Session PO5: HED Equation of State and Materials Properties

Direct Measurements of the Ionization Potential Depression in a Dense Plasma

We have used the Linac Coherent Light Source to generate solid-density aluminum plasmas at temperatures of up to 180~eV [1]. By varying the photon energy of the X-rays that both create and probe the plasma, and observing the K-$\alpha$ fluorescence, we can directly measure the position of the K-edge of the highly-charged ions within the system. The results are found to disagree with the predictions of the extensively used Stewart-Pyatt (SP) model, but are consistent with the earlier model of Ecker and Kr\"oll, which predicts significantly greater depression of the ionization potential [2]. The results are of interest, as the ionization potential depression can significantly impact the equation of state and opacity, yet the SP model is widely used in astrophysical and ICF simulations. (N.B. The full author list of this paper includes all authors of [1] and [2]).\\[4pt] [1] S.M. Vinko {\it et al.}, Nature (London) {\bf 482}, 59 (2012).\\[0pt] [2] O. Ciricosta {\it et al.}, Phys. Rev. Lett. (to be published).   

EXAFS study of solid iron up to 560 GPa

Dynamic compression with ramp-shaped laser pulses is a technique for creating off-Hugoniont solid states at pressures well above the limit of static compression. Using a series of weak shocks to approximate a ramp drive, iron is compressed up to 560 GPa, the highest pressure ever reached in solid iron. EXAFS (extended x-ray absorption fine structure) study of the quasi-ramp-compressed iron is performed with an implosion backlighter on OMEGA laser. EXAFS data provide simultaneous measurements of density, temperature and the short-range atomic structure, showing the first clear evidence in the pressure-temperature map for off-Hugoniont states by quasi-ramp-compression. It is found that the close-packed structure of Fe is stable up to 560 GPa. The final temperature results from heating due to work against the strength of iron in addition to heating by the first shock.   

Equation of state measurement of warm dense aluminum and carbon

The equation of state of light elements is essential to understanding the structure of Jovian planets and inertial confinement fusion (ICF) experiments. Here we present results from a combination of experimental techniques used to characterize thermodynamic properties of warm dense matter (WDM). The Omega laser was used to create WDM conditions, solid density at $\sim$ 10 eV, using the novel technique of laser driven shock and release. This technique takes advantage of recent shock results on low density aerogel foam that enable the initially strongly shocked target material to undergo a large pressure release into a well-characterized low density pressure standard. The primary diagnostic is for the WDM target is spatially resolved x-ray Thomson scattering, which provides a direct and simultaneous measurement of the density, temperature, and ionization state of the WDM target material, either aluminum or carbon. To complete the EOS determination, VISAR is used to determine the shock velocity in the pressure standard and therefore to determine the pressure in the WDM material. Recent developments in the design of the new imaging spectrometer to enable better scattering data will be presented. Various equation of state models are compared to the experimental results.   

Temperature measurements along the principal Hugoniot for 0.2g/cc aerogel foam

Aerogel (SiO2) foams are used in a variety of HED experiments such as radiation flow experiments and more recently as a low-density shock standard for WDM equation of state experiments. Many of these experiments can be sensitive to the equation of state (EOS) of the foam. Despite recent very successful Hugoniot measurements of 0.2 g/cc aerogel foam, the temperature of these foams at a given pressure has not been measured and many EOS models for foams ignore important physics, thus predicting very different temperatures for a given condition. We have completed a set of temperature measurements of 0.2 g/cc aerogel foam shocked along the principal Hugoniot from 100 to 400 GPa. The experiments were done using 12 beams at the Omega laser facility to launch strong steady shocks into the foam targets. The temperature of the shocked foam was determined from measurements using the streaked optical pyrometer (SOP). The range of pressures covered established the behavior of the temperature through the important dissociation and initial ionization range. Equation of state models, where available, are compared to the data.   

The Release of Shocked Materials

When a shock wave encounters lower-density matter, its pressure and density relax until the impedance across the material interface is constant. This process is the basis for the impedance-match equation-of-state (EOS) measurements. Frequently, only the Hugoniot of material is known and the release is assumed to follow an isentrope. At high pressures, significant entropy is produced in the shock material. This and high-pressure ($>$1 Mbar) phase transitions complicate this process. We present methods to measure the release behavior of shocked materials. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-08NA28302.   

Quasi-Isentropic drive development for peak pressure $>$ 10 Mbar

We have tested key components necessary to the development of a quasi-isentropic pressure drive with a peak pressure greater than 10 Mbar at the National Ignition Facility. The quasi-isentropic pressure drive is produced by the recompression of a multi-material reservoir undergoing shock release across a gap. The magnitude of the initial shock, the initial density profile, and the materials' behavior under release and recompression of the reservoir define the pressure profile created in the sample during reservoir stagnation. Previously shown results have confirmed the ability to create a 5 Mbar drive for 50 -- 100 $\mu $m thick samples from a three-layer reservoir with an initial peak density of 2 g/cc (BrC$_{4}$H$_{3})$[1]. This paper presents the results of a four-layer reservoir with peak density of 8.94 g/cc (Cu). We correlate the measured results with the development of a quasi-isentropic drive that will induce peak pressures of greater than 10 Mbar in 100 $\mu $m thick samples while maintaining the sample well below its melt temperature. \\[4pt] [1] S. T. Prisbrey et al, Phys. of Plasmas, vol. \textbf{19}, pp. 056311 (2012).   

Properties of solid state metals under high pressures using laser driven plasma drives

We present the results from study of tantalum material strength at high pressures and high strain rates using the Omega laser system. The Ta sample is maintained in the solid state via a quasi-isentropic ramped drive using a reservoir-gap-sample configuration at high pressures ($>$1 Mbar) and high strain rates (10$^{6}$ - 10$^{8}$ sec$^{-1})$. The strength is inferred by measurement of Rayleigh-Taylor induced growth in pre-imposed sinusoidal ripples on a Ta sample [1]. Our study of the samples with 0.25 $\mu $m, 15 $\mu $m and 90 $\mu $m average grain sizes shows that there is no obvious Hall-Petch effect under such extreme conditions. We also show that RT growth is linear as long as the RT growth is below 0.15 of the original sample thickness. We show a comparison of experimental results with the recently developed Livermore Multiscale model that integrates the atomistic scale physics to macro hydro flow simulations. The NIF experimental design at will also be presented.\\[4pt] [1] H. S. Park et al., PRL. 104, 135504 (2010).   

Dynamic Yield Strength of Single Crystal Tantalum Measured from in-Situ Bragg Diffraction

Laser driven shock experiments featuring in situ Bragg diffraction were performed at the Omega EP facility on single crystal Tantalum to study the dynamic yield strength and lattice dynamics. Polished tantalum samples were shocked along the [111] direction to peak stresses in the range of $\sim $20-90 GPa and probed using a 22 keV x-ray source foil driven using the Omega EP petawatt beam. Diffraction from (222) and (231) lattice planes was obtained and the patterns recorded on time-integrating image plate detectors using the Lawrence Livermore Diffraction Imager (LLDI). The diffraction profiles were analyzed using the profile synthesis method to infer the detailed strain profile in the shock compressed material. Yield strength inferred from the data is compared with predictions from various rate-independent and rate-dependent models, including the LLNL multi-scale strength model for Ta.   

Theory of Strength and High-Rate Plasticity in BCC Metals Laser-Driven to High Pressures

High-rate plastic deformation is the subject of increasing experimental activity. High energy laser platforms such as those at the National Ignition Facility and the Laboratory for Laser Energetics offer the possibility to study plasticity at extremely high rates in shock waves and, importantly, in non-shock ramp-compression waves. Here we describe the theory of high-rate deformation of metals and how high energy lasers can be, and are, used to study the mechanical strength of materials under extreme conditions. Specifically, we describe how LLNL's multiscale strength model has been used to interpret the microscopic plastic flow in laser-driven Rayleigh-Taylor strength experiments, and how molecular dynamics (MD) and plasticity theory have been used to help understand in-situ diffraction based strength experiments for tantalum. The multiscale model provides information about the dislocation flow associated with plasticity and makes predictions that are compared with the experimental in-situ radiography of the Rayleigh-Taylor growth rate. We also use multi-million atom MD simulations inform the analytic theory of 1D to 3D plastic relaxation and compare to diffraction.   

Dynamic Strength Analysis of Tantalum using a Multimode Rippled Target under Laser Driven Quasi-Isentropic Compression

We present results from a material strength analysis of tantalum using a multimode rippled target under quasi-isentropic plasma loading at pressure greater than 100GPa and strain rate above 106 s-1. The results are compared with test data measured at Omega Laser. A conventional approach [1,2] utilizes the RTI (Rayleigh-Taylor Instability) mechanism to infer material strength from the growth of a single sinusoidal mode pre-imposed on a target. This method was proven reliable [2,3], but there is room for improvement in efficiency. By deploying an initial perturbation with two or more sinusoidal modes superimposed onto a single target, we are able to collect more test data in a single experiment. Presented in this paper are the verification of a multimode approach against single mode; mode coupling development during the loading sequence; the behavior of induced modes; and the detection of those modes in both simulation and test measurements.\\[4pt] [1] B.A. Remington et at., Material Science and Technology, Vol. 22, No. 4, 2006\\[0pt] [2] H.S. Park et al., PRL. 104, 135504 (2010)\\[0pt] [3] N. R. Barton et al., J. of Applied Physics, 109, 073501, 2011   

Beryllium Strength under Extreme Dynamic Loading Conditions

Beryllium strength has been investigated under dynamic loading conditions using platforms that span a limited range of pressure and strain-rate space. Multiple Be strength models persist that are ostensibly calibrated to these experiments and yet predict different outcomes for results beyond the limited phase space where data exist. We discuss experiments using the high explosives (HE) to accelerate a solid rippled Be target quasi-isentropically. In this experiment a small HE charge is detonated nearby the Be sample. As the gaseous HE products expand they accelerate the target. The interface between the low-density gas and the perturbed face of the solid target is Rayleigh-Taylor (RT) unstable, and the amplitude of the ripples will grow with time. The ripple growth is mitigated by the strength of the Be. By measuring and modeling the amplitude growth we can discriminate among various strength models for Be. Our RT designs extend the pressures up to 50 GPa and the strain-rates near $10^6$ s$^{-1}$. As a part of the design process we analyze existing plate impactor and Taylor anvil experiments using available models. In this paper we present the results of this analysis as well as the designs and preliminary experimental results from the RT experiments.   

Strength of Shock-Loaded Single-Crystal Tantalum [100] Determined using In-Situ Broadband X-ray Laue Diffraction

We report on recent experiments to determine the strength of shock-loaded single-crystal tantalum [100] using in-situ broadband x-ray Laue diffraction to measure the strain state of the compressed crystal, and elastic constants calculated from first principles. The experiments were conducted at the OMEGA laser facility in Rochester NY, USA. The inferred strength reaches 35 GPa at a shock pressure of 181 GPa and is in excellent agreement with a multiscale strength model (N. R. Barton et al. J. Appl. Phys. 109, 073501 (2011)), which employs a hierarchy of simulation methods over a range of length scales to calculate strength from first principles.   

High Energy X-Ray Diagnostic for Multi-Frame Radiography

Laser-driven high-energy ($>$22 keV) x-ray radiography has been employed as a diagnostic tool in many different types of HED experiments, with applications ranging from material strength studies (Edwards 2004, Park 2010, Park 2010) to capsule implosion experiments. We have developed a new multi-frame radiography technique that takes advantage of the multiple beams available at state-of-the-art laser facilities such as Omega and the National Ignition Facility (NIF). This concept is of particular importance to the NIF and NIF Advanced Radiographic Capability (ARC) since it will yield twice the amount of data per shot. Experiments were performed at the OMEGA/EP laser facility utilizing two short pulse (100 ps) beams to independently irradiate two 300x300x10 $\mu $m foils (Cu and Ag). The beams were delayed in time to produce two distinct x-ray pulses. A collimator assembly was employed such that two distinct and spatially separate images were generated by the Cu and Ag sources. A shield was placed between the two foils to protect the delayed backlighter from the hydrodynamic expansion and x-ray emission from the first backlighter.   

High spatial and temporal resolution phase contrast imaging of shock wave using the LCLS beam

A new technique using the Linac Coherent Light Source (LCLS), the x-ray free electron laser source, was developed at Matter in Extreme Conditions (MEC) endstation to provide high spatial and temporal resolution phase contrast imaging of shock waves in matter. The LCLS has high peak brightness enabling a high beam current of a few mJ/pulse to be focused into a small spot to achieve high imaging resolution $<$ 1 $\mu $m. 150 ps, 140 mJ, 800 nm short pulse laser beam was focused to produce shock waves in a material. We collected the first high resolution phase contrast movies of shock propagation inside materials. These results provide the first in-situ imaging of the shock front width, deformation length and time scale behind the shock of materials with free electron laser.