The outer core of the Earth is composed primarily of liquid iron, and the inner core boundary is governed by the intersection of the melt line and the geotherm. While there are many studies on the thermodynamic equation of state for solid iron, the equation of state of liquid iron is relatively unexplored. We use dynamic compression to diagnose the high-pressure liquid equation of state of iron by utilizing the shock-ramp capability at Sandia National Laboratories’ Z-Machine. This technique enables measurements of material states off the Hugoniot by initially shocking samples and subsequently driving a further, shockless compression. Planetary studies benefit greatly from isentropic, off-Hugoniot experiments since they can cover pressure-temperature (P-T) conditions that are close to adiabatic profiles found in planetary interiors. We used this method to drive iron to P-T conditions similar to those of the Earth’s outer-inner core boundary, along an elevated-temperature isentrope in the liquid from 275 GPa to 400 GPa. We derive the equation of state using a hybrid backward integration – forward Lagrangian technique on particle velocity traces to determine the pressure-density history of the sample. Our results are in excellent agreement with SESAME 92141, a previously published equation of state table. With our data and previous experimental data on liquid iron we provide new information on the iron melting line and derive new parameters for a Vinet-based equation of state. The table and our parameterized equation of state are applied to provide an updated means of modeling the pressure, mass, and density of liquid iron cores in exoplanetary interiors.
The limiting frequency resolution of a PDV measurement is: σf = $\sqrt\frac{6 η}{fsτ^3π}$ where fs is the sample rate, τ is the analysis time duration, and 11 is the noise fraction. Although T is a strong lever for reducing uncertainty, this parameter must be kept small to preserve time resolution. Consider a PDV measurement with sampled at 80 GS/s and analyzed in 1 ns durations. A 1% noise fraction corresponds to 0.87 MHz of frequency uncertainty, which at 1550 nm works out to 0.68 m/s. A 10% noise fraction has a limiting velocity resolution of about 7 m/s; for comparison, a VISAR system with similar response time (0.5 ns delay, 532 m/s fringe constant) would have a limiting uncertainty of 5-6 m/s. Noise fractions of 10-20% or less are desirable for measurements at this time scale.
By deploying a photon Doppler velocimetry based plasma diagnostic, we have directly observed low density plasma in the load anode/cathode gap of cylindrically converging pulsed power targets. The arrival of this plasma is temporally correlated with gross current loss and subtle power flow differences between the anode and the cathode. The density is in the range where Hall terms in the electromagnetic equations are relevant, but this physics is lacking in the magnetohydrodynamics codes commonly used to design, analyze, and optimize pulsed power experiments. The present work presents evidence of the importance of physics beyond traditional resistive magnetohydrodynamics for the design of pulsed power targets and drivers.
A critical component of the magnetically driven implosion experiments at Sandia National Laboratories is the delivery of high-current, 10s of MA, from the Z pulsed power facility to a target. In order to assess the performance of the experiment, it is necessary to measure the current delivered to the target. Recent Magnetized Liner Inertial Fusion (MagLIF) experiments have included velocimetry diagnostics, such as PDV (Photonic Doppler Velocimetry) or Velocity Interferometer System for Any Reflector, in the final power feed section in order to infer the load current as a function of time. However, due to the nonlinear volumetrically distributed magnetic force within a velocimetry flyer, a complete time-dependent load current unfold is typically a time-intensive process and the uncertainties in the unfold can be difficult to assess. In this paper, we discuss how a PDV diagnostic can be simplified to obtain a peak current by sufficiently increasing the thickness of the flyer. This effectively keeps the magnetic force localized to the flyer surface, resulting in fast and highly accurate measurements of the peak load current. In addition, we show the results of experimental peak load current measurements from the PDV diagnostic in recent MagLIF experiments.
Photonic Doppler velocimetry tracks motion during high-speed, single-event experiments using telecommunication fiber components. The same technology can be applied in situations where there is no actual motion, but rather a change in the optical path length. Migration of plasma into vacuum alters the refractive index near a fiber probe, while intense radiation modifies the refractive index of the fiber itself. These changes can diagnose extreme environments in a flexible, time-resolved manner.
VISAR measurements are typically analyzed in the time domain, where velocity is approximately proportional to fringe shift. Moving to the frequency domain clarifies the limitations of this approximation and suggests several improvements. For example, optical dispersion preserves high-frequency information, so a zero-dispersion (air delay) interferometer does not provide optimal time resolution. Combined VISAR measurements can also improve time resolution. With adequate bandwidth and reasonable noise levels, it is quite possible to achieve better resolution than the VISAR approximation allows.