very challenging for density-functional-theory-based methods using exchange-correlation functionals (McMahon et al. 2012, Preising et al. 2018, Soubiran et al. 2012, Stixrude and Jeanloz 2008).
Some of the advances made during this project will be leveraged in a new research project that will include increased complexity platforms to study the extreme chemistry of planetary ices. This project also paves the way for future studies of materials relevant for stockpile stewardship science.
Brygoo, S., et al. 2015. "Analysis of Laser Shock Experiments on Precompressed Samples Using a Quartz Reference and Application to Warm Dense Hydrogen and Helium." Journal of Applied Physics 118(19): 195901.
Celliers, P., et al. 2004. "Line-Imaging Velocimeter for Shock Diagnostics at the OMEGA Laser Facility." Review of Scientific Instruments 75(11): 4916.
——— . 2010. "Insulator-to-Conducting Transition in Dense Fluid Helium." Physical Review Letters 104(18): 184503.
——— . 2018. "Insulator-Metal Transition in Dense Fluid Deuterium." Science 361(6403): 677–682.
Dougherty, M. K., et al. 2018. "Saturn's Magnetic Field Revealed by the Cassini Grand Finale." Science 362(6410), eaat5434.
Eggert, J. S., et al. 2008. "Hugoniot Data for Helium in the Ionization Regime." Physical Review Letters 100(12): 1–4.
Graziani, F., et al. 2014. Frontiers and Challenges in Warm Dense Matter, Vol. 96, arXiv:arXiv:1309.3043v1.
Guillot, T., et al. 2018. "A Suppression of Differential Rotation in Jupiter's Deep Interior." Nature. 555(7695): 227-230.
Loubeyre, P., et al. 2004. Coupling Static and Dynamic Compressions: First Meausrements in Dense Hydrogen." High Pressure Research 24(1) 25–31.
——— . 2012. "Extended Data Set for the Equation of State of Warm Dense Hydrogen Isotopes." Physical Review B 86(14): 144115.
McMahon, J., et al. 2012. "The Properties of Hydrogen and Helium Under Extreme Conditions." Review of Modern Physics 84(4): 1607–1653.
Miller, J. C. 2013. "Optical Properties of Liquid Metals At High Temperatures." Journal of Chemical Information Modeling 53 (July): 1689–1699.
Millot, M., et al. 2018. "Experimental Evidence for Superionic Water Ice Using Shock Compression." Nature Physics 14(3): 297–302.
Preising, M., et al. 2018. "Equation of State and Optical Properties of Warm Dense Helium." Physics of Plasmas 25(1): 012706.
Soubiran, F., et al. 2012. "Helium Gap in the Warm Dense Matter Regime and Experimental Reflectivity Measurements." Physical Review B 86(11): 115102.
Stixrude, L. and R. Jeanloz. 2008. "Fluid Helium at Conditions of Giant Planetary Interiors." Proceedings of the National Academy of Sciences 105(32): 11071–11075.
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