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.
The CHEDS researchers are engaged in a collaborative research project to study the properties of iron and iron alloys under Earth’s core conditions. The Earth’s core, inner and outer, is composed primarily of iron, thus studying iron and iron alloys at high pressure and temperature conditions will give the best estimate of its properties. Also, comparing studies of iron alloys with known properties of the core can constrain the potential light element compositions found within the core, such as fitting sound speeds and densities of iron alloys to established inner- Earth models. One of the lesser established properties of the core is the thermal conductivity, where current estimates vary by a factor of three. Therefore, one of the primary goals of this collaboration is to make relevant measurements to elucidate this conductivity.
Howard, Marylesa; Diaz, Abel; Briggs, Matthew E.; Crawford, Kristen; Dolan, Daniel H.; Furlanetto, Michael R.; Furnish, Michael D.; Holtkamp, David B.; La Lone, B.M.; Strand, Oliver T.; Stevens, Gerald D.; Tunnell, Thomas W.
Photonic Doppler Velocimetry is an interferometric technique for measuring the beat frequency of a moving surface, from which the calculated velocity profile of the surface can be used to describe the physical changes the material undergoes after high-impact shock. Such a technique may also be used to characterize the performance of small detonators and determine the time at which the surface began moving. In this work, we develop a semi-automated technique for extracting the time of initial movement from a normalized lineout of the power spectrogram near the offset frequency of each probe. We characterize the response bias of this method and compare with the time of initial movement obtained by hand calculation of the raw voltage data. Results are shown on data from shock experiments such as gas gun setups and explosives-driven flyer plates.
Optical diagnostics play a central role in dynamic compression research. Currently, streak cameras are employed to record temporal and spectroscopic information in single-event experiments, yet are limited in several ways; the tradeoff between time resolution and total record duration is one such limitation. This project solves the limitations that streak cameras impose on dynamic compression experiments while reducing both cost and risk (equipment and labor) by utilizing standard high-speed digitizers and commercial telecommunications equipment. The missing link is the capability to convert the set of experimental (visible/x-ray) wavelengths to the infrared wavelengths used in telecommunications. In this report, we describe the problem we are solving, our approach, our results, and describe the system that was delivered to the customer. The system consists of an 8-channel visible-to- infrared converter with > 2 GHz 3-dB bandwidth.
The SMASH (Sandia Matlab AnalysiS Hierarchy) toolbox is a collection of MATLAB code for data analysis. The toolbox contains general purpose functions, custom class defini- tions, and self-contained programs aimed at the needs of experimental physicists working in pulsed power research. The initial release (version 1.0) supports file access, signal/image analysis, and user interface creation; custom graphics and generic system tools are also pro- vided. Much of the package is object oriented, encouraging users to build new capabilities from established classes. Future releases will continue this goal, expanding capabilities and streamlining application development.
We report on a new technique for obtaining off-Hugoniot pressure vs. density data for solid metals compressed to extreme pressure by a magnetically driven liner implosion on the Z-machine (Z) at Sandia National Laboratories. In our experiments, the liner comprises inner and outer metal tubes. The inner tube is composed of a sample material (e.g., Ta and Cu) whose compressed state is to be inferred. The outer tube is composed of Al and serves as the current carrying cathode. Another aluminum liner at much larger radius serves as the anode. A shaped current pulse quasi-isentropically compresses the sample as it implodes. The iterative method used to infer pressure vs. density requires two velocity measurements. Photonic Doppler velocimetry probes measure the implosion velocity of the free (inner) surface of the sample material and the explosion velocity of the anode free (outer) surface. These two velocities are used in conjunction with magnetohydrodynamic simulation and mathematical optimization to obtain the current driving the liner implosion, and to infer pressure and density in the sample through maximum compression. This new equation of state calibration technique is illustrated using a simulated experiment with a Cu sample. Monte Carlo uncertainty quantification of synthetic data establishes convergence criteria for experiments. Results are presented from experiments with Al/Ta, Al/Cu, and Al liners. Symmetric liner implosion with quasi-isentropic compression to peak pressure ∼1000 GPa is achieved in all cases. These experiments exhibit unexpectedly softer behavior above 200 GPa, which we conjecture is related to differences in the actual and modeled properties of aluminum.
We report on the progress made to date for a Laboratory Directed Research and Development (LDRD) project aimed at diagnosing magnetic flux compression on the Z pulsed-power accelerator (0-20 MA in 100 ns). Each experiment consisted of an initially solid Be or Al liner (cylindrical tube), which was imploded using the Z accelerator's drive current (0-20 MA in 100 ns). The imploding liner compresses a 10-T axial seed field, B z ( 0 ) , supplied by an independently driven Helmholtz coil pair. Assuming perfect flux conservation, the axial field amplification should be well described by B z ( t ) = B z ( 0 ) x [ R ( 0 ) / R ( t )] 2 , where R is the liner's inner surface radius. With perfect flux conservation, B z ( t ) and dB z / dt values exceeding 10 4 T and 10 12 T/s, respectively, are expected. These large values, the diminishing liner volume, and the harsh environment on Z, make it particularly challenging to measure these fields. We report on our latest efforts to do so using three primary techniques: (1) micro B-dot probes to measure the fringe fields associated with flux compression, (2) streaked visible Zeeman absorption spectroscopy, and (3) fiber-based Faraday rotation. We also mention two new techniques that make use of the neutron diagnostics suite on Z. These techniques were not developed under this LDRD, but they could influence how we prioritize our efforts to diagnose magnetic flux compression on Z in the future. The first technique is based on the yield ratio of secondary DT to primary DD reactions. The second technique makes use of the secondary DT neutron time-of-flight energy spectra. Both of these techniques have been used successfully to infer the degree of magnetization at stagnation in fully integrated Magnetized Liner Inertial Fusion (MagLIF) experiments on Z [P. F. Schmit et al. , Phys. Rev. Lett. 113 , 155004 (2014); P. F. Knapp et al. , Phys. Plasmas, 22 , 056312 (2015)]. Finally, we present some recent developments for designing and fabricating novel micro B-dot probes to measure B z ( t ) inside of an imploding liner. In one approach, the micro B-dot loops were fabricated on a printed circuit board (PCB). The PCB was then soldered to off-the-shelf 0.020- inch-diameter semi-rigid coaxial cables, which were terminated with standard SMA connectors. These probes were recently tested using the COBRA pulsed power generator (0-1 MA in 100 ns) at Cornell University. In another approach, we are planning to use new multi-material 3D printing capabilities to fabricate novel micro B-dot packages. In the near future, we plan to 3D print these probes and then test them on the COBRA generator. With successful operation demonstrated at 1-MA, we will then make plans to use these probes on a 20-MA Z experiment.
The Sandia Data Archive (SDA) format is a specific implementation of the HDF5 (Hierarchal Data Format version 5) standard. The format was developed for storing data in a universally accessible manner. SDA files may contain one or more data records, each associated with a distinct text label. Primitive records provide basic data storage, while compound records support more elaborate grouping. External records allow text/binary files to be carried inside an archive and later recovered. This report documents version 1.0 of the SDA standard. The information provided here is sufficient for reading from and writing to an archive. Although the format was original designed for use in MATLAB, broader use is encouraged.
Created at Sandia National Laboratories, the Portable File Format (PFF) allows binary data transfer across computer platforms. Although this capability is supported by many other formats, PFF files are still in use at Sandia, particularly in pulsed power research. This report provides detailed PFF specifications for accessing data without relying on legacy code.
The ThermalDiffusion class was created to simulate one-dimensional thermal diffusion across one or more material layers. Each layer is assumed to have constant conductivity K and diffusivity κ . Interface conductance between layers may be specified. Internal heating as a function of position and time is also supported. The ThermalDiffusion class is included in the SMASH package [1] as part of the PDE (Partial Differential Equation) subpackage.
Streak cameras are important for high-speed data acquisition in single event experiments, where the total recorded information (I) is shared between the number of measurements (M) and the number of samples (S). Topics of this meeting included: streak camera use at the national laboratories; current streak camera production; new tube developments and alternative technologies; and future planning. Each topic is summarized in the following sections.
This report summarizes LDRD project number 151365, \Dynamic Temperature Measurements with Embedded Optical Sensors". The purpose of this project was to develop an optical sensor capable of detecting modest temperature states (<1000 K) with nanosecond time resolution, a recurring diagnostic need in dynamic compression experiments at the Sandia Z machine. Gold sensors were selected because the visible re ectance spectrum of gold varies strongly with temperature. A variety of static and dynamic measurements were performed to assess re ectance changes at di erent temperatures and pressures. Using a minimal optical model for gold, a plausible connection between static calibrations and dynamic measurements was found. With re nements to the model and diagnostic upgrades, embedded gold sensors seem capable of detecting minor (<50 K) temperature changes under dynamic compression.
Signal estimates are crucial to the design of time-resolved pyrometry measurements. These estimates affect fundamental design decisions, including the optical relay (fiber versus open beam), spectral range (visible or infrared), and amplification needs (possibly at the expense of time resolution). The pyrosim program makes such estimates, allowing the collected power, photon flux, and measured signal to be determined in a broad range of pyrometry measurements. Geometrical collection limits can be applied; sample emissivity, transfer efficiency, and detector sensitivity may also be specified, either as constants or functions of wavelength.
An important part of velocimetry analysis is the recovery of a known velocity history from simulated data signals. The fringen program synthesizes VISAR and PDV signals, given a specified velocity history, using exact formulations for the optical signal. Time-dependent light conditions, non-ideal measurement conditions, and various diagnostic limitations (noise, etc.) may be incorporated into the simulated signals. This report describes the fringen program, which performs forward VISAR (Velocity Interferometer System for Any Reflector) and PDV (Photonic Doppler Velocimetry, also known as heterodyne velocimetry) analysis. Nearly all effects that might occur in VISAR/PDV measurement of a single velocity can be modeled by fringen. The program operates in MATLAB, either within a graphical interface or as a user-callable function. The current stable version of fringen is 0.3, which was released in October 2010. The following sections describe the operation and use of fringen. Section 2 gives a brief overview of VISAR and PDV synthesis. Section 3 illustrates the graphical and console interface of fringen. Section 4 presents several example uses of the program. Section 5 summarizes program capabilities and discusses potential future work.
External modifications can transform a conventional photonic doppler velocimetry (PDV) system to other useful configurations - Non-standard probes and Frequency-conversion measurements. This approach is easier than supporting every conceivable measurement in the core PDV design. Circulator specifications may be important - -30 dB isolation (common) probably not be enough, -50 dB isolation is available, and some bench testing may be needed.
The limiting performance of PDV is determined by power spectrum location resolution - The uncertainty principle overestimates error and peak fit confidences underestimates error. Simulations indicate that PDV is: (1) Inaccurate and imprecise at low frequencies; (2) Accurate and (potentially) precise otherwise; (3) Limiting performance can be tied to sampling rate, noise fraction, and analysis duration. Frequency conversion is a good thing. PDV is competitive with VISAR, despite wavelength difference.
SIRHEN (Sandia InfraRed HEtrodyne aNalysis) is a program for reducing data from photonic Doppler velocimetry (PDV) measurements. SIRHEN uses the short-time Fourier transform method to extract velocity information. The program can be run in MATLAB (2008b or later) or as a Windows executable. This report describes the new Sandia InfraRed HEtrodyne aNalysis program (SIRHEN; pronounced 'siren') that has been developed for efficient and robust analysis of PDV data. The program was designed for easy use within Sandia's dynamic compression community.
Proceedings of SPIE - The International Society for Optical Engineering
Malone, Robert M.; Dolan, Daniel H.; Hacking, Richard G.; McKenna, Ian J.
A gated spectrometer has been designed for real-time, pulsed infrared (IR) studies at the National Synchrotron Light Source at the Brookhaven National Laboratory. A pair of 90-degree, off-axis parabolic mirrors are used to relay the light from an entrance slit to an output IR recording camera. With an initial wavelength range of 1500-4500 nm required, gratings could not be used in the spectrometer because grating orders would overlap. A magnesium oxide prism, placed between these parabolic mirrors, serves as the dispersion element. The spectrometer is doubly telecentric. With proper choice of the air spacing between the prism and the second parabolic mirror, any spectral region of interest within the InSb camera array's sensitivity region can be recorded. The wavelengths leaving the second parabolic mirror are collimated, thereby relaxing the camera positioning tolerance. To set up the instrument, two different wavelength (visible) lasers are introduced at the entrance slit and made collinear with the optical axis via flip mirrors. After dispersion by the prism, these two laser beams are directed to tick marks located on the outside housing of the gated IR camera. This provides first-order wavelength calibration for the instrument. Light that is reflected off the front prism face is coupled into a high-speed detector to verify steady radiance during the gated spectral imaging. Alignment features include tick marks on the prism and parabolic mirrors. This instrument was designed to complement singlepoint pyrometry, which provides continuous time histories of a small collection of spots from shock-heated targets.
Diamond is an attractive dynamic compression window for many reasons: high elastic limit,large mechanical impedance, and broad transparency range. Natural diamonds, however, aretoo expensive to be used in destructive experiments. Chemical vapor deposition techniquesare now able to produce large single-crystal windows, opening up many potential dynamiccompression applications. This project studied the behavior of synthetic diamond undershock wave compression. The results suggest that synthetic diamond could be a usefulwindow in this field, though complete characterization proved elusive.3
THRIVE (THRee Interferometer VElocimetry) is an analysis package for reducing three-phase interferometry measurements. Three-phase displacement interferometry measurements are the primary application of this program, although velocity interferometry is also supported. THRIVE uses a push-pull approach to transform measured signals to a pair of quadrature signals, from which fringe shift, target position, and target velocity are inferred. The program can analyze the signals in an ideal sense or compensate for non-ideal measurement conditions using ellipse characterization. The program can be run in any current version of MATLAB (release 2007a or later) or as a Windows XP executable.
Temperature measurements are crucial to equation of state development, but difficult to perform reliably. In the case of infrared pyrometry, a large uncertainty comes from the fact that sample emissivity (the deviation from a blackbody) is unknown. In this project, a method for characterizing the emissivity of shocked materials was developed. By coupling infrared radiation from the National Synchrotron Light Source to a gas gun system, broad spectrum emissivity changes were studied to a peak stress of 8 GPa. Emissivity measurements were performed on standard metals (Al, Cr, Cu, and Pt) as well as a high emissivity coating developed at Sandia.
The Velocity Interferometer System for Any Reflector (VISAR) is a widely used diagnostic at Sandia National Laboratories. Although the operating principles of the VISAR are well established, recently deployed systems (such as the fast push-pull and air delay VISAR) require more careful consideration, and many common assumptions about VISAR are coming into question. This report presents a comprehensive review of VISAR analysis to address these issues. Detailed treatment of several interferometer configurations is given to identify important aspects of the operation and characterization of VISAR systems. The calculation of velocity from interferometer measurements is also described. The goal is to derive the standard VISAR analysis relationships, indicate when these relationships are valid, and provide alternative methods when the standard analysis fails.
Using shock wave reverberation experiments, water samples were quasi-isentropically compressed between silica and sapphire plates to peak pressures of 1-5 GPa on nanosecond time scales. Real time optical transmission measurements were used to examine changes in the compressed samples. Although the ice VII phase is thermodynamically favored above 2 GPa, the liquid state was initially preserved and subsequent freezing occurred over hundreds of nanoseconds only for the silica cells. Images detailing the formation and growth of the solid phase were obtained. These results provide unambiguous evidence of bulk water freezing on such short time scales.