Session UO07: ICF: Hydrodynamic Instability

High-Resolution Planar-Foil In-Flight Density Profile Measurements on OMEGA EP

The in-flight density profile of the driven shell in an inertial confinement fusion implosion is an important quantity that depends on the shell adiabat and affects shell convergence and peak density. An experimental platform has been developed on OMEGA EP at the Laboratory for Laser Energetics to access similar physics by measuring the density profile of a planar foil. A 1 × 0.4 × 0.04-mm CH foil was driven by a 3-ns UV beam with 3 kJ focused to a 750-µm spot using a distributed phase plate. The density profile in the driven direction was measured using x-ray radiography and a Fresnel zone plate to achieve a spatial resolution of ~1 µm. Spatial blur from the movement of the driven target was minimized by using a 20-ps laser to drive the x-ray probe (Ti He_α = 4.75 keV). The interaction was probed at four time delays, starting from before the shock breaks out of the foil to the density profile during in-flight acceleration. The status of analysis, platform improvements, and comparison to DRACO hydrodynamic simulations will be presented.   

Numerical simulations of high-resolution in-flight density profile measurements on Omega EP

The in-flight shell-density profile is an important characteristic of an Inertial Confinement Fusion implosion which depends on the shell adiabat and affects shell convergence and peak density. Experiments on OMEGA-EP at the Laboratory for Laser Energetics were performed to measure the density profile of a planar CH foil driven by a single OMEGA EP beam. X-ray radiography imaging used Fresnel Zone Plates to achieve, for the first time, an unprecedented resolution of about 1 mm. Images were obtained at four time moments capturing the first-shock transit through the foil and the foil density profile evolution during acceleration. The measured profiles are compared with simulations using radiation-hydrodynamic code DRACO. Multi-dimensional effects which are consequence of the laser beam being wider than the foil are assessed. Sensitivity of the density profile to the equation of state, thermal and radiation transport, as well as the laser pulse shape is discussed.   

Laser wavelength dependence of laser imprint

A typical laser pulse in an inertial confinement fusion implosion includes a narrow-intensity pulse (picket) followed by the main drive pulse. The first picket launches a shock that sets the shell on a desired adiabat α. To minimize the asymmetry effects on implosion, laser beams typically have smoothing by spectral dispersion (SSD), which reduces single-beam imprint on a target surface seeded as the first shock travels through the shell. Current laser-direct-drive (LDD) experiments conducted on OMEGA show that imprint is a dominant performance-degradation mechanism for designs with α < 3, and that supplemental SSD techniques will be required to improve the performance of low-adiabat implosions. It is well understood that thermal-conduction smoothing plays a critical role in the smoothing of early-time perturbation seeds, and that increasing the size of the conduction zone should help in mitigating the laser imprint. Since longer-wavelength lasers deposit their energy at lower electron densities, the size of the conduction zone increases with the laser wavelength λL. This work will study the sensitivity of the laser imprint on λL, propose experiments on OMEGA to test the code predictions, and aid in the design of future laser facilities for high-yield LDD experiments.   

Amplification of laser imprint in the presence of strongly imposed target-normal magnetic fields

An experiment was performed on OMEGA EP investigating the predicted amplification of laser imprint by target-normal magnetic fields. A 30-µm-thick CH target was directly driven with a single beam without smoothing by spectral dispersion, allowing spatial modulations to be transferred to the target surface. Magnetic fields up to 45 T were imposed, and Rayleigh-Taylor amplification of the imprint seed was captured using x-ray radiography from a driven Gd backlighter. Analysis of these radiographs showed a 60% increase in the surface perturbation amplitudes in the presence of magnetic fields, consistent for all unsaturated frequencies and at all times probed. Similar 1-D hydrodynamics were observed, indicating that this increase was due to greater levels of laser imprint coming from the suppression of electron motion across the magnetic field lines and subsequent reduction in thermal smoothing. This shows that target-normal magnetic fields remain in the conduction zone of a driven target, consistent with theoretical predictions, though some discrepancy exists in the magnitude of predicted versus observed imprint effects. This provides important insights into the role of Nernst advection in magnetohydrodynamics.   

The Bosque Campaign on the National Ignition Facility to Understand the Coupling of Incomplete Material Mixing and Incomplete Thermalization on Thermonuclear Burn

Incomplete mixing and thermalization play a critical role in determining thermonuclear reaction rates in inertial confinement fusion (ICF) implosions [1-3]. Understanding this relationship is therefore critical to determine the impact of contaminant in ICF hot spots on yield.  The Bosque campaign is a polar-direct drive separated reactants implosion platform on the NIF to systematically study these effects in support of model development for radiation-hydrodynamics codes.  Bosque capsules contain 3D printed deuterated plastic lattices and are filled with mixtures of tritium with various other gases. By varying the composition of the gas fill, we can control the level of thermalization between the reactants.  By varying the lattice geometry, we can control the level of mixedness between the reactants. In this talk, we will discuss plans for the campaign as well as the results of platform development shots performed on NIF and OMEGA as well as plans for supporting campaigns on NIKE and LCLS.

 

 

[1] Haines et al., Nature Comm. 11:544, 2020.

[2] Albright et al., Phys. Plasmas 29:022702, 2022.

[3] Haines et al, Phys. Plasmas, 30:072705, 2023.   

Influences of Laser-Driven and Shock-Driven Preheat on 3D-printed Porous Media

Mixing of materials in porous media can cause a significant impact on fusion yield as previously demonstrated by the NIF MARBLEⁱ Campaign. Initially, the reactants are separated, with deuterium in the lattice struts and a tritium gas fill in the voids. Lattice parameters such as the strut thickness and relative pitch, provide a control for the mix parameters in the experiment. Los Alamos National Laboratory’s (LANL) BOSQUE project looks to better understand how the mixⁱⁱ of the reactants and shell materials impact the fusion burn and resultant yield on various laser platforms.

This study will aim to uncover how the sensitivities due to sources of preheat such as laser driven hard x-rays, hot electrons, and radiative shock effects alter the structure of the two- photon polymerization (2pp) lattice. We will explore various experimental setups and laser platforms as well as radiographic measurements of shock position and disk expansion to estimate preheat due to shock and preheat due to laser drive respectively.

ⁱ B. J. Albright et al., “Experimental Quantification of the impact of heterogenous mix on thermonuclear burn,” Physics of Plasmas 29, 022702 (2022)

ⁱⁱ B. M. Haines et al., “Observation of persistent species temperature separation in inertial confinement fusion mixtures,” Nat. Commun. 11, 544 (2020)   

Inertially confined fusion experiments using a 3D printed spherical capsule

Los Alamos National Laboratory’s Bosque experimental platform investigates the effects of heterogeneous mix on thermonuclear burn, as well as explores the capabilities of 3D printed capsules. This experimental campaign on the OMEGA Laser Facility used 3D printed 2PP (two photon polymerization) plastic lattices inside spherical capsule shells that are filled with either H₂ gas for carbon-deuterium-oxygen (CDO) printed lattices or D₂ gas for carbon-hydrogen-oxygen (CHO) printed lattices. Experimental results were compared to numerical simulations, which assumes complete atomic mixing. Observed yields agree with the simulations in the case of the CHO lattices with a D₂ fill gas; however, in the case of CDO lattices with an H₂ fill gas the experiment produced lower yields than what the simulations predicted. This discrepancy is possibly due to the inadequacy of the assumption of thermal equilibrium between CDO lattices and H₂ gas. This possible inadequacy of thermal equilibrium is further investigated through the analysis of Spectrally Resolved Electron Temperature (SRTe) diagnostics on the OMEGA platform. From this experimental campaign, predictive capabilities on the effects of material mix have been improved for on-going Bosque experiments on the National Ignition Facility.   

Electrothermal Filamentation of Fusion Plasmas

Electron currents within extremely dense (n > 10³² m^-3) , hot (T > 500 eV) plasmas are susceptible to filamentation via the electrothermal instability, yielding significant temperature and magnetic structures. The mechanism driving this instability has an intuitive picture; supposing that the temperature of an electron current is perturbed in the direction transverse to the current axis, hotter regions have an enhanced conductivity, giving an increased rate of Ohmic heating and thus increased temperature. The system of fluid equations describing a current, return current and background plasma are linearised to obtain the corresponding dispersion relation for the instability. Considering the particular plasma parameters of the cold, dense fuel layer of an imploded ICF capsule, this linear analysis predicts unstable modes for wavelengths larger than 2nm, with growth rates of the order 10¹⁵ s^-1. Particle-in-cell simulations are then employed to benchmark the growth rates, providing also a kinetic prediction for the non-linear growth and eventual saturation of the instability. The resulting temperature filaments are a candidate explanation for the non-Maxwellian nature of the fusing ions observed at the NIF.   

Comparing simulation and experiment for fuel-ablator mixing in HDC implosions at the NIF

A variety of features in high-density-carbon (HDC) ablators, such as pits, voids, high-Z inclusions, and the intrinsic microstructure of the HDC itself, are believed to lead to mixing of fuel and ablator in inertial confinement fusion (ICF) implosions. While ICF implosions with HDC have achieved ignition and delivered record fusion yields, significant uncertainty remains around whether performance in HDC implosions will be limited by pollution of larger-radius regions of the dense fuel with ablator, due to uncertainties around mix sources and modeling them. A series of experiments at the National Ignition Facility (NIF) has measured in-flight mixing of fuel and ablator for a variety of HDC implosions using high-resolution radiography. Here we present comparisons of high-resolution simulations, including modeling of HDC microstructure or defects, with these experiments. We assess resulting constraints on the modeling of perturbation sources in HDC implosions.   

The Role of Secular (Non-Exponential) Growth Caused by Mass Modulations in Inertial Confinement Fusion Implosions

It is well understood that nonuniformity seeds are amplified due to Rayleigh–Taylor (RT) instability developed during shell acceleration in inertial confinement fusion (ICF) implosions. If the perturbation amplitude a is sufficiently small (a < 0.1λ, where λ is the perturbation wavelength), the perturbations grow exponentially with the growth rate dependent on λ. In addition, because of finite shell thickness, developed modulation in shell areal density leads to modulation in acceleration g̃ across the shell. This results in an additional g̃t2 or secular growth,[1] which affects the amplitude of the exponentially growing mode. This talk will review the role of secular growth in ICF implosions and highlight a path for more-robust target designs.

Modeling Target Defects in Direct-Drive Inertial Confinement Fusion

A range of evidence from both radiation-hydrodynamic simulations and experiments 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. The highly nonlinear growth is not ablatively stabilized and can be an important degradation even for current best-performing OMEGA cryogenic implosions. A cryogenic target may have thousands of surface defects that originate during the high-pressure permeation fill and cooling cycle and range in size from microns to tens of microns. 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 [I. V. Igumenshchev et al., Phys. Plasmas 20, 082703 (2013)]. In this talk, we present the results of 2-D radiation-hydrodynamic simulations with DRACO 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.

Surface defect evolution in direct-drive ICF targets

Imperfections in ICF targets come in many forms, all of which generate seeds for hydrodynamic instability growth that ultimately degrade implosion performance. Surface defects, such as domes or divots on the surface of the outer-most plastic layer, have been shown to reduce areal density and compromise shell integrity during shock-transit and at the beginning of the acceleration phase. A recent campaign at the OMEGA facility performed in-depth surface characterizations and back-lit cone-in-shell implosions to image defect growth. Results from 2D axisymmetric simulations and experimental data will be presented.   

Stability of planar accretion shock fronts

Accretion shocks accompany stagnation, propagating into a fluid incident at an obstacle at supersonic velocity. Examples are the impacts of laser-driven foils (M. Karasik et al., Phys. Plasmas 17, 056317, 2010) or inverse z-pinch plasma flows (S. Merlini et al., arXiv:2306.01847v1) on stationary obstacles. Accretion shocks are not isolated, maintaining a causal contact between the obstacle and the shock front. Hence, the results of the planar shock-front linear stability analysis pioneered in the 1950s by D’yakov and Kontorovich (DK) for isolated shock waves are not directly applicable to the accretion shocks. We report theoretical and numerical analysis of the planar accretion shock front stability problem that puts to rest some long-standing controversies. We have found new eigenmodes of the spontaneous acoustic emission accompanying the DK instability and calculated the growth rate of 1D instability associated with normally incident sound-wave amplification at the shock front.   

Improving analytical models of Rayleigh-Taylor instability within plasmas

The linear Rayleigh-Taylor (R-T) instability with transport effects has long been studied analytically in the neutral fluid regime. However, the ways in which this picture may differ in plasmas has been given less consideration. By leveraging previous (plasma transport effect incorporating) numerical simulations of R-T at binary plasma interfaces, we show how multi-ion plasma diffusion, viscosity, and ion kinetic effects alter the linear R-T dispersion relation. Our insights inform an improved analytical dispersion relation for plasmas, which better matches the simulation data than previously established models. Additionally, we demonstrate that accurately capturing plasma R-T growth within fluid simulations requires employing asymptotically-correct viscosity coefficients.   

HED hydrodynamic modeling in 2D versus 3D: comparing anisotropy

A new method to quantify anisotropy as a function of length-scales is applied  to simulations of 2D and 3D Rayleigh-Taylor (RT) turbulence, which is inhomogeneous and anisotropic. We show that 3D RT has clear shape anisotropy at large scales with approximately 4:3 vertical to horizontal aspect ratio, but tends toward isotropy at small scales as expected. In sharp contrast, we find that RT in 2D simulations, which are still the main modeling framework for many applications,  is isotropic at large scales and its shape anisotropy increases at smaller scales where structures tend to be horizontally elongated. While this may be surprising, it is consistent with recent results in [1]; large-scale isotropy in 2D RT is due to the generation of a large-scale overturning circulation via an upscale cascade, while small scale anisotropy is due to the stable stratification resultant from such overturning and the inefficient mixing in 2D.

[1] Zhao, D., Betti, R., Aluie, H., J. Fluid Mech. 930, A29 (2022).