Session PO6: Hydrodynamic Instabilities

Analysis of Laser-Imprinting Reduction in Spherical-RT Experiments with Si-Doped Plastic Targets

Nonuniformities seeded by both long- and short-wavelength laser perturbations\footnote{ V. N. Goncharov\textit{ et al.}, Phys. Plasmas \textbf{10}, 1906 (2003).} grow during shell implosion as a result of the RT instability, affecting the target performance.\footnote{S. X. Hu\textit{ et al.}, Phys. Plasmas \textbf{17}, 102706 (2010).} To study the effect of high-$Z$ dopants in the ablator material on laser imprint, spherical-RT experiments have been performed at the Omega Laser Facility using Si-doped plastic targets in the cone-in-shell configuration.\footnote{V. A. Smalyuk\textit{ et al.}, Phys. Rev. Lett. \textbf{103}, 105001 (2009).} Compared to the pure plastic target, radiation preheating from the dopant is expected to decrease the mass density at the ablation front and increase the stand-off distance between the ablation front and laser-deposition region, reducing the imprinting efficiency and the RT growth.\footnote{A. N. Mostovych\textit{ et al.}, Phys. Rev. Lett. \textbf{100}, 075002 (2008).} Analyses of experimental data using two-dimensional \textit{DRACO} simulations for cases with and without dopants will be presented. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-08NA28302.   

Preparing for OMEGA EP Validation of 1-D Multi-FM SSD for the NIF

Single-beam smoothing has been shown to be crucial for successful direct-drive target implosions. One-dimensional, Multi-FM smoothing by spectral dispersion (SSD) has been proposed to provide the required level of smoothing for the current NIF ignition point design. Validation experiments are being designed for OMEGA EP to verify Multi-FM SSD performance. Imprint studies in laser-driven planar foils will be performed. Corrugated foils with a sinusoidal surface modulation will provide a reference for calculating the equivalent surface roughness of the imprint. \textit{DRACO} simulations are being used to design the foil experiments, and set the foil thickness, laser spot size, and intensity. Results of \textit{DRACO} simulations, which include modeling of Multi-FM SSD, will be presented, comparing the expected experimental x-ray radiographs for a variety of SSD parameters (1-D, 1-D Multi-FM, and 2-D). This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-08NA28302.   

Laser imprint reduction with an under-dense foam and its effect on hydrodymamic instability growth

In the direct drive approach, inhomogeneities in the laser beam intensity distribution may create pressure perturbations on the target surface and induce hydrodynamic instabilities. These instabilities may decrease the fuel compression and reduce the energy gain. The control of the latter is one of the crucial problem of the Inertial Confinement Fusion. In order to control the laser energy distribution in the plasma, optical techniques of laser beam smoothing are implemented. Unfortunately, these techniques are not operational at early time and the instantaneous intensity fluctuations are imprinted in the solid target. It has been shown that an under-dense and under-critical foam, placed in front of the target could smooth the laser imprint at the beginning of the laser pulse [Depierreux et al, Phys. Rev. Lett. 102, 195005 (2009)]. In a recent experiment at the GEKKO XII facility, we have directly studied the effects of the foam on the hydrodynamic instability growth. The principles, the design and the first results of the experiment will be presented.   

Measurements of turbulent Kelvin-Helmholtz growth in planar targets on OMEGA

Kelvin-Helmholtz (KH) growth of pre-imposed 2D single-mode and 3D broadband modulations was measured with side-on, x-ray radiography on OMEGA. In experiments, a strong, laser-driven shock wave propagates along the plane separating carbonized resorcinol foam (CRF) with a density of 0.1 g/cc and Iodine-doped polystyrene (CH) with density of 1.4 g/cc. Modulations on the foam-CH interface grow due to KH instability after the shock sets a flow of foam material along the interface. The growth results of 2D and 3D modulations will be presented along with comparisons with 2D simulations and 3D turbulent KH models.   

Simulation and analysis of planar Kelvin-Helmholtz experiments on OMEGA

A recent series of experiments on OMEGA provided the first observation of the Kelvin-Helmholtz (KH) instability in a high-energy-density physics context (E. C. Harding, et al., Phys. Rev. Lett., \textbf{103}, 045005, 2009; O. A. Hurricane, et al., Phys. Plasmas, \textbf{16}, 056305, 2009 ). In these experiments, a laser initiated blast wave deposits vorticity along a perturbed foam-plastic interface, which rolls up due to the KH instability. We present three-dimensional simulations that resolve some of the finer aspects of these experiments, including a possible origin of the low-density ``bubbles'' that appear in the x-ray radiographs at late times. We comment on previously reported discrepancies between the initial experiments and two-dimensional simulations, and also provide comparisons with more recent data (V. A. Smalyuk, et al., unpublished, 2011). This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.   

Rayleigh Taylor Instability Growth in NIC Capsules with Engineered Defects

In order to achieve thermonuclear burn and energy gain in ICF capsules, the growth of hydrodynamic instabilities must be understood and controlled. Experiments are planned to measure time dependent hydrodynamic instability growth of engineered defects on the surface of NIC capsules using x-ray radiography. We will present an analysis of synthetic radiography from 2D and 3D HYDRA simulations with various x-ray drive fluxes and show how these results will be used to assess code predictions of instability growth and mix. We will also discuss how these results correlate with capsule performance and observables from hot spot self emission imaging and Ge spectroscopy.   

Preliminary results investigating mix in colliding-shock experiments

Experiments have been performed at the Omega laser facility to investigate turbulence-driven mix from two colliding shocks, such as expected in ICF ignition capsules. Two shocks were generated at either end of a cylindrical, CH foam. The evolution of an Al tracer layer at one end of the foam was measured using point-projection radiography. Comparison of this data with simulations from the code, RAGE has been done to improve its predictive capability for ICF experiments. RAGE implements the Besnard-Harlow-Rauenzahn (BHR) model, which is intended for turbulent transport in fluids with large density variations.   

Preliminary results from a shear-driven mix experiment

We present preliminary experimental results of a shear driven mix experiment. The target consists of two foam half-cylinders, cut lengthwise, in a Be cylinder. Between the two pieces of foam is an Al tracer layer. A plastic ablator is irradiated by laser beams, which drives a shock. The shock propagates at a different velocity in each foam, which creates a velocity shear. This shear in turn drives the turbulence. Using x-ray radiography, we measure the hydrodynamic evolution of the al layer. We will present the experimental results and compare them to simulations.   

Experimental investigation of bright spots in broadband, gated x-ray images of ignition-scale implosions on NIF

Bright spots in the intensity profile of broadband (h$\nu$ $>$ 8 keV), gated (dt = 30-80 ps) x-ray images of implosions have been observed and are attributed to hot-spot mix [Hammel et al, Phys. Plasmas 18, 056310 (2011)]. Bright spots form when the CH ablator material doped with Ge mixes with the lower Z (T, H, D, He) hot spot plasma, enhancing the local x-ray emission. The signal level of the bright spots was quantified for THD, DT, symcap and convergent ablator implosions using Fourier analysis. The power spectral density of the x-ray intensity profile has a low wavenumber (k$<$0.09 m-1) portion characteristic of the envelope of the framed image used to examine implosion symmetry, and high wavenumber (0.09 m-1$<$k$<$0.63 m-1) features caused by the bright spots. The power corresponding to the high-wavenumber portion of the spectrum is compared to hot-spot mix mass inferred from Ge K-shell x-ray spectroscopy [Regan et al., aps/dpp'11]. The potential of using this technique to assess hot-spot mix for capsule shells without Ge dopant are discussed.   

Investigation of hydrodynamic stability of OMEGA low-adiabat implosions using x-ray spectrally-resolved images recorded with MMI

Spherical plastic shells doped with a titanium tracer-layer on the inner surface and filled with deuterium gas were driven at OMEGA with low-adiabat shaped laser pulses. The titanium x-ray emission is primarily emitted at the collapse of the implosion and recorded with the gated, multi-monochromatic x-ray imager (MMI) instrument. The spectrally-resolved image data were processed to obtain narrow-band images and spatially-resolved spectra based on the x-ray line emission of titanium.\footnote{T. Nagayama, R.C. Mancini, R. Florido, R. Tommasini, J. Koch, J. Delettrez, S. P. Regan, V. Smalyuk, J. App. Phys. \textbf{109}, 093303 (2011).} The narrow-band images reveal the spatial distribution of titanium in the implosion core and thus provide an indication of the hydrodynamic stability of the implosion. The spatially-resolved titanium line spectra can be analyzed to extract the spatial distribution of electron temperature and density, and mixing in the implosion core.   

Observation of strong oscillations of areal mass in an unsupported shock wave produced by a short laser pulse

The first experimental study of hydrodynamic perturbation evolution in a strong unsupported shock wave, which is immediately followed by a rarefaction wave, is reported. Our planar solid polystyrene laser-machined targets, 50 to 100 $\mu $m thick, rippled from the front side with a single-mode wavelength 30 or 45 $\mu $m and peak-to-valley amplitude 4 to 6 $\mu $m, were irradiated with a 350 ps long Nike KrF laser pulse at peak intensity of up to 330 TW/cm$^{2}$. The perturbation evolution in the target was observed using face-on monochromatic x-ray radiography while the pulse lasted and for 3 to 4 ns after it ended. While the driving pulse was on, the areal mass modulation amplitude in the target was observed to grow by a factor of up to $\sim $4 due to the ablative Richtmyer-Meshkov instability. After the end of the pulse, while the strong unsupported shock wave propagated through the unperturbed target, the theoretically predicted large oscillations of the areal mass [A. L. Velikovich \textit{et al}., Phys. Plasmas \textbf{10}, 3270 (2003)] were observed. Multiple phase reversals of the areal mass modulation have been detected.   

First Measurements of Rayleigh-Taylor-Induced Magnetic Fields

The Rayleigh-Taylor (RT) hydrodynamic instability has been a concern for shell integrity during the acceleration phase of Inertial Confinement Fusion (ICF) implosions. However, RT can also induce magnetic fields and reduce electron thermal conduction to the ablation front. RT-induced magnetic fields on the order of a mega-Gauss have been theoretically predicted and simulated, but never measured. If present, these self-generated fields will reduce heat flux and affect implosion dynamics. An experimental method for measuring these elusive fields using a combination of mono-energetic proton radiography and Monte-Carlo simulations is described, and experimental measurements of RT-induced magnetic fields are presented. This work was performed at LLE and was supported in part by US DoE, the NLUF and FSC at U. of R., LLE, and LLNL.   

NIF Science Use: plan and designs for highly nonlinear ablative Rayleigh-Taylor Instability experiments

In the context of NIF Science User program we propose to study on the NIF ablative Rayleigh-Taylor Instability (RTI) in transition from weakly nonlinear to highly nonlinear regimes. NIF provides a unique platform to study the rich physics of nonlinear and turbulent mixing flows in High Energy Density plasmas because it can accelerate targets over much larger distances and longer time periods than previously achieved on the NOVA [1] and OMEGA [2,3] lasers. In one shot, growth of RT modulations can be measured from the weakly nonlinear stage near nonlinear saturation levels to the highly nonlinear bubble-competition, bubble-merger regimes and perhaps into a turbulent-like regime. The role of ablation on highly-nonlinear RTI evolution will be comprehensively studied by varying ablation velocity using indirect and direct-drive platforms. We will present detailed hydrocodes designs of these platforms and discuss the path forward for these experiments which use NIF diagnostics already qualified. [1] B. Remington \textit{et al.}, Phys. Plasmas \textbf{2}, 1, (1995). [2] L. Masse, \textit{et al.}, Phys. Rev. E \textbf{83}, 055401 (2011). [3] V. Smalyuk \textit{et al.}, Phys. Plasmas \textbf{13}, 056312 (2006).   

Late-time evolution of Rayleigh-Taylor instability in a domain of a finite size

For the first time a theoretical analysis was developed to systematically study the late-time evolution of Rayleigh-Taylor instability in a domain of a finite size. The nonlinear dynamics of fluids with similar and contrasting densities are considered for two-dimensional and three-dimensional flows driven by sustained or time-dependent acceleration. The flows are periodic in the plane normal to the direction of acceleration and have no external mass sources. Group theory analysis is applied to accurately account for the mode coupling. Asymptotic nonlinear solutions are found to describe the interface dynamics far from the boundaries and near the boundaries. The influence of the size of the domain on the diagnostic parameters of the flow is identified. In particular, it is shown that in a finite size the domain the flow is decelerating compared to spatially extended case. The theory outcomes for the numerical modeling of Rayleigh-Taylor instability and for the design of experiments in high energy density plasmas are discussed.   

Simulation of quasi spherical direct drive capsules for pulsed-power driven inertial fusion energy

Magnetic pressure from 35-MA current in a 1-mm-radius liner is equivalent to the ablation pressure in the beryllium pusher of an inertial fusion capsule in a 300 eV hohlraum and can, in principle, drive a Quasi Spherical Direct Drive (QSDD) fusion capsule to yields of $\sim $600 MJ with a 45 MA, 40 ns pulsed power driver. Analytic theory and 1D and 2D simulations of QSDD capsules show insensitivity to magnetic Rayleigh-Taylor instability, internal pulse shaping, efficient compression of cryogenic fuel on a low ($\alpha $=1.5) adiabat, hot spot heating, current diffusion into the hot spot with alpha trapping, and burn. However, practical QSDD capsules require a large rate of change of current dI/dt $\sim $1.5 MA/ns and are susceptible to a wall instability, which must be further mitigated.