Session PO6: Hydrodynamic Instability

Equal-Channel-Angular-Extrusion Be-Cu as a NIF Ablator

Equal channel angular extrusion (ECAE) Be-Cu is an alloy that may be useful as an ignition target ablator at the National Ignition Facility (NIF). Planar samples have been diamond turned to create a 0.25-$\mu $m amplitude sinusoid on one side. These have been mounted in hohlraum targets at the OMEGA laser and driven by a pressure approaching 2 Mbar and a radiation temperature that peaks near 160 eV in $\sim $6 ns. The resulting growth of the Rayleigh-Taylor instability has been examined with x-ray backlighting. With face-on imaging, we see no growth. However, with side-on radiography, parallel the grooves of the sinusoid, the twenty-times-greater \textit{$\rho $r} permits us with a 16-frame gated x-ray imager to see modulation of the Be-Cu foil as it is launched out of the end of the hohlraum. The x-ray transmission is deduced. Hydrodynamic modeling matches the radiation temperature of the hohlraum, and calculations are compared to the velocity of ejection of the sample. A 2D-Rad-Hydro code is used to calculate the sample mean x-ray mass absorption coefficient for the broadband backlighter energy. The time-dependent growth factor of the instability is estimated.   

NIF-ablator characterization experiments on the Omega laser system

A detailed understanding of the performance of candidate ablator materials is important for guiding the design of indirect drive ICF capsules for ignition. This includes, but is not limited to understanding measurements of preheat and instability growth. We have previously reported on the development of a high-growth planar Rayleigh Taylor platform in which we have demonstrated growth factors of 200x for sinusoidal 2-D modulations in CH foils. The technique has now been adapted to study 3D surface perturbations in actual NIF ablator materials. In this presentation we show the results of experiments carried out on sputtered Cu-doped Be with random surface perturbations at levels close to those expected on the NIF ignition capsule.   

Simulations of high-mode Rayleigh-Taylor growth in NIF ignition capsules

The inner surface smoothness requirement for NIF ignition capsules is driven by maintaining acceptable Rayleigh-Taylor (R-T) growth at the pusher/fuel interface. During the implosion, the DT fuel reaches higher density than the pusher material accelerating it. Growth near this interface is stabilized only by density gradient effects, plasma viscosity and mass diffusion. The density gradient is influenced by thermal conduction across the interface, in response to the difference in temperature in the x-ray absorbing pusher and the relatively transparent fuel. Thermal conduction models are uncertain in this regime ($\sim$10 g/cc and $\sim$30 eV), and may be significant in determining the overall R-T growth. The growth can be modified by varying the radial profile of a high-Z dopant in the ablator. To optimize capsule designs, we are performing 2D and 3D HYDRA simulations that resolve up to mode $\sim$2000. The results of this work will be presented.   

Effects of viscosity and mass diffusion on the Richtmyer-Meshkov instability at the DT-ice/Be interface

We use Miranda to simulate the Richtmyer-Meshkov (RM) instability at the DT-ice/Be interface of a National Ignition Facility (NIF) capsule in order to determine the stabilizing effects of viscosity and mass diffusion. The RM instability is driven by the first shock of the NIF drive. The simulations are in planar geometry and the interface includes a finite density gradient. We compare our numerical results with two linear analytical models that include viscous effects and comment on the fits. Preliminary results suggest that a new model that incorporates both viscosity and diffusion can be developed.   

Late time nonlinear hydrodynamic instabilities evolution-- theoretical and numerical investigation.

The dependence of the instability dynamics on the initial conditions (amplitude and spectrum) was studied numerically and analytically, using a mode coupling extension to Haan's and Ofer's models. Regimes of initial conditions, in which the growth rate of the instabilities are dominated either by the initial conditions or by mode coupling, were identified. Using these modal models in the mode coupling regime we were able to determine the different asymptotic power laws and coefficients of the growth rates of the different instabilities and present new relationships between them. Comparison between the newly derived power laws and those obtained in experiments, full numerical simulations and bubble competition models, in two and three dimensions, will be discussed.   

Multimode simulations of indirectly-driven high-convergence plastic capsules on Omega

An extensive Omega database of indirect-drive implosions with Ge-doped CH ablators and deuterium (DD) fuel has been developed over the past several years. Previously, nominally smooth capsules with fuel pressures from 5 to 50 atm were successfully analyzed [1] using the weakly nonlinear Haan saturation model. More recently, high-convergence (10 atm DD) targets were fielded with intentionally roughened ablators to test our modeling tools in a more nonlinear regime. Improved hohlraum modeling to accommodate the measured ($\approx$ 2x) enhancement (relative to nominal XSN opacity modeling) in gold M-band (2-5 keV) preheat and the use of thin walls ($\approx$ 2 micron) for non-perturbative diagnosis of core symmetry is implemented. A frequency-dependent source is then extracted to drive separate capsule-only simulations with HYDRA [2] in 2-D. Results of multimode simulations spanning RMS capsule roughness from 10-350 nm are presented and compared with data. \newline [1] P. Amendt, R.E. Turner, and O.L. Landen, PRL 89, 165001 (2002). \newline [2] M. Marinak \textit{et al}., PoP 8, 2275 (2001).   

Inference of ICF Implosion Core Mix using Experimental Data and Theoretical Mix Models

The mixing between fuel and shell materials in Inertial Confinement Fusion implosion cores is a topic of great interest. Mixing due to hydrodynamic instabilities can affect implosion dynamics and could also go so far as to prevent ignition. The goal of this work was to design direct-drive ICF experiments on OMEGA which have varying levels of mix, and subsequently to extract information on mixing directly from the experimental data using spectroscopic arguments. The experimental design was accomplished using hydrodynamic simulations and Haan's and Youngs' mix models, which make it possible to predict the mix levels of each experimental platform. These theoretical predictions were then compared to the information on mixing which was extracted from the experimental data. We aim to increase our confidence in the methods used to extract mixing information from experimental data, as well as to assess the range of validity and predictive capability of the mix models.   

Irradiation Uniformity in Direct-Drive Simulations Using 3-D Ray Trace

A crucial component in calculating the drive uniformity in ICF simulations with direct illumination is a detailed treatment of laser-ray propagation through the plasma atmosphere using information about the orientation of the individual laser beams and nonuniformity structure on the beams. The resulting nonuniformity in laser deposition can contain short-wavelength structure that would not appear in uniformity estimates that simply project laser beams onto a sphere. Further, the ray-trace simulations can be sensitive to details of how well the region around critical density has been resolved in the hydrodynamic simulation. The sensitivity of the resulting target drive to the numerical modeling of the ray-trace physics is discussed. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement DE-FC52-92SF19460.   

Stabilizing effect of anisotropic thermal diffusion on the ablative Rayleigh-Taylor instability

For more than twenty years, numerous analyses have been devoted to the instability of the ablation front in the context of inertial confinement fusion. It has been shown by several authors that the ablative Rayleigh-Taylor instability (RTI) is stabilized during the linear stage in contrast to the classical RTI. The physical origin of the dominant stabilizing effect has been attributed to blow-off convection or dynamical pressure correlated with the rocket effect. First, the work presented here clearly recalls that the main stabilizing effect can be understood as a transversal diffusive mechanism. This understanding suggests that anisotropic diffusion could be used to reduce the ablative RTI growth. In this Letter, we show, both on the basis of a linear theory of the ablative RTI and 2D hydrodynamic simulations, that anisotropic diffusion leads to a strong reduction of the ablative RTI growth rates, the mean flow being left unchanged. We then provide a simple method to produce such an anisotropy, using a laminated structure of the ablated material made up of successive layers of high and low conductivities. Finally, we present numerical simulations of the ablative RTI in a planar experimental configuration, confirming the theoretical predictions.   

Rayleigh--Taylor Growth and Spherical Compression Measurements of Silicon-Doped Ablators

X-ray emission from coronal photons emitted by high-atomic-number ($Z)$ layers has been proposed to shape the adiabat in the shell and reduce ablative Rayleigh--Taylor (RT) growth rates during shell acceleration.\footnote{ S. E. Bodner \textit{et al}., Phys. Plasmas \textbf{5}, 1901 (1998).} This effect has been studied with planar-foil experiments to measure the RT growth and low-adiabat spherical implosions to measure the total areal density for a mid-$Z$, silicon (Si), dopant using the OMEGA laser. Growth of perturbations at the ablation interface due to the RT instability is sensitive to the outer-shell adiabat. An implosion target's areal density is sensitive to the inner-shell adiabat and is a sensitive measure of preheat of the inner fuel. Plastic (CH) shells and planar foils are doped with Si with an atomic concentration of 4{\%} to 6{\%}. Experimental data are compared with the hydrodynamic modeling of both the ablation-interface RT growth and the spherical implosion total areal density. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement DE-FC52-92SF19460.   

Numerically Simulating Collisions of Plastic and Foam Laser-Driven Foils

Interest in experiments on colliding planar foils has recently been stimulated by (a) the Impact Fast Ignition approach to laser fusion [1], and (b) the approach to a high-repetition rate ignition facility based on direct drive with the KrF laser [2]. Simulating the evolution of perturbations to such foils can be a numerical challenge, especially if the initial perturbation amplitudes are small. We discuss the numerical issues involved in such simulations, describe their benchmarking against recently-developed analytic results, and present simulations of such experiments on NRL's Nike laser. \newline [1] M. Murakami \textit {et al}., Nucl. Fusion \textbf{46}, 99 (2006) \newline [2] S. P. Obenschain \textit{et al}., Phys. Plasmas \textbf{13}, 056320 (2006).   

Collisions of plastic and foam laser-driven foils studied by orthogonal x-ray imaging.

We report an experimental study of hydrodynamic Rayleigh-Taylor and Richtmyer-Meshkov-type instabilities developing at the material interface produced in double-foil collisions. Our double-foil targets consist of a plastic foil irradiated by the 4 ns Nike KrF laser pulse at $\sim $50 TW/cm$^{2}$ and accelerated toward a stationary plastic or foam foil. Either the rear side of the front foil or the front side of the rear foil is rippled. Orthogonal imaging, i. e., a simultaneous side-on and face-on x-ray radiography of the targets has been used in these experiments to observe the process of collision and the evolution of the areal mass amplitude modulation. Its observed evolution is similar to the case of the classical RM instability in finite thickness targets first studied by Y. Aglitsky \textit{et al}., Phys. Plasmas \textbf{13}, 80703 (2006). Our data are favorably compared with 1D and 2D simulation results.   

Effects of Preheating on Compression and Rayleigh--Taylor Growth in Planar Plastic Targets on OMEGA

Direct-drive inertial confinement fusion ignition target performance is sensitive to the details of thermal coupling, transport, and preheat that directly affect the fuel adiabat. The results of plastic, planar thin-foil acceleration and thick-foil compression experiments on OMEGA at laser intensities from $\sim $2 $\times $ 10$^{14}$ W/cm$^{2}$ agree well with 2-D simulations using a constant flux limiter (0.06). However, at intensities of $\sim $1 $\times $ 10$^{15}$~W/cm$^{2}$, a nonlocal thermal-transport model or time-dependent flux limiter is necessary to explain the experimental results. In addition, a deposited preheating of $\sim $30 J must be included into simulations at high drive intensities to match the experimental results. The reduction of the Rayleigh--Taylor growth of preimposed modulations at higher intensities correlates with measured hot-electron preheat. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement DE-FC52-92SF19460.   

Validation of Thermal Transport Modeling in Direct-Drive Targets Using Planar{\-}Foil Experiments on OMEGA

Ignition target designs for the direct-drive inertial confinement fusion rely on accurate modeling of thermal transport. Planar-foil OMEGA experiments were used to validate physics models used in 2-D hydrodynamic simulations. The acceleration experiments with 20-\textit{$\mu $}m-thick CH foil were conducted at laser intensities varying from $\sim $2 $\times $ 10$^{14}$~W/cm$^{2}$ to $\sim $1 $\times $ 10$^{15}$ W/cm$^{2}$. The acceleration was measured using side-on, streaked x-ray radiography. At low laser intensities of $\sim $2 $\times $ 10$^{14}$ W/cm$^{2}$, the 2-D simulations with a constant flux limiter of 0.06 agree very well with the experimental measurements, while at high laser intensities up to $\sim $1 $\times $ 10$^{15}$ W/cm$^{2}$, a nonlocal thermal transport model or time-dependent flux limiter is necessary to explain experiments. Results of simulations and comparison with the OMEGA experiments will be presented. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement DE-FC52-92SF19460.   

Laser direct-drive IFE targets: sensitivity to fabrication and drive asymmetries

A major challenge for direct-drive inertial fusion energy (IFE) is to create targets that produce significant gain and yet are resistant to the hydrodynamic instabilities that degrade yield. The seeds for these instabilities are the imperfections in both target manufacture and laser illumination. We consider fabrication flaws that occur primarily at surfaces and interfaces, and tend to peak at long wavelengths, although they are appreciable at small scales. Drive non-uniformities include those produced by optical smoothing, beam misalignment and power imbalance. Thus for laser direct-drive, the range of important unstable modes extends over a large wavelength range and to very small amplitudes. Accurate simulation of these modes places severe constraints upon the modeling. We discuss this, and present results using our massively-parallel radiation-hydrocode FAST, which is being used to simulate a variety of different IFE-based targets, including targets with low ignition energy ($E_{laser} \sim 500 kJ, G \sim 10-50$), higher energy, high gain targets ($E_{laser}>1MJ, G>100$), and shock-ignition designs.