Inertial Confinement Fusion Targets Research Articles

A physics-informed deep learning description of Knudsen layer reactivity reduction

A physics-informed neural network (PINN) is used to evaluate the fast ion distribution in the hot spot of an inertial confinement fusion target. The use of tailored input and output layers to the neural network is shown to enable a PINN to learn the parametric solution to the Vlasov–Fokker–Planck equation in the absence of any synthetic or experimental data. As an explicit demonstration of the approach, the specific problem of Knudsen layer fusion yield reduction is treated. Here, the predictions from the Vlasov–Fokker–Planck PINN are used to provide a non-perturbative solution of the fast ion tail in the vicinity of the hot spot, thus allowing the spatial profile of the fusion reactivity to be evaluated for a range of collisionalities and hot spot conditions. Excellent agreement is found between the predictions of the Vlasov–Fokker–Planck PINN and the results from traditional numerical solvers with respect to both the energy and spatial distribution of fast ions and the fusion reactivity profile, demonstrating that the Vlasov–Fokker–Planck PINN provides an accurate and efficient means of determining the impact of Knudsen layer yield reduction across a broad range of plasma conditions.

Confinement effects of mandrel degradation in ICF target fabrication.

Understanding and further regulating the degradation of mandrel materials is a key aspect of target fabrication in inertial confinement fusion (ICF). Here, a quasi-one-dimensional confinement model is developed using a series of single-walled carbon nanotubes with varying diameters (Dm), and the degradation of poly-α-methylstyrene (PAMS) as a typical mandrel material is investigated under such confined conditions by using the combined method of quantum mechanics and molecular mechanics. In comparison to the isolated system, the calculations show that confinement can decrease or increase the energy barriers of PAMS degradation, which directly depends on Dm. Following which a clear exponential relationship between the degradation rate of PAMS and its own density is derived, indicating that the density of PAMS can be used to regulate mandrel degradation. This work highlights the important effects of confinement on degradation and provides a valuable reference for further development of polymer degradation technologies in ICF target fabrication and other fields.

Magnetron sputter deposition of ultrathick boron carbide coatings on spherical substrates for inertial confinement fusion

Most designs of inertial confinement fusion (ICF) targets require ablators in the form of hollow spherical shells with an outer diameter of ∼1−3 mm and a wall thickness of ∼20−200 microns. Vapor deposition onto rolling spherical substrates (templates) is the generally preferred method for the fabrication of ICF ablators. Amorphous boron carbide (B4C) is a promising material for use as an ablator due to its favorable properties. However, the challenge lies in creating ultrathick B4C coatings with submicron-scale density uniformity on rolling spherical substrates. Here, we show examples from our ongoing systematic study of the deposition of B4C onto 2-mm-diameter Si spheres by radio-frequency magnetron sputtering (RFMS). We start with a RFMS recipe developed for depositing planar amorphous B4C films with close-to-zero residual stress and transfer the deposition process from stationary planar substrates to rolling spherical substrates. A major challenge of the deposition onto rolling spheres is preventing the formation of so-called nodular defects, attributed to the incorporation of particulates into the growing film. To address this challenge, we explore ways to minimize the generation and accumulation of particulates on the substrate holder by a combination of enhanced film adhesion to the substrate holder surface and removal of particulates from the holder area where spherical substrates are rolling. With this approach, we demonstrate the deposition of an ∼75-micron-thick B4C coating on a Si sphere.

X-ray continuum spectroscopy of inertial confinement fusion implosions at the National Ignition Facility

A methodology for measuring x-ray continuum spectra of inertial confinement fusion (ICF) implosions is described. The method relies on the use of ConSpec, a high-throughput spectrometer using a highly annealed pyrolytic graphite crystal [MacDonald et al., J. Instrum. 14, P12009 (2019)], which measures the spectra in the ≃20–30 keV range. Due to its conical shape, the crystal is sagittally focusing a Bragg-reflected x-ray spectrum into a line, which enhances the recorded x-ray emission signal above the high neutron-induced background accompanying ICF implosions at the National Ignition Facility. To improve the overall measurement accuracy, the sensitivity of the spectrometer measured in an off-line x-ray laboratory setting was revised. The error analysis was expanded to include the accuracy of the off-line measurements, the effect of the neutron-induced background, as well as the influence of possible errors in alignment of the instrument to the ICF target. We demonstrate how the improved methodology is applied in the analysis of ConSpec data with examples of a relatively low-neutron-yield implosion using a tritium–hydrogen–deuterium mix as a fuel and a high-yield deuterium–tritium (DT) implosion producing high level of the background. In both cases, the shape of the measured spectrum agrees with the exponentially decaying spectral shape of bremsstrahlung emission to within ±10%. In the case of the high-yield DT experiment, non-monotonic deviations slightly exceeding the measurement uncertainties are observed and discussed.

Bayesian inferences of electrical current delivered to shocked transmission lines

Small radius Bdot measurements of electrical current delivered by pulsed power devices are routinely compromised by electrode/convolute plasmas endemic to multiterawatt transmission lines. Inferences of delivered current unaffected by these issues have recently been obtained by numerically optimizing consistency between model predictions and local experimental velocimetry data, but these are only unique for shockless velocity profiles. Here, we describe a more general Bayesian method capable of inferring current despite the presence of shocks. Additionally, we describe uncertainty estimates and use of the technique on experimental data. This technique is the first to provide uncertainty estimates on the full current trace delivered to an inertial confinement fusion target.

Time-dependent density-functional-theory calculations of the nonlocal electron stopping range for inertial confinement fusion applications.

Nonlocal electron transport is important for understanding laser-target coupling for laser-direct-drive (LDD) inertial confinement fusion (ICF) simulations. Current models for the nonlocal electron mean free path in radiation-hydrodynamic codes are based on plasma-physics models developed decades ago; improvements are needed to accurately predict the electron conduction in LDD simulations of ICF target implosions. We utilized time-dependent density functional theory (TD-DFT) to calculate the electron stopping power (SP) in the so-called conduction-zone plasmas of polystyrene in a wide range of densities and temperatures relevant to LDD. Compared with the modified Lee-More model, the TD-DFT calculations indicated a lower SP and a higher stopping range for nonlocal electrons. We fit these electron SP calculations to obtain a global analytical model for the electron stopping range as a function of plasma conditions and the nonlocal electron kinetic energy. This model was implemented in the one-dimensional radiation-hydrodynamic code lilac to perform simulations of LDD ICF implosions, which are further compared with simulations by the standard modified Lee-More model. Results from these integrated simulations are discussed in terms of the implications of this TD-DFT-based mean-free-path model to ICF simulations.

Exploration of cross-beam energy transfer mitigation constraints for designing an ignition-scale direct-drive inertial confinement fusion driver

The compression of direct-drive inertial confinement fusion (ICF) targets is strongly impacted by cross-beam energy transfer (CBET), a laser-plasma instability that limits ablation pressure by redirecting laser energy outward and that is projected to be mitigated by laser bandwidth. Here, we explore various CBET mitigation constraints to guide the design of future ICF facilities. First, we find that the flat, Gaussian, and Lorentzian spectral shapes have similar CBET mitigation properties, and a flat shape with nine spectral lines is a good surrogate for what can be obtained with other spectral shapes. Then, we conduct a comprehensive study across energy scales and ignition designs. 3D hydrodynamic simulations are used to derive an analytical model for the expected CBET mitigation as a function of laser and plasma parameters. From this model, we study the bandwidth requirements of conventional and shock ignition designs across four different energy scales and find that they require between 0.5 and 3±0.2% relative bandwidth. Best mitigation is achieved when the beam radius over critical radius Rb/Rc is kept low during the drive while the plasma temperature is kept high. In a steady state, we find that the bandwidth required to mitigate 85% of CBET scales as (Rb/Rc)2.15Ln−0.58I0.7, where Ln is the density scale length, and I the laser intensity. Finally, we find that the chamber beam port layout does not influence CBET mitigation. In the case of a driver using many monochromatic beamlets, we find that ∼10 beamlets per port is required, with diminishing returns above ∼20.

Using Laboratory-Based X-ray Tomography for Metrological Measurements of Inertial Confinement Fusion Targets.

Using Laboratory-Based X-ray Tomography for Metrological Measurements of Inertial Confinement Fusion Targets.

Correcting Hohlraum Drive Asymmetry with Glow Discharge Polymerization Coated Capsule Shims

In inertial confinement fusion target design, the shape discrepancy between the cylindrical hohlraum and the spherical capsule creates a low mode asymmetry in the implosion. One way to correct such asymmetry is to shim the target capsule surface with extra mass in specific locations following a three-dimensional P4 Legendre mode. Previously, the desired surface pattern was precision machined out of the capsule. The resulting 2DConA experiments that investigated the implosion’s shape demonstrated the shimming method’s success. However, machining leaves large defects on the capsule surface that will degrade neutron yield in a DT implosion. An alternative shimming approach is to grow the pattern on the capsule surface using a glow discharge polymerization coating process in a stencil lithography application. In this paper, we discuss the fabrication, characterization, and challenges of making shimmed target capsules with this new method.

Study on the morphology of liquid–gas interface inside inertial confinement fusion target under the condition of temperature gradient based on Young–Laplace equation

This study investigates the morphology of the liquid–gas interface inside inertial confinement fusion targets with temperature gradients from the perspective of force balance. The effects of contact angle, liquid volume, temperature gradient, and target size on the interface morphology are discussed. The filling of the fuel and the preparation of the ice layer inside the target are carried out near the deuterium–deuterium triple point at 18.71 K, accompanied by temperature gradient distributions of different magnitudes. The morphology of the liquid–gas interface has a significant impact on the subsequent laser experiments. The differential equation for calculating the morphology of the liquid–gas interface under non-uniform temperature field is derived based on the Young–Laplace equation. In order to verify the accuracy and applicability of the model as well as to provide guidance for practical applications such as process optimization, experimental data within a temperature gradient range of 0.69–1.38 K/cm during the fuel filling process were selected. Image processing techniques, including denoising and edge detection, were applied to the experimental images. The obtained structured data were compared with the numerical solutions of the equation for the liquid–gas interface morphology. The accuracy of the equation was verified by the results. Based on this, the morphology of the liquid–gas interface of deuterium–deuterium inside targets under different experimental conditions was calculated. It was found that a smaller target radius, higher filling temperature, smaller contact angle, and larger temperature gradient are more conducive to subsequent experiments.

Advances in Electroplating Gradients and Thick Metallic Coatings on Microspherical Targets for Inertial Confinement Fusion

Electroplating remains an attractive deposition approach for fabricating metal microspherical targets for inertial confinement fusion because of its relatively fast deposition rates and ability to produce full-density small grain coatings. Here, we discuss recent advances that allow for coating thick (>60 µm) leak-free gold capsules and capsules with gradients of gold and silver. We present a new apparatus used for electroplating hollow microspherical (typically 2-mm diameter) mandrels and discuss the resulting surface roughness and sphericity obtained using this plating method.

Coupling multi-fidelity xRAGE with machine learning for graded inner shell design optimization in double shell capsules

Bayesian optimization has shown promise for the design optimization of inertial confinement fusion targets. Specifically, in Vazirani et al. [Phys. Plasmas 28, 122709 (2021)], optimal designs for double shell capsules with graded inner shells were identified using one-dimensional xRAGE simulation yield calculations. While the machine learning models were able to accurately learn and predict one-dimensional simulation target performance, using simulations with higher fidelity would improve design optimization and better match with the expected experimental performance. However, higher fidelity physics modeling, i.e., two-dimensional xRAGE simulations, requires significantly larger computational time/cost, usually at least an order of magnitude, in comparison with one-dimensional simulations. This study presents a multi-fidelity Bayesian optimization, in which the machine learning model leverages low-fidelity (one-dimensional xRAGE) and high-fidelity (two-dimensional xRAGE) simulations to more accurately predict “pre-shot” target performance with respect to the expected experimental performance. By building a multi-fidelity Bayesian optimization framework coupled with xRAGE, the low-fidelity and high-fidelity simulations are able to inform one another, such that we have: (1) improved physics modeling in comparison with using low-fidelity simulations alone, (2) reduced computational time/cost in comparison with using high-fidelity simulations alone, and (3) more confidence in the expected performance of optimized targets during real-world experiments. In the future, we plan to use this robust multi-fidelity Bayesian optimization methodology to expedite the design of graded inner shells further and eventually full capsules as a part of the current double shell campaign at the National Ignition Facility.

Ultrathick Boron Carbide Coatings for Nuclear Fusion Targets

Boron carbide is an attractive ablator for next-generation inertial confinement fusion (ICF) targets. Here we describe several aspects of our ongoing systematic studies of the deposition and processing of B4C coatings for ICF targets. We show that residual compressive stress in films can be reduced and the deposition rate increased by N-doping. We also demonstrate successful Si substrate etching and surface polishing and discuss remaining challenges and offer potential solutions to the buildup of particulates in the deposition chamber during prolonged coating runs, control of nodular growth defects, and lateral nonuniformity of film properties for deposition conditions with relatively low target-to-substrate distances.

Development of New Magnetron Sputter Deposition Processes for Laser Target Fabrication

Magnetron sputter deposition is an enabling technology for laser target fabrication. Solutions are readily available for the deposition of most sub-micron-thick elemental films on planar substrates. However, major challenges still remain for the development of robust deposition processes in regimes of ultrathick (over μm) coatings and nonplanar substrates. These challenging deposition regimes are directly relevant to laser target applications, including both sphero-cylindrical hohlraums and spherical ablators for inertial confinement fusion (ICF) targets. Understanding underlying physical mechanisms for a specific material system is crucial for process development, given the overall complexity of the deposition process, its nonlinear dependence on deposition parameters, and a very large process space, often precluding conventional process optimization approaches. Here, we describe our approach to developing new deposition processes and give practical advice with examples of new results from our ongoing studies of glassy boron carbide ceramics for next-generation ICF ablators and nonequilibrium gold-tantalum alloys for hohlraums for magnetized ICF schemes. Emphasis is given to two major challenges of ultrathick coatings related to achieving process stability and reducing residual stress.

Shock-induced metallization of polystyrene along the principal Hugoniot investigated by advanced thermal density functionals

To date, none of the ab initio molecular dynamics simulations of polystyrene, often used as an ablator material in inertial confinement fusion targets, with the standard ground-state exchange-correlation (XC) functional in density-functional theory can satisfactorily agree with experiments in terms of reflectivity measurements. We use recently developed thermal strongly constrained and appropriately normed Laplacian-dependent metageneralized gradient approximation XC density functional (T-SCAN-L) and thermal hybrid XC density functional (KDT0) to show that the inclusion of thermal and inhomogeneity effects is crucial for accurate prediction of structural evolution and corresponding insulator-metal transition (IMT) during shock compression. Optical reflectivity calculated as an indicator of IMT is in perfect accord with experimental data.

Fabricating Novel Geometries of GA-CH Aerogels Through Wax Infiltration and Leaching of Fused Quartz

General Atomics-Carbon Hydrogen (GA-CH) and General Atomics-Carbon Deuterium (GA-CD) aerogels have applications as inertial confinement fusion (ICF) targets at the National Ignition Facility, Omega Laser Facility, and Z Pulsed Power Facility. However, fusion experiments at these facilities require the fabrication of precise geometries of aerogels, achievable only by machining. Unfortunately, machining low-density (<50 mg/cm3) GA-CH aerogels is difficult, given their fragile structure. Higher-density GA-CH aerogels, although easier to machine, are left with a small nub after machining. This work investigates filling the GA-CH gel pores with wax to increase their machinability. The wax was added by exchanging the solvent of the GA-CH gel with melted wax. In addition, 1- to 2-mm spherical voids were created within the aerogels using fused quartz beads that were leached with hydrofluoric acid. Samples were characterized for contaminants, structural damage, dopant loss, and surface roughness using size measurements, scanning electron microscopy, Fourier transform infrared spectroscopy, micro-computed tomography imaging, and optical profilometry. Through advances in aerogel fabrication techniques, progress is made toward testing new ICF target designs.

Invited article: X-ray phase contrast imaging in inertial confinement fusion and high energy density research.

X-ray phase contrast imaging (XPCI) provides enhanced image contrast beyond absorption-based x-ray imaging alone due to refraction and diffraction from gradients in the object material density. It is sensitive to small variations in density, such as internal voids, cracks, grains, defects, and material flow, as well as to stronger density variations such as from a shock wave. Beyond its initial use in biology and materials science, XPCI is now routinely used in inertial confinement fusion (ICF) and high energy density (HED) research, first to characterize ICF capsules and targets, and later applied in dynamic experiments, where coherent x-ray sources, ultrafast x-ray pulses, and high temporal and spatial resolution are required. In this Review article, XPCI image formation theory is presented, its diverse use in ICF and HED research is discussed, the unique requirements for ultrafast XPCI imaging are given, as well as current challenges and issues in its use.

Studying the Marangoni effect in double emulsions with a hybrid multi-relaxation time lattice Boltzmann method–finite difference method

Two-phase mass transfer is a critical process in preparing the inertial confinement fusion target microsphere. It is essential to reveal the effect of Marangoni convection on the flow and mass transfer in double emulsions to prepare high-quality microspheres. This paper develops a two-dimensional two-phase flow and mass transfer model based on multi-relaxation time lattice Boltzmann method and finite difference method. The study of the Marangoni effect within the double emulsion under a shear flow is carried out. The results indicate that the slope parameter (which measures the sensitivity of surface tension to the variation of solvent) and initial solvent concentration crucially affect the mass transfer behavior and the magnitude of the Marangoni convection of double emulsions. When the slope parameter is zero, there is no Marangoni convection in the flow field, the magnitude of the vorticity field is minimal, and solvent diffuses uniformly and slowly to the outer water phase. However, at low values of slope parameter, the Marangoni vortex formed within the emulsion is weak, and few plumes appear in the concentration field; at higher values, the magnitude of the vorticity field increases, and a large number of plumes appear and merge. Compared with the slope parameter, the mass transfer process is less sensitive to the initial solvent concentration. Plumes appear and merge at three different initial solvent concentrations. The time required for double emulsions to develop into equilibrium is inversely proportional to the initial solvent concentration.

Accuracy of three-dimensional proton imaging of an inertial confinement fusion target assessed by Geant4 simulation

The Geant4 toolkit was used to perform benchmark Monte Carlo simulations of proton micro-tomography imaging. A phantom of an inertial confinement fusion (ICF) target was designed, based on experimental data. Simulations of STIM (Scanning Transmission Ion Microscopy) and PIXE (Particle Induced X-ray Emission) tomography were performed. Quantitative images were obtained from the TomoRebuild and JPIXET software packages, chosen for their ability to handle large solid angles of X-ray detection. The tomographic images were compared with the original phantom, used as a reference. For STIM-T, the accuracy of the calculated mass density was ≤ 2 % for TomoRebuild and ≤ 14 % for JPIXET. Corrections of X-ray production cross section and X-ray absorption were tested for the quantification of Ge, used as a dopant in the ICF target. The accuracy on the obtained Ge density was ≤ 2.9 % for TomoRebuild and ≤ 6.4 % for JPIXET, whereas the error was about 40 % without correction.

The importance of laser wavelength for driving inertial confinement fusion targets. II. Target design

We describe details of radiation-hydrodynamics simulations of directly driven targets for inertial confinement fusion using laser drivers with different laser wavelengths. Of particular interest here are comparisons of frequency-tripled glass (laser wavelength 351 nm) lasers with the argon fluoride (193 nm) and krypton fluoride (248 nm) excimer lasers and the effects that these laser wavelengths have on the target designs. We explore the effect these drivers have on the compromise involved between lowering laser plasma instabilities (LPIs) or hydrodynamic instabilities while providing high gains and seek to quantify this trade-off. Short-wavelength drivers have significant advantages, primarily in using less power and energy to drive targets. Additionally, they expand the allowed operating regime that is constrained by LPI avoidance and the production of higher pressures needed for more hydrodynamically stable targets. Potential disadvantages to shorter drive wavelengths, such as increased imprint, are examined and found to be unimportant.