Session VO2: ICF IV: Hydrodynamic Instability

Direct-Drive, Foam-Target ICF Implosions

CH foam targets with a glow discharge polymer (GDP) outer layer are mass-equivalent surrogates of cryogenic D$_{2}$ targets that can be used at room temperatures. The GDP layer is typically 5 \textit{$\mu $}m thick with a 1000-{\AA} Al overcoat and acts as a gas retention barrier for these targets that can be filled with either D$_{2}$ or DT. The $\sim $90-\textit{$\mu $}m-thick CH foam with a density of 0.18 g/cc is the ablator and the imploding fuel layer. The possible adiabats (\textit{$\alpha $}, defined as the fuel pressure divided by the Fermi pressure) for these targets are similar to those of cryogenic targets ranging from 1 $\le $ \textit{$\alpha $} $\le $ 25. High-gain targets are being scaled to the OMEGA laser energy to study and optimize low-adiabat, and shaped-adiabat, direct-drive implosions. The shell adiabat is shaped with the laser pulse by either launching a decaying shock wave (DS),\footnote{ V. N. Goncharov \textit{et al}., Phys. Plasmas \textbf{10}, 1906 (2003).} propagating a supported shock in a relaxing density profile (RX),\footnote{ K. Anderson and R. Betti, Phys. Plasmas \textbf{11}, 5 (2004).} or a combination of these two techniques. Target implosions will be analyzed with both 1-D and 2-D hydrodynamic simulations and this information will be used to optimize an overall target design for ignition experiments on the NIF. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC2-92SF19460.   

Numerical Investigation of Proposed OMEGA Cryogenic Implosions Using Adiabat-Shaping Techniques

The Laboratory for Laser Energetics continues to examine the performance of cryogenically fueled D$_{2}$ and DT direct-drive capsule implosions. Of particular concern is the experimental demonstration of the benefit of proposed adiabat-shaping techniques in implosion performance, especially in light of the current NIF baseline levels of laser smoothing. We present an overview of the predicted performance of the NIF 1.5-MJ, direct-drive point design under a series of laser-smoothing levels. This will serve to identify experimental scenarios that will be studied on the OMEGA Laser System. A series of laser-smoothing calculations employing current OMEGA cryogenic-system parameters, such as ice roughness and target positioning, will then be presented. These simulations will further determine the accessibility of implosions on OMEGA to the design space set by the NIF simulations and serve to outline the schedule for these critical cryogenic implosions on the OMEGA Laser System for the next few years. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement No. DE-FC52-92SF19460.   

Laser imprint suppression using high-{Z} layers at high foot intensities

Laser imprint experiments are carried out on the Nike KrF laser with induced spatial incoherence (ISI) smoothing. Most of the imprint occurs during the initial low-intensity (``foot'') part of the pulse, which is necessary to compress the target to achieve high gain. It has been found previously that a thin high-Z overcoat on the laser side of the target can be effective in suppressing imprint [S. P. Obenschain et al. Phys. Plasmas 9, 2234 (2002)]. The present experiments are designed to extend this method to higher foot intensities $(\sim10^{13} W/cm^2)$, approaching those of the current high gain pellet designs. Measurements of Raleigh-Taylor (RT) amplified areal mass non-uniformity are made by face-on x-ray radiography using Bragg reflection from a curved crystal coupled to an x-ray streak camera. X-ray flux from the high-Z layer is monitored using absolutely calibrated time-resolved x-ray spectrometers. Simultaneous side-on radiography using a curved crystal allows target trajectory measurement for comparison with simulations. The effect of the high-Z layers of varying thicknesses on ISI imprint as well as re-imposed ripple growth will be presented for two different materials (Au and Pd). This work is supported by US DOE/NNSA.   

Hydrodynamics of laser-driven double-foil collisions studied by orthogonal x-ray imaging

With this experiment we start the study of the physics of hydrodynamic instability seeding and growth during the deceleration and stagnation phases. Our first targets consisted of two separated parallel plastic foils -- flat and rippled. The flat foil was irradiated by the 4 ns Nike KrF laser pulses at 50 TW/cm$^{2}$ and accelerated towards the rippled one. Orthogonal imaging, i. e., a simultaneous side-on and face-on radiography of the targets has been used in these experiments. Side-on x-ray radiography and VISAR data yield shock and target velocities before and after the collision. Face-on streaks revealed well-pronounced oscillatory behavior of the single-mode mass perturbations. Both sets of synchronized data were compared with 1D and 2D simulations. Observed velocities, timing and the peak value of areal mass variation are in good agreement with the simulated ones.   

Measuring the character of mix in directly driven ICF implosions with pure tritium gas and a deuterated shell

We have designed, built, and fielded a unique experiment to measure the character and time dependence of atomic mix in directly driven plastic capsules. The DT yield, ion temperature, and time history of the burn are measured in two types of capsules, a reference capsule of 15-24 $\mu$m thick plastic (CH) and an experimental capsule of the same thickness but with a 1$\mu$m thick deuterated plastic (CD) layer on the inner surface. Both capsules are filled with 10 atm of nearly pure tritium gas containing $\sim$0.2 atm {\%} deuterium. Without atomic mix the DT yield of the experimental capsule should be comparable to the reference capsule. Measured yields of the CD capsules were 24 to 110 times larger than the CH capsules confirming the dominant role of atomic mix. By using a mix model to degrade the performance of the CH capsules to observed, and then comparing the results of that model, which assumes 100{\%} atomic mix, on the CD capsule, we can estimate the amount of atomic mix. We conclude atomic mix accounts for 40-75{\%} of the mixing. Non-atomic or ``chunk'' mix accounts for the rest. This work is funded by the U.S. DOE at Los Alamos and the U. of Rochester.   

Instability Analysis for Beryllium Ignition Capsules: Graded, Ungraded, and No Doping

Graded copper doped Beryllium capsules were introduced to dampen hydrodynamic instability growth during ICF ignition. A pure Be design with no doping may provides similar protection against instability growth. We have considered three designs with a uniform copper dopant: the first has 0.9\% Cu, the next has 0.3\% Cu, and the last is pure Be with no Cu doping. We have chosen the uniform designs so that their corresponding radiation pulses are similar to that of graded dopant designs, thereby allowing for their use in the same hohlraum as a graded dopant capsule. We have compared our capsules with a typical 5-layer graded design, and our uniformly doped designs performed in a similar fashion. Not only does the instability growth of the various capsules depend strongly upon where the initial perturbation has been seeded, but it also depends upon which mode has been dominantly excited. No capsule outperforms any other capsule at all modes. Consequently, the specific designs fielded at NIF will depend critically upon the ignition failure mode, and should be chosen to reduce the mode numbers most closely associated with failure.   

Mode-coupling and 3D effects in Indirect-Drive Rayleigh-Taylor experiments on OMEGA

Indirect-Drive Rayleigh-Taylor experiments have been performed on the OMEGA laser facility since 2002 with rugby-ball shaped hohlraums [1]. A set of consistent data has been acquired for different single mode wavelengths ($\lambda $ = 35, 50 and 70 $\mu $m) machined on brominated and germanium-doped samples. Hohlraum energetics was characterized by Dante measurements through the LEH while complementary shock breakout measurements or side-on radiography allow us to assess the x-ray flux incident on the wall-mounted sample. We recently address the problem of mode-coupling by comparing the growth of 2-mode patterns ($\lambda $ = 35 and 70 $\mu $m), either in phase or in opposite phase. Depending on phase one or the other wavelength becomes predominant. Comparison between the FCI2 code calculations and the experimental data will be shown. We will also compare the experimental growth of 3D pattern (70 $\mu$m * 70 $\mu $m) with the equivalent 2D ($\lambda $ =50 $\mu$m) one. \newline \newline [1] A. Casner \textit{et al.}, Proceedings of the 4$^{th}$IFSA Conference, Biarritz (2005).   

Experimental study of fill-tube hydrodynamic effects on implosions using capsules with plastic stalks

Cryogenic ignition experiments at the National Ignition Facility (NIF) are expected to use a fill tube to introduce liquid DT into the capsule prior to solid layer formation. This fill tube is expected to form a hydrodynamic jet during the deceleration phase of the implosion. Numerical simulations indicate that a 10$\mu $m tube with a 3$\mu $m hole has an acceptable impact on implosion performance, but experimental data validating these simulations are lacking. We therefore initiated experiments at the Omega laser facility to explore the hydrodynamic effects of stalks on implosion performance, and we recently obtained high-quality x-ray images of hydrodynamic jets created by 9-37 $\mu $m diameter stalks made of PAMS (polyalpha-methylstyrene). We discuss the experiments and compare the results to simulations   

Non-linear evolution of localized perturbations in the deceleration-phase of an imploding ICF capsule

The Rayleigh-Taylor instability at the interface layer between the hot spot and the dense fuel of an ICF shell can cause hot spot distortion resulting in ignition failure. The linear growth of this instability is reduced by the ablation of the dense shell due to electron conductivity and fusion alpha-particle transport. Here, we present high resolution numerical simulations of the evolution of localized mass perturbations well beyond the linear regime. We track the actual three-dimensional development of the instability by using a 2D code and initializing the perturbations in a narrow cone around the symmetry axis. The effectiveness of ablative stabilization is addressed by switching on and off the energy transport mechanisms in the code. It is found that the growth of the spikes is greatly reduced by the ablation from the hot spot. The effect is larger the smaller the perturbation wavelength. This stabilization mechanism is instead not very effective in limiting the amplification of the bubbles. We also compare the growth of 2D and 3D perturbations, both in the ablative and in the classical case.   

Bubble Acceleration in the Ablative Rayleigh--Taylor Instability

The deeply nonlinear evolution of the single-mode Rayleigh--Taylor instability (RTI) at the ablation front of an accelerated target is investigated in the parameter range typical of direct-drive inertial confinement fusion implosions. A new phase of the nonlinear bubble evolution is discovered. After the linear growth phase and a short constant-velocity phase, it is found that the bubble is accelerated to velocities well above the classical value. This acceleration is~ driven by the vorticity accumulation inside the bubble resulting from the mass ablation and vorticity convection off the ablation front. While the ablative growth rates are slower than their classical values in the linear regime, the ablative RTI grows faster than the classical RTI in the deeply nonlinear regime for DT ablators. This work was supported by the U.S. Department of Energy Office of Inertial Confinement Fusion under Cooperative Agreement Nos. DE-FC02-04ER54789 and DE-FC52-92SF19460.   

Initial condition versus mode-coupling dominance in the RT, RM, and KH hydrodynamic instabilities evolution-- theoretical and numerical investigation.

The Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholz (KH) instabilities evolution and scaling are subjects of intensive experimental and theoretical research because of its importance in inertial confinement fusion (ICF)$^{ }$and astrophysics. In this work, we analytically and computationally study the dependence of the instability dynamics on the initial conditions (amplitude and spectrum) using a mode-coupling extension to Haan's model [1-3]. We identify the regimes of initial conditions (i.c.), in which the growth rate of the instabilities are dominated either by the i.c. or by mode coupling, and find the transition region between the two regimes, similar to [4]. Using these modal models we were able to determine the different power laws and coefficients of the growth rates of the different instabilities and present new relationships between them. Comparison between the newly derived relationship and those derived from the bubble competition model [5] will be discussed. 1. S.W. Haan, Phys. Rev. A \textbf{39}, 5812 (1989) 2. S.W. Haan, Physics of Fluids B, \textbf{3}, 2349 (1991) 3. D. Ofer et al., Physics of Plasmas, \textbf{3}, 3073 (1996) 4. G. Dimonte et al., Phys. Rev. E \textbf{69}, 056305 (2004) 5. Oron et al., Physics of Plasmas, \textbf{8}, 2883 (2001)   

Distribution of Sizes and the Internal Structure of the Fragmented (``Mixed'') State Induced by Rayleigh-Taylor Instability

A study, based on simulations and experiments as well as analytical derivations, of the fragmented (``mixed'') state induced by the Rayleigh-Taylor instability at the interface between two fluids is presented. The distribution of sizes and the energy spectrum in the fragmented state are derived from the symmetries exhibited by the data. The exact (but not closed) kinetic equations for the distribution functions which describe the internal structure of the mixed state are derived. These equations resemble the kinetic equations for single-component inhomogeneous turbulence (T. S. Lundgren, Phys. Fluids \textbf{10}, 969 (1967)) but with additional terms which account for the effect of the sharp interface between the components. The capacity of these equations is tested by using a simple ``Vlasov-like'' closure. As expected, in the linear limit, the equations lead to the Rayleigh-Taylor dispersion relation.   

Stochastic model of the Rayleigh-Taylor turbulent mixing

We propose a stochastic model, which describes the random character of the Rayleigh-Taylor turbulent mixing. Fluctuations of the rate of momentum loss are accounted for through multiplicative noise with uniform and log-normal distributions. We show that the mixing growth-rate (so-called ``alpha,'' alpha = h/gt$^2$) is extremely sensitive to the stochastic effects and long tails of the distributions. The ratio between the rates of momentum loss and momentum gain as well as the rates of energy dissipation and energy gain is the statistic invariant and a robust parameter to diagnose for either sustained or time-dependent acceleration.   

Invariant, scaling and spectral properties of Rayleigh-Taylor turbulent mixing

Turbulent mixing induced by the Rayleigh-Taylor (RT) instability plays a key role in a variety of plasma phenomena, ranging from astrophysical and micro-scales. Based on the new theoretical concept, the rate of momentum loss, we develop a model, which accounts for the highly anisotropic and non-local character of the mixing dynamics and describes the transports of momentum and energy in the turbulent flow. It is shown that invariant, spectral and scaling properties of RT turbulent mixing are substantially different from those in isotropic Kolmogorov turbulence. For instance, the rate of momentum loss is the basic quantity of the turbulent mixing, similarly to the rate of energy dissipation in Kolmogorov turbulence. The velocity scales as square root of length scale and the spectrum of kinetic energy is proportional to k$^{-2}$ in RT flow, compared to the power 1/3 for velocity scale and k$^{-5/3}$ for velocity spectrum in classical turbulence. We discuss the model validation and the diagnostics of the turbulent flow quantities.   

Navier-Stoke And MHD Turbulence Based Similarity Scaling Criteria For Studying Astrophysics Using High Energy Density Laboratory Experiments

The Euler similarity criteria for the laboratory experiment of astrophysics phenomena and the time-dependent mixing transition are important concepts introduced recently for the laboratory astrophysics. Nevertheless, the Euler scaling cannot consider the distinctive spectral range of high Reynolds number turbulent flows found in the astrophysics problems. The time-dependent mixing transition could not indicate whether a flow that has just passed the mixing transition is sufficient to capture all the physics of the important spectral range. In this presentation, a new approach, based on Navier-Stokes and MHD turbulence, is developed in order to consider the distinctive spectral scales associated with the high Reynolds number flows. The Reynolds numbers required to reproduce the most important spectral range of the astrophysical flows are determined. Finally, the implications of our theory in planning future laser experiments or simulations are discussed.