Session UO05: ICF Hydro Instabilities & Numerical Methods

Modeling Target Defects in Direct-Drive Inertial Confinement Fusion

A range of experimental and simulation evidence suggests that isolated defects on the outside of cryogenic targets are able to play a significant role in degrading direct-drive inertial confinement fusion implosion performance, particularly in implosions with a low in-flight adiabat. A cryogenic target may have dozens of these defects, which originate during the high-pressure permeation fill and cooling cycle, and range in size from microns to tens of microns. Both simulations and experimental data have shown that small-scale laser imprint, while capable of generating hydrodynamic mix, does not appear to be the dominant mechanism of mixing ablator material into the hot spot. Previous modeling of defects tens of microns in size has shown that the resulting local perturbation growth can inject ablator mass into the hot spot, contributing to radiative cooling and loss of performance. In this talk we present the results of multidimensional simulations of smaller (micron-scale) defects in the context of more recent cryogenic target designs, addressing both the reduction in areal density and the transport of ablator material into the hot spot.   

Author not Attending

Meteors of emission arise from the growth of capsule perturbations and can inhibit yield amplification. High Z particulates, surface pits and internal voids have been identified as meteors seeds. Meteors of emission may also be caused by growth of inherent seeds at unstable interfaces. In conjunction, the metrology and calculations indicate that in nano-crystaline HDC, both pits and voids can inject ablator material. In this presentation we analyse how the void perturbation lead to the generation of meteors in NIF implosions, we investigate the dependence of the injected mass in function of void volume and depth and finally we show how the interaction between multiple void perturbation act like en effective roughness.   

Hydrodynamic Evolution of Perturbations Seeded by Rear Surface Isolated Defects

The hydrodynamic growth of pre-imposed isolated rear surface defects, 20 µm deep by 20 µm wide grooves, has been measured on the Nike laser. High resolution monochromatic x-ray imagers captured streaked and two-dimensional images of the defect evolution. High resolution FASTRAD3D simulations and analytic theory show excellent agreement with experimental results. Material accelerated into the groove produces an initial jet which is overtaken by multi-mode bubble and spike Rayleigh-Taylor growth. Similarities and differences between front and rear side seeds, as well as the role of the rarefaction wave will be discussed.

    

Measurements of laser bandwidth effect on laser imprinting.

Broad bandwidth promises to be an important improvement for future laser drivers with regard to LPI mitigation. Increased bandwidth is also an effective means for reducing laser imprint through more rapid laser smoothing, such as with induced spatial incoherence (ISI) or smoothing by spectral dispersion (SSD). Measuring this effect and benchmarking simulations is important for understanding the increased parameter space made available by the new drivers. The Nike laser has demonstrated capability to provide a wide range (0.2 – 3 THz) bandwidth on target. We will present results of using this capability together with the curved crystal monochromatic x-ray radiography to measure the effect of bandwidth on laser imprint.   

Measurements of Laser-Imprint Mitigation Using an Above-Critical-Density Foam Layer for Direct-Drive Inertial Confinement Fusion

In laser-direct-drive inertial confinement fusion, laser imprint caused by nonuniformities in the laser drive due to laser speckle can seed the Richtmyer–Meshkov and Rayleigh–Taylor hydrodynamic instabilities, which adversely affect the compression of the imploding shell. Reducing the growth rate of the Rayleigh–Taylor instability caused by laser imprint relies on increasing ablation velocity and density scale length at the ablation surface. To achieve these parameters and mitigate imprint we have proposed layering an above-critical-density foam layer on the surface of the target. Experimental validation of the foam-based imprint mitigation using x-ray radiography in planar experiments will be presented. Foams and solid targets were generated through the two-photon polymerization 3-D printing process and were compared to mass-equivalent polystyrene typically used in direct-drive shells. The targets with foam had a significant reduction in rR modulations (a factor of over 2.5 in rms) and the modulations that were measured were primarily caused by foam structure rather than laser imprint. The data collected from these experiments have allowed for iteration and improvements in target design, which are being used in the creation of 3-D printed spherical targets for the upcoming year.   

Magnetized Shock-Driven Implosion Platform at Omega for studies of Magnetized Transport Physics in Inertial Fusion Implosions

External magnetic fields applied to an inertial confinement fusion (ICF) implosion make the fuel ions gyrate around the B-field lines, which can improve the probability for fusion and potentially boost fusion energy gain. With recent advances facilitating the generation of very high B-fields, it is essential to experimentally investigate and characterize the effects of strong magnetization on the dynamics and symmetry of an ICF implosion. We have developed an experimental platform at the Omega laser facility for producing plasma conditions with the electrons and ions both strongly magnetized, suitable for the studies of magnetized transport properties in high-energy-density plasmas. The first observation [1] of how a strong, 500 kG, externally applied B-field increases the mode-2 asymmetry in these shock-heated ICF implosions will be discussed. Strongly magnetized electrons (ω_eτ_e ≫ 1) and ions (ω_iτ_i > 1) in the implosion restrict the cross-field heat transport necessary for lateral distribution of the laser and shock heating from the implosion pole to waist, causing an enhanced mode-2 asymmetry. This work was supported in part by the US DOE, the National Laser Users Facility and Laboratory for Laser Energetics. 

    

Effects of self-generated magnetic fields on the stagnation phase of cryogenic OMEGA implosions

In this work, the magnitude and evolution of self-generated magnetic fields in an Omega implosion is studied using the deceleration-phase code DEC2D. DEC2D simulates the stagnation-phase of implosions using an Eulerian moving mesh solver and models the growth of the Rayleigh-Taylor instability at the shell hot-spot interface. This instability can generate anti-parallel temperature and density gradients, producing Biermann battery magnetic fields. In order to model these magnetic fields, MHD solvers have been added in DEC2D: this includes advection, resistive diffusion, Nernst, thermal suppression, and the Righi-Leduc term. Maximum magnetic fields of ≈500 MG are estimated, with corresponding Hall parameters of ≈10. These estimates are in agreement with estimates in GORGON. However, we find that these magnetic fields in the Omega implosions occupy very small regions within the hot-spot ( ≈1-10 μm), with the field magnitude being significant only within 10 ps of stagnation, causing marginal increase in yield and ion temperature.   

Simulations of magneto-Rayleigh-Taylor instability growth in liner implosions at the Z facility

The magneto-Rayleigh-Taylor instability (MRTI) is a common feature of Z-pinch liner implosions, since the magnetic pressure driving the implosion also drives hydrodynamic instability growth at the outer liner surface. In the magnetized liner induced fusion (MagLIF) concept [1], MRTI can cause the liner to break up in-flight, degrading its ability to compress the fusion fuel. We present magnetohydrodynamic simulations of a series of experiments [2] at the Z-facility studying MRTI growth in metallic liner implosions with pre-machined sinusoidal initial conditions. We compare the instability amplitude growth and evolution of MRTI structure from the experimental radiographic images with synthetic data from multi-physics simulations in the ARES code. The role of the low density vacuum plasma, including the importance of anomalous resistivity, will be assessed.   

Design of a direct-drive experimental platform for exploring the effects of heterogeneous mix on fusion burn

      Recent experiments to quantify the impact of heterogeneous mix on thermonuclear burn have demonstrated that assumptions of a single temperature in the mix region and a single scale length describing mix morphology may not be adequate for a heterogenous mix burn model.  The experiments were performed at the NIF and utilized indirectly driven plastic capsules filled with a deuterated plastic foam of controlled coarseness, with tritium gas filling the voids in the foam.  A new approach utilizing larger (~2X diameter) directly driven capsules with higher laser drive coupling will enable much higher (~100X to 1000X) thermonuclear yields in a much larger (~100X) burn volume.  The higher yields will enable more constraining diagnostics including burn history measurements, neutron imaging, and spectroscopy (using dopants).  The new, direct-drive capsules will be filled with a recently developed 3D printed lattice – opening a wide range of possible experiments, including specified location of a deuterated lattice, controlled density and coarseness of the lattice, and structures imprinted in the lattice.  The proposed direct-drive platform (the “Bosque campaign”) will be compared with the previous indirect-drive platform (the “Marble campaign”).

    

Results of OMEGA Direct Drive and Polar Direct Drive implosions using 2-D simulations

The Defect Induced Mix Experiment (DIME) campaign¹ was a series of OMEGA capsule implosions designed to study mix in the present of quasi 2-D defects, such as equatorial trenches and fake fill tubes. The results could be compared to 2-D simulations. The capsules had ~430 micron outer radius, with 15 to 20 micron thick CH ablators and a 5 atm deuterium gas fill. These capsules were imploded in both 60 beam direct drive and 40 beam Polar Direct Drive (PDD) configurations with a 1 ns square pulse. The polar direct drive results were used to design subsequent National Ignition Facility PDD capsule implosions. We use the xRAGE Eulerian Adaptive-Mesh-Refinement computer code to model these implosions in 2-D with laser ray tracing and energy deposition. We find that we need to adjust the relative laser drive weight of the two beam angles in polar direct drive to account missing Cross Beam Energy Transfer physics. We compare our results to DD neutron yields, burn weighted DT Tion value, burn width, and synthetic x-ray emission images. We match most results for the direct drive capsules, but have more trouble matching the data in our PDD simulations.

 

¹M.J. Schmitt et al., Phys. Plasmas, 20, 056310 (2013)

    

Author not Attending

Over the past few years, the NRL theory group has presented and published a variety of theoretical works on the effect of nonlocal electron energy transport on fuel preheat and ablation layer broadening in direct drive laser fusion targets.  The goal is not an exact model arrived at by say a Monte Carlo simulation, but rather a model accurate enough and simple enough that it can be utilized at each time step of a fluid simulation.  This work focuses on the instability generated energetic electrons, from the 2 omega p instability (OMEGA) or from the Raman side scatter instability (NIF).   It looks into the preheat and ablation layer broadening specifically for structured targets like those spherical targets shot on the NIF facility by the URLLE and NIF group.  So far, the results agree reasonably well with the experimental results.  Also, the theory can be similarly formulated for the nonlocal deposition from the energetic tail of a Maxwellian.

    

Multispecies hybrid model applied to ICF pre-heat mixing

The assumptions behind hydrodynamic models can break down in certain regimes (e.g. shocks). Alternatively, kinetic models provide more accurate solutions, but require many more degrees of freedom. A hybrid model combines both hydro and kinetic models into a single system of equations and applies kinetic models where needed. We present a new hybrid model for multispecies plasmas which generalizes Degond et al.’s work [1] from a single species to a multi-species model and includes electric fields. Specifically, it combines multispecies Euler with Haack, Hauck, Murillo’s [2] recently formulated model. We apply this method to study species mixing in inertial confinement fusion experiments [3]. Simulation results indicate that more than one momentum transport equation is required to capture mixing. We determine which physical regions require multiple momentum equations using the Chapman-Enskog closure of the kinetic model in conjunction with numerical estimates of the Knudsen number.

[1] Degond, P., Jin S., Mieussens L., 2005, ‘A smooth transition model between kinetic and hydrodynamic equations’, Journal of Computational Physics, 209, 665-694, Elsevier

[2] Haack, J., Hauck, C., Murillo, M., 2017, ‘A Conservative, Entropic Multispecies BGK Model’, Journal of Statistical Physics, 168, 826-856, Springer

[3] Murphey, T., et al. 2021, ‘Results from single-shock Marble experiments studying thermonuclear burn in the presence of heterogeneous mix on the National Ignition Facility’, Journal of High Energy Density Physics, 38, Page, Elsevier

    

Vlasov–Fokker–Planck Modeling of Heat Flow Modifications Caused by Laser Absorption and Pondermotive Transport Effects

It has long been recognized that intense laser fields can modify electron transport in inertial confinement fusion (ICF) plasmas, especially near the critical density where a steep intensity gradient develops. A detailed kinetic understanding of transport in this scenario demands accounting for ponderomotive forces, collisional absorption, and electron–electron collisions with minimal approximations. To study these effects, we developed an extended Vlasov–Fokker–Planck approach where the distribution function is split into quasi-static (dc) and quasi-harmonic (ac) components, which obey coupled kinetic equations. The coupling terms give rise to inverse bremsstrahlung absorption, pondermotive forces, and modifications to the electron–electron collision operator. We demonstrate that these effects combine to dramatically alter the heat flux near the critical density. We discuss implications for direct-drive ICF and highlight the role of bandwidth relevant to next-generation broadband laser systems.

    

Studies of non-Maxwellian electron distributions in the coronal plasma of inertial confinement fusion implosions

Laser ablation of materials is mediated through inverse Bremsstrahlung heating, which converts laser energy into plasma thermal energy, and is an important process for Inertial Confinement Fusion (ICF). Inverse Bremsstrahlung heating has been predicted to modify the electron distribution function through preferentially heating slow-moving electrons [B. A. Langdon PRL (1980)]. The modification to the distribution function affects the electron transport and heat conduction, which are critical to model correctly in the context of ICF. To study this physics, we have conducted a set of implosion experiments at OMEGA where thin-glass spherical targets were imploded with 9 kJ of energy in a 1-ns pulse. Measurement of the x-ray emission history in multiple energy bands provided the primary data, which shows evidence for non-Maxwellian electron distributions in the coronal plasma. The reason for this is that the emission history is sensitive to the shape of the electron distribution function. The interpretation of the data is aided by simulations of the x-ray emission using a variety of electron distribution functions. The results show the electron distribution function is best described by the Langdon distribution. This work is supported by the DOE, the MIT/NNSA CoE and NLUF   

Low-Mode Asymmetries in Direct-Drive Implosion Prediction and Correction Using 3-D Modeling of Beam Balance, Beam Pointing, and Beam-Polarization Cross-Beam Energy Transfer Effects

A growing body of evidence suggests OMEGA implosions are more asymmetric than predictions. In particular, the low-mode-number asymmetries of core flow (mode 1) and a prolate/oblate shape to the core (mode 2) are commonly observed in the compressed core during cryogenic implosions. The source of these persistent drive nonuniformities has been studied using warm implosions that remove some of target-related uncertainties of cryogenic implosions. Fully 3-D cross-beam energy transfer modeling of implosions beam balance, beam pointing, and beam polarization is shown to predict mode‑1 absorption asymmetries that correspond well to the observed core flow direction. Modeling of implosions also predict absorption mode-2 asymmetries that correlate to observed compressed core shapes. The low-mode effects of beam balance, pointing, and polarization are found to be systematic and persistent from shot to shot, raising the possibility of correcting low-mode absorption nonuniformity by adjusting the beam balance to zero the modes. This may have advantages over the current procedure of using target offset to attempt to zero the core flow during cryogenic implosions.