Session PO03: HED Hydro

Intricate structure of the ablative plasma Rayleigh Taylor instability in shock tubes

Spikes and bubbles grow on unstable interfaces that are accelerated in high-energy-density shock tubes. If a shock propagates ahead of the interface, the plasma can be heated to extreme conditions where conduction and radiation fluxes influence the hydrodynamics. For example, a National Ignition Facility experiment found reduced single-mode nonlinear mixed-width growth in conditions scaled from a supernova explosion [Kuranz et al., Nat. Commun. 9, 1564 (2018)]. We present high-resolution two-dimensional radiation hydrodynamic simulations with the Flash code that quantitatively reproduce the experiment. Radiative fluxes are primarily responsible for ablating the spike and removing the mushroom caps. The ablated plasma increases the mixed mass and forms a low-density halo. This is considerably more complex than the classical instability. The halo is sensitive to ablative physics, so radiographing it may aid in the verification of energy transport modeling. The radiation transport mostly suppresses the growth via increasing the shocked foam density, thus decreasing the Atwood number. A terminal velocity model including the rarefaction expansion agrees with the experimental mixed-width growth.   

Modeling Composition Gradients in Planar Shock Experiments

We present results of planar shock experiments where acceleration pushes a less dense material into a more-dense one. Such an interface is Rayleigh-Taylor (RT) unstable and the instability growth is governed partly by the Atwood number gradient. The double shell inertial confinement fusion capsules have a foam spacer layer that pushes on an inner capsule composed of a beryllium tamper and a high-Z inner shell. We benchmark a planar shock experiment with beryllium/tungsten targets to assess our ability to match the shock velocity through the Be and W. One target had the normal bilayer construction of beryllium and tungsten in two distinct layers; the second target had the beryllium grading into tungsten with a quasi-exponential profile, motivated by the potential for reduced RT growth with the gradient profile. Simulations mimic the shock profiles for both targets and match the shock velocity to within 5%. These results validate the ability of our simulations to model double shell capsules with bilayer or graded layer Be/W inner shells, which are needed to design future experiments at the National Ignition Facility.   

Radiographic measurement of high-pressure, gas-filled pore collapse due to preheat

The Marble experiments on NIF explored the degree of mixing between a porous foam and a gas fill as a function of pore size, but initial measurements displayed an unexpected insensitivity to pore size. It was hypothesized that the pores were collapsing due to preheat, which destroyed the initial porosity condition, and therefore a high-Z gas fill was introduced so that the additional electron pressure would support the pores against collapse. We conducted a separate set of experiments on Omega-60 to explore this pore collapse in greater detail by radiographically measuring the size of a macro-pore in a shock tube filled with a 6 atm high-Z gas mix. We compare the collapse of the macro-pore for two conditions: one with a pure Krypton gas fill and the other with a Krypton/Hydrogen mix, where we expect the latter case to have a lower pressure and to result in a more compressed macro-pore. LA-UR-23-27433   

Tracking the transition to turbulence in simulations of hydrodynamic instabilities of National Ignition Facility shock-tube experiments

The development of an experimental campaign at the National Ignition Facility (NIF) is underway to study the hydrodynamic growth of Rayleigh-Taylor (RT) and Richtmyer–Meshkov (RM) instabilities in nonlinear and turbulent regimes. The campaign is also developing the diagnostic capabilities to improve spatial resolution, which will enable visualization of fine flow details. With a sufficiently optimized platform and by applying multiple shocks to the interface, the transition to turbulence may be observed in the short duration of a high-energy-density experiment. We compare analyses of synthetic data from the multi-physics code ARES with experimental radiograph images from NIF to assess the prospect of utilizing Fourier modes to track progress into the turbulent regime. The results will be used to guide the optimization of the diagnostics and to define metrics that can be applied to higher-resolution data to validate our simulations. 

 

Prepared by LLNL under Contract DE-AC52-07NA27344. LLNL-ABS-851379    

Density fluctuation measurements of HED thin-layer Richtmyer-Meshkov experiments

The applicability and implementation of turbulent mix models in the high-energy-density regime is a fundamental question for ICF as the impact of mix includes the quenching of ignition experiments by mixing hot fuel with cold external materials. LANL has developed an experimental suite on the NIF capable of studying RM growth and transition to turbulence in the ICF-relevant regime, with a fundamental focus to test the applicability and performance of the BHR mix model in this complex, HED regime. To constrain mix model performance, we built on previous work [Kurien et al. Physics D, 2020] to develop an analysis method to extract statistics of density fluctuations from radiographs, specifically the BHR density-specific-volume covariance, b = -<ρ′ (1/ρ)′>, where ρ is the density, ρ′ is the density fluctuation, and the fluctuations are ensemble averaged. We present results from the NIF thin-layer Mshock reshock experiment [T. R. Desjardins et al., HEDP 2019], demonstrating the ability to extract 1D profiles of b in addition to traditional mix width measurements. Comparisons show good agreement with simulations, and potentially a method for disambiguating EOS and mixing effects in our modeling.    

Calculating mix model parameters from ensemble turbulence experiments in the HED regime

Hydrodynamic instabilities are ubiquitous on interfaces that interact with shocks. These instabilities are often seeded by surface roughness that is too computationally expensive to resolve directly. Furthermore, the instability growth is often initially laminar, so that the best way to initialize sub-grid turbulence models (such as LANL's BHR) isn't readily apparent. Recent campaigns in the HED regime have used spanwise spatial lineout averaging when calculating turbulence quantities such as "b", the density-specific volume covariance. However, during the transition to turbulence the type of averaging used may be an important consideration when comparing experiments to turbulence models. Here, we will present the analysis of Omega-EP experiments in which a nominally identical single mode perturbation (up to surface roughness), heavy-to-light, RM with delayed onset RT experiment was repeated multiple times to generate an ensemble dataset. Experimental radiographs are converted to density maps, which are then registered and finally ensemble averaged in order to calculate 2D maps of density-specific volume covariance.   

Simulations of HED ensemble experiments of shock-driven turbulence in a transitional state

Shock-driven turbulence may develop when shocks interact with perturbations present at material interfaces. Thus, shock-driven turbulence can drive mixing between the multiple layers inside inertial confinement fusion capsules and play an important role in performance, and often necessitates the use of mix models to simulate these systems. In this work, we evaluate the performance of LANL’s BHR mix model in a transitional state, in which the meaning of ensemble averaging that the model is based on for fully developed turbulence problems is not straightforward. We conduct three-dimensional ensemble simulations of recent Omega-EP experiments in which multiple instances of the same target (same single-mode nominal profile but different surface roughness) are repeated to provide one of the first HED ensemble data sets of coupled Richtmyer-Meshkov and Rayleigh-Taylor instability growth. Turbulence statistics such as the turbulent kinetic energy (TKE) and density-specific-volume covariance are computed and serve as validation quantities for the BHR model. A large suite of two-dimensional simulations with BHR is undertaken, providing estimates for initial values of BHR-relevant parameters such as the initial TKE and initial turbulent length scale, useful for the modeling of future experiments.

This work conducted under the auspices of the U.S. DOE by LANL under contract 89233218CNA000001   

Experiments exploring the effect of prescribed roughness on Richtmeyer-Meshkov growth in HED shock-tube targets

The LANL Multi-Shock (MShock) campaign on the NIF explores the Richtmeyer-Meshkov (RM) growth of initially solid, prescribed perturbation profiles after undergoing multiple shocks. In the ongoing Same-sided successive-shock (S4) experiments of this campaign the shock tube system is shocked twice from the same side at a time delay through a hybrid direct and indirect laser drive platform. Theory predicts many different cases for the growth of a twice-shocked sinusoidal perturbation depending on the perturbation scale and shock energy, some of which have been confirmed experimentally in a recent publication from this campaign. Recent experiments have explored the growth of single- and multi-mode perturbations under the effects of small-scale roughness to test whether these growth cases still hold. To reduce the number of shots needed on the NIF we also developed a scaled experimental analog for the Omega-EP laser to test the direct-drive growth. We present data from both the Omega and NIF experiments, with initial analysis of the effect of small-scale roughness on the growth rate.   

Investigating Richtmyer-Meshkov Instabilities at High Energy Densities on the Z Machine

Hydrodynamic instabilities are ubiquitous in inertial confinement fusion implosion scenarios, leading to loss of energy for compression and to mix of dissimilar materials. In order to study them and assess their impact, dedicated instability experiments have been performed using the Z Machine at Sandia National Laboratories. Complementary to laser-driven instability experiments, pinch-driven experiments naturally drive interfaces in their light-to-heavy configuration and include the effects of cylindrical convergence. We present experimental results and simulations of a suite of platforms investigating the Richtmyer-Meshkov (RM) process and interfacial feedthrough. Liners filled with liquid deuterium are magnetically imploded, driving a converging shock to the central axis and creating a magnetically isolated region suitable for studying hydrodynamic processes. The first platform investigates the interaction of this shock with a solid beryllium rod machined with sinusoidal perturbations that then grow under RM. The second replaces the on-axis rod with another cylindrical liner, enabling investigation of the feedthrough of these instabilities to the inner surface.   

Modeling the Z Exploding Cylinder Platform with the FLAG Radiation Magneto-Hydrodynamics Code

The Exploding Cylinder platform, recently demonstrated on the Z machine at Sandia National Laboratories, provides a means to study the evolution of unstable flows over many dynamical timescales.  The platform involves driving a cylindrical flyer plate radially outward which impacts a cylindrical target.  The target consists of an unstable interface between a low- and high-density material.  The combination of azimuthal symmetry and the long drive times provided by Z allow the unstable interface to be driven for very long timescales, potentially enabling the study of the transition to turbulence.  We present modeling of this platform using the FLAG code, along with comparison to available data, to assess the prospects for this platform to study the transition to and evolution of HED turbulence.   

Measuring Viscosity in Materials At High Pressure and High Temperature

A material’s viscosity, or resistance to flow, is highly dependent on its thermodynamic conditions. Little is understood about the viscosity of systems under warm dense matter conditions (pressures above 100 GPa), as there are no viscosity measurements taken at pressures above 25 GPa and temperatures above 3000 K. We are developing an experimental platform to obtain viscosity measurements for materials under warm dense matter conditions through utilizing the viscous effect on the evolution of a sinusoidal shock front travelling through a planar target. We have preliminary viscosity measurements for both SiO2 and diamond at pressures above 500 GPa using this platform.   

Experimental measurements of rippled shock evolution in laser-driven targets at extreme pressures using 1D VISAR

We present the first results on time-resolved measurements of rippled-shock evolution at high energy density (HED) pressures using 1D VISAR and SOP diagnostics on the OMEGA EP laser. The experiment involves irradiating a target consisting of CH ablator and fused-silica sample with a modulated interface using two beams (~2.5 kJ, 20 ns), resulting in a ~300 GPa shock. The planar shock, driven by ablation, acquires the modulation at the interface, transitioning into a rippled shock. Initial shock amplitude is determined through shock-breakout times and impedance matching at the interface. Spatially and temporally resolved velocity of the rippled shock, extracted from VISAR data, enabled continuous tracking of its spatial amplitude. Our results are compared with synthetic diagnostics from 2D FLASH simulations, which not only qualitatively reproduce the observed data but also provide insights into the experiment's hydrodynamics. Expanding upon Sakharov et al.'s (1965) novel approach of estimating shear viscosity via perturbation decay on a rippled shock front, our technique shows promise in quantifying viscosity under extreme pressures in laser-driven experiments.   

Investigation of Richtmyer-Meshkov growth to study material viscosity at high pressures

An accurate understanding of viscosity trends of materials approaching the warm dense matter regime are poorly constrained and yet are important for diverse problems including mantle dynamics of super-Earths. Mantle dynamics drive a wide range of processes that shape terrestrial planets and the viscosity of a planet’s mantle at relevant pressures (>100 GPa) is a critical transport property. A major constituent in the mantle of Earth is MgO and is thus predicted to be prevalent in the mantle of super-Earths.  This work focuses on novel experiments to measure the viscosity of MgO at lower mantle conditions. Experiments were performed on OMEGA-EP to measure the growth of a shocked interface. We present preliminary computational results and analysis. We use an in-house finite volume code with AMR and a stiffened equation of state to simulate the Richtmyer-Meshkov instability. We present features of the Richtmyer-Meshkov instability in materials with a stiffened equation of state that deviate from the impulsive model. Lastly, we discuss how the features of our simulations are used in the design and analysis of the experiments.   

Viscosity Measurements in Shock-compressed Epoxy

Viscosity determines momentum transport in a system and plays a crucial role in mixing and growth of hydrodynamic instabilities. Viscosity measurements in High Energy Density (HED) states are particularly important to accurately develop hydrodynamic models and to bridge the gap between simulations and experimental results of complex systems such as Inertial Confinement Fusion (ICF). Inclusion of viscous dissipation in the modelling of ICF implosions has led to a better understanding of hot spot turbulence, demonstrating the pressing need for developing empirical viscosity diagnostics.

We measured viscosity in dynamically compressed Stycast 1266 (CH, 1.1 g/cc) by tracing the acceleration of particles embedded in the target. The OMEGA-60 laser facility was used to drive a shock (peak⁓248 GPa) through the CH target, which was embedded with stainless steel (7.8 g/cc) and titanium (4.56 g/cc) microspheres that were accelerated by the flow behind the shock. The particle positions were recorded with time-resolved X-ray radiography. The velocities of the particles and CH were used to determine the viscous and inviscid force contributions acting on the particles using a shock-particle forcing model. From the forces, we calculated the dynamic viscosity of CH to be less than 10 Pa-sec. A Bayesian inference analysis on the force model was performed to determine the probability distribution of viscosity for a given range of input variables.