Investigation of warm dense matter by combining static and dynamic compression

Warm dense matter (WDM) belongs to a part of high energy density physics, which includes both extensive and rich physics phenomena. It is an important state of the evolution and presence of matters in inertial confinement fusion (ICF), heavy-ion fusion, Z-pinch processes and so on. In particular, thermodynamic, optical, and radiated characteristic of warm dense matter plays an important role in determining for the macro fluid movement of matter and determining for the energy transportation and transfer in the interactions of radiated field with matter in the evolution process. Therefore, further investigation of the properties of warm dense matter and precision improvements on its related parameters, such as equations of state and radiation transportation, are of science significant and applied background in many research fields such as ICF, Z-pinch, earth’s and planetary interior structure. The important research progress in the techniques of production, diagnostics, and simulation of warm dense matter under the laboratory conditions are briefly introduced and reviewed. The topics on the techniques of creating WDM were discussed, including experimental capabilities and facilities enabling the synthesis and confinement of warm dense states. These experimental capabilities include energetic materials, short pulse and high-energy-density lasers, ion beams, static high-pressure diamond-anvil cells, radiation- synchrotron sources, and mechanical impact techniques such as gas-gun launchers. Advanced diagnostics required for the characterization and interrogation of warm dense states were employ in these experiments accordingly. A general review on the theoretical approaches and computational capabilities enabling the prediction of the thermodynamic properties of matter in the warm dense regime were given. These approaches include quantum-based finite-temperature methods based on density functional theory, finite-temperature average-atom method, molecular dynamics, and various plasma physics-based theoretical approaches. In our National Key Laboratory for Shock Wave and Detonation Physics (LSD), warm dense matter was created by multiple shock reverberation technique. The multi-shock compressed states were directly determined by the multi-wavelength channel optical transience radiance pyrometry (MCOP), Doppler pins system (DPS), streak optical pyrometer (SOP), and spectrum analyser. The gas sample is confined between a 304 steel baseplate at the impact end and a composite window at the other end. The strong plain shock wave was produced using the flyer plate impact accelerated up to about several km/s by a two-stage light gas gun on the target baseplate and introduced into the plenum gas sample, which was pre-compressed from environmental pressure to 20–40 MPa. The optical radiation histories recorded by two sets of MCOPs were used to determine shock velocity. Simultaneously, the particle velocity profiles of gas sample-window interface were measured with four DPSs and the time-resolved spectrum was determined by SOP. The states of multi-shock compression gas sample were determined from the measured shock velocities combining the particle velocity profiles. The multi-shock temperatures were obtained from the measured radiation histories and spectrum of warm dense matter. We performed the experiments on warm dense helium, deuterium, argon, and xenon to reach to above one hundred GPa. The experimental results are used to validate our developed self-consistent fluid variational theoretical model, to check the existing WDM theoretical model, and to create new theoretical ones. Finally, some suggestions, summary, and outlook in the future development tendency and direction of warm dense matter are presented.

A static pressure of 2.75 Mbars has been generated in a diamond-anvil pressure cell. This pressure is 1 Mbar higher than the highest static pressure previously produced in a laboratory, 1.72 Mbar by Mao and Bell [Science 200, 1145 (1978)]. Improvements in the geometry of the cut of beveled anvil surfaces, selection of diamond anvils for a high concentration of nitrogen platelets, and modifications in the design of the supporting cell for the diamond anvils resulted in the attainment of 2.75 Mbars. Pressures from 1 bar to 1.85 Mbar were measured by the ruby fluorescence method. The ruby fluorescence, however, was found to diminish in intensity with increasing pressure and to become undetectable at 1.85 Mbar. Pressures above 1.85 Mbar were calculated on the assumption of elastic behavior for the diamond anvils in two ways: (1) by extrapolation of the relationship between central pressure and force applied to the anvils, and (2) by extrapolation of radial pressure profiles. Three lines of evidence confirm that the diamond anvils behaved elastically, rather than deforming plastically, to the highest pressure achieved. The design improvements reported in this paper should result in the acquisition of a wide range of data in diamond cells at pressures above 1 Mbar, pressures at which virtually no static data have been obtained. Pressures substantially above 2.75 Mbars are probably attainable with the present design of the diamond-cell apparatus.

The knowledge of the equation of state (EOS) of materials at high pressures in excess of 10 Mbar is important in several branches of physics including astrophysics and inertial confinement fusion. It is possible to access this high pressure regime in the laboratory using shock waves launched by the interaction of a high power laser with a solid target. To study laser driven shock waves in plastic (Polyvinyl alcohol) (C2H4O)n targets, a multiframe optical shadowgraphy technique has been developed, with spatial and temporal resolution of 12 μm and 500 ps respectively. The experiments were performed using the 1064 nm 20 J /500 ps Nd: Glass laser at BARC. The focused laser intensity on target was varied between 6 × 1013 W/cm2 and 2.7 × 1014 W/cm2. The experimental data have been compared with the results of previous experimental and theoretical studies. The results are also found to be in agreement with SESAME data. The maximum pressure attained in the experiments was 30 Mbar, achieved with a laser intensity of 2.7 × 1014 W/cm2.

We have derived 300‐K isotherms for static pressures as high as 300 GPa for Al, Cu, Ta and W. These isotherms are state‐of‐the‐art equation‐of‐state (EOS) standards to calibrate the shift of the ruby fluorescence line as a function of pressure in diamond anvil cells (DACs). Recent measurements by Dewaele et al up to pressures of about 150 GPa in DACs motivated derivation of these isotherms. All experimental data used in this analysis were published previously. Hugoniot data are reduced to isotherms using thermal pressures calculated with mean field potential (MFP) theory and, for the first time, corrections were made using measured shock‐induced strengths. Because this process has small systematic differences between different metal standards, it is important to obtain pressure by averaging results using many metals. Our purposes are (i) to give a brief description of how Hugoniots are reduced to isotherms and (ii) to articulate quasi‐isentropes, Hugoniot data, and material strengths that need to be measured in the future for Al, Cu, Ta, W, Mo, Au, and Pt to improve the accuracies of the isotherms of these metals and to extend them to higher pressures. For calibration purposes, it is important that error bars be reported with such measurements.

An evaluation method for warm dense matter (WDM) with similar timescale in inertial confinement fusion (ICF) by isochoric heating using intense pulsed power generator ETIGO-II is considered for evaluating target behavior. The temperature increase of the sample is estimated from the numerical calculation using the measured current. As a result, in the case that the shape of sample is ϕ2 mm x 10 mm and the density is 0.01 times solid density of copper, the temperature of sample increases up to 30000 K. It is expected that the WDM is generated using the proposed method with ICF implosion timescale.

In order to investigate properties of warm dense matter (WDM) in inertial confinement fusion (ICF), evaluation method for the WDM with isochoric heating on the implosion time-scale using an intense pulsed power generator ETIGO-II (∼1 TW, ∼50 ns) has been considered. In this study, the history of input energy into the sample is measured from the voltage and the current waveforms. To achieve isochoric heating, a foamed aluminum with pore sizes 600 μm and with 90% porosity was packed into a hollow glass capillary (ø 5 mm × 10 mm). The temperature of the sample is calculated from the numerical calculation using the measured input power. According to the above measurements, the input energy into a sample and the achievable temperature are estimated to be 300 J and 6000 K. It indicates that the WDM state is generated using the proposed method with ICF implosion time-scale.

We present a reduced model for the energy transfer via coupled collective modes in two-temperature plasmas based on quantum statistical theory. The model is compared with exact numerical evaluations of the coupled-mode (CM) energy transfer rate and with alternative reduced approaches over a range of conditions in the warm dense matter (WDM) and inertial confinement fusion (ICF) regimes. Our approach shows excellent agreement with an exact treatment of the CM rate and supports the importance of the coupled-mode effect for the temperature and energy relaxation in WDM and ICF plasmas. We find that electronic damping of collective ion density fluctuations is crucial for correctly describing the mode spectrum and, thus, the energy exchange. The reduced CM approach is studied over a wide parameter space, enabling us to establish its limits of applicability.

Shock Pressure measurements are made with the use of PVDF gauges applied on the back face of 0.1 to 1 mm thick targets, covered with glass windows and irradiated by laser pulses of 25 ns duration, at incident intensity between 108 and 1010 W/cm2. Standard PVDF gauges of 25 μm thickness and also new copolymer gauges of 450 μm thickness are used. Results obtained from thin and thick gauges are quite consistent. From the experimental results, a complete description of the shock evolution through the target is obtained, including a determination of induced peak pressures (1 to 50 kbar) and estimates of pressure decay during the shock propagation. Multiple reverberation of shock and release waves are also observed. The experimental results are analyzed by the way of computer simulations, reproducing features of the measured shock profile evolution.

Synchrotrons can provide very intense and focused X-ray beams, which can be used to study the structure of matter down to the atomic scale. In many experiments, the quality of the results depends strongly on detector performance; in particular, experiments studying dynamics of samples require fast, sensitive X-ray detectors. “LAMBDA” is a photon-counting hybrid pixel detector system for experiments at synchrotrons, based on the Medipix3 readout chip. Its main features are a combination of comparatively small pixel size (55 μm), high readout speed at up to 2000 frames per second with no time gap between images, a large tileable module design, and compatibility with high-Z sensors for efficient detection of higher X-ray energies. A large LAMBDA system for hard X-ray detection has been built using Cr-compensated GaAs as a sensor material. The system is composed of 6 GaAs tiles, each of 768 by 512 pixels, giving a system with approximately 2 megapixels and an area of 8.5 by 8.5 cm2. While the sensor uniformity of GaAs is not as high as that of silicon, its behaviour is stable over time, and it is possible to correct nonuniformities effectively by postprocessing of images. By using multiple 10 Gigabit Ethernet data links, the system can be read out at the full speed of 2000 frames per second. The system has been used in hard X-ray diffraction experiments studying the structure of samples under extreme pressure in diamond anvil cells. These experiments can provide insight into geological processes. Thanks to the combination of high speed readout, large area and high sensitivity to hard X-rays, it is possible to obtain previously unattainable information in these experiments about atomic-scale structure on a millisecond timescale during rapid changes of pressure or temperature.

The material testing machine and the split Hopkinson pressure bar (SHPB) were adopted, respectively, to conduct the static and dynamic compression tests on granite specimens heat treated by different temperatures. The effects of strain rate and heat-treatment temperature on the mechanism of energy evolution of the specimen during deformation and failure process were studied. The results show a significant strain rate effect on the granite, with the energy dissipation density increasing with increasing impact velocity (or strain rate), regardless of the treatment temperature. The specimens heat treated at 300 °C and 700 °C have the minimum and maximum energy dissipation densities, respectively. The specimen in the SHPB tests easily broke into pieces or even powder; while under static compression, only macroscopic fracture surfaces and spalling phenomenon on the specimen were detected. The energy dissipation density is inversely proportional to the compressive strength of the specimen. The rate of energy dissipation change is defined, which can be used to identify the stages in the deformation process of rock and to determine the position of the failure point in the stress-strain curve. For both the dynamic and static compression tests, the value of energy utilization ratio is relatively low, with a maximum value of about 35%.

In this research, we use the generalized quantum multistream model to describe collective qusiparticle excitations in electron gas with arbitrary degree of degeneracy and relativity. The effective Schrödinger–Poisson and square-root Klein–Gordon–Poisson models are applied to study the energy band structure and statistical parameters of finite temperature quantum and relativistic quantum electron gas in neutralizing background charge. Based on the plasmon energy bandgap appearing above the Fermi level, a new equation of state for quasiparticle (collective) excitations with new plasma parameter definition is suggested for dense plasmas applicable to a wide range of electron temperature and density. The new criterion for quasiparticle excitations reveals some interesting aspects of relativistic quantum matter at extreme condition, such as the plasmon blackout and collective quantum pressure collapse, which are studied in the frameworks of both non-relativistic and relativistic quantum phenomena. Current quasiparticle model predicts density-temperature regimes in warm-dense matter for which collective excitations become ineffective. On the other hand, the energy band structure model predicts the quasiparticle pressure collapse in temperature–density regime close to that of white dwarf stars. The energy band structure is a powerful concept in condensed matter physics and is shown to have applications for collective quantum excitations in electron gas. It can also have direct applications in quasiparticle dielectric response and thermodynamic properties of electron gas in inertial confinement fusion, stellar core, compact stars, and charged relativistic quantum environments. It is interesting that the basic thermodynamic behavior of non-relativistic and relativistic quantum electron gases closely match up to temperature and number density of typical white dwarfs where the gravitational collapse is prone to occur. This evidently confirms the relevance of non-relativistic quantum plasmon model to study the collective excitations in warm dense matter and white dwarfs.

Ion beam heated target simulations for warm dense matter physics and inertial fusion energy

We demonstrate a grazing-incidence X-ray platform that simultaneously records time-resolved grazing-incidence small-angle X-ray scattering (GISAXS) and grazing-incidence X-ray diffraction (GID) from a femtosecond-laser-irradiated gold film above the melting threshold, with picosecond resolution using an X-ray free-electron laser (XFEL). By tuning the X-ray incidence angle, the probe depth is set to tens of nanometres, enabling depth-selective sensitivity to near-surface dynamics. GISAXS resolves ultrafast changes in surface nanomorphology (correlation length, roughness), while GID quantifies subsurface lattice compression, grain orientation, melting and recrystallization. The approach overcomes photon-flux limitations of synchrotron grazing-incidence geometries and provides stringent, time-resolved benchmarks for complex theoretical models of ultrafast laser-matter interaction and warm dense matter. Looking ahead, the same depth-selective methodology is well suited to inertial confinement fusion (ICF): it can visualize buried-interface perturbations and interfacial thermal resistance on micron to sub-micron scales that affect instability seeding and burn propagation.

Ion-beam-plasma-interaction plays an important role in the field of Warm Dense Matter (WDM) and Inertial Confinement Fusion (ICF). A spherical theta pinch is proposed to act as a plasma target in various applications including a plasma stripper cell. One key parameter for such applications is the free electron density. A linear dependency of this density to the amount of energy transferred into the plasma from an energy storage was found by C. Teske. Since the amount of stored energy is known, the energy transfer efficiency is a reliable parameter for the design of a spherical theta pinch device. The traditional two models of energy transfer efficiency are based on assumptions which comprise the risk of systematical errors. To obtain precise results, this paper proposes a new model without the necessity of any assumption to calculate the energy transfer efficiency for an inductively coupled plasma device. Further, a comparison of these three different models is given at a fixed operation voltage for the full range of working gas pressures. Due to the inappropriate assumptions included in the traditional models, one owns a tendency to overestimate the energy transfer efficiency whereas the other leads to an underestimation. Applying our new model to a wide spread set of operation voltages and gas pressures, an overall picture of the energy transfer efficiency results.

The Time Dependent Schrödinger Equation In A Strong Laser Field