Measuring the melting curve of iron at super-Earth core conditions.

The discovery of more than 4500 extrasolar planets has created a need for modeling their interior structure and dynamics. Given the prominence of iron in planetary interiors, we require accurate and precise physical properties at extreme pressure and temperature. A first-order property of iron is its melting point, which is still debated for the conditions of Earth's interior. We used high-energy lasers at the National Ignition Facility and in situ x-ray diffraction to determine the melting point of iron up to 1000 gigapascals, three times the pressure of Earth's inner core. We used this melting curve to determine the length of dynamo action during core solidification to the hexagonal close-packed (hcp) structure. We find that terrestrial exoplanets with four to six times Earth's mass have the longest dynamos, which provide important shielding against cosmic radiation.

Non-iterative characteristics analysis for high-pressure ramp loading.

In the canonical ramp compression experiment, a smoothly increasing load is applied to the surface of the sample, and the particle velocity history is measured at two or more different distances into the sample, at interfaces where the surface of the sample can be probed. The velocity histories are used to deduce a stress-density relation, usually using iterative Lagrangian analysis to account for the perturbing effect of the impedance mismatch at the interface. In that technique, a stress-density relation is assumed in order to correct for the perturbation and is adjusted until it becomes consistent with the deduced stress-density relation. This process is subject to the usual difficulties of nonlinear optimization, such as the existence of local minima (sensitivity to the initial guess), possible failure to converge, and relatively large computational effort. We show that, by considering the interaction of successive characteristics reaching a free surface, the stress-density relation can be deduced directly by recursion rather than iteration. This calculation is orders of magnitude faster than iterative analysis and does not require an initial guess. Direct recursion may be less suitable for very noisy data, but it was robust when applied to trial data. The stress-density relation deduced was identical to the result from iterative Lagrangian analysis.

Atom-in-jellium equations of state in the high-energy-density regime.

Recent path-integral Monte Carlo and quantum molecular dynamics simulations have shown that computationally efficient average-atom models can predict thermodynamic states in warm dense matter to within a few percent. One such atom-in-jellium model has typically been used to predict the electron-thermal behavior only, although it was previously developed to predict the entire equation of state (EOS). We report completely atom-in-jellium EOS calculations for Be, Al, Si, Fe, and Mo, as elements representative of a range of atomic number and low-pressure electronic structure. Comparing the more recent method of pseudoatom molecular dynamics, atom-in-jellium results were similar: sometimes less accurate, sometimes more. All these techniques exhibited pronounced effects of electronic shell structure in the shock Hugoniot which are not captured by Thomas-Fermi based EOS. These results demonstrate the value of a hierarchical approach to EOS construction, using average-atom techniques with shell structure to populate a wide-range EOS surface efficiently, complemented by more rigorous three-dimensional multiatom calculations to validate and adjust the EOS.

Crystal structure and equation of state of Fe-Si alloys at super-Earth core conditions.

The high-pressure behavior of Fe alloys governs the interior structure and dynamics of super-Earths, rocky extrasolar planets that could be as much as 10 times more massive than Earth. In experiments reaching up to 1300 GPa, we combine laser-driven dynamic ramp compression with in situ x-ray diffraction to study the effect of composition on the crystal structure and density of Fe-Si alloys, a potential constituent of super-Earth cores. We find that Fe-Si alloy with 7 weight % (wt %) Si adopts the hexagonal close-packed structure over the measured pressure range, whereas Fe-15wt%Si is observed in a body-centered cubic structure. This study represents the first experimental determination of the density and crystal structure of Fe-Si alloys at pressures corresponding to the center of a ~3-Earth mass terrestrial planet. Our results allow for direct determination of the effects of light elements on core radius, density, and pressures for these planets.

Properties of plastic ablators in laser-driven material dynamics experiments.

Radiation hydrodynamics simulations were used to study the effect of plastic ablators in laser-driven shock experiments. The sensitivity to composition and equation of state was found to be 5%-10% in ablation pressure. As was found for metals, a laser pulse of constant irradiance gave a pressure history which decreased by several percent per nanosecond. The pressure history could be made more constant by adjusting the irradiance history. The impedance mismatch with the sample gave an increase o(100%) in the pressure transmitted into the sample, for a reduction of several tens of percent in the duration of the peak load applied to the sample, and structured the release history by adding a release step to a pressure close to the ablation pressure. Algebraic relations were found between the laser pulse duration, the ablator thickness, and the duration of the peak pressure applied to the sample, involving quantities calculated from the equations of state of the ablator and sample using shock dynamics.

Shock formation and the ideal shape of ramp compression waves.

We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shape for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. Example applications are presented for several classes of laser-loading experiment, identifying conditions where shocks are desired but not formed, and where long-duration ramps are desired.