Inertial Confinement Fusion Capsule Research Articles

Nonlinear flow of couple stress fluid layer over an inclined plate

The issue of stability of a thin couple-stress liquid layer flows on an inclined plane was inspected. The thin-film approximation was employed to obtain a Benney-like differential equation, that described the time record of the interface profile The linear transition state and reduction ratio of maximum classical (Newtonian) growth-rate were discussed. The complete evolution equation was solved numerically using the method of lines in order to support the novelty of the work. The linear stability could be enhanced by increasing the couple-stress coefficient and surface tension as well as reducing the inclination. However, the ordinary viscosity played an irregular role. The linear results predicted conditions (windows) in which the non-Newtonian film was more stable than its Newtonian counterpart. The nonlinear stimulation anticipated the existence of sock waves in certain situations. The appearance of instability through the linear subcritical region as well as irregular influences with respect to surface tension and couple-stress property was revealed. The nonlinear approach was more accurate in describing the stability issue than the linear one. Such results could be employed to attain the optimum statuses with regard to the film stability, and control the shock waves. They would not only enable accurate practical implementation in the design of inertial confinement fusion capsules and supernova explosions and implosions modelling, but also would allow for precise numerical simulation.

A Physical Metric for Inertial Confinement Fusion Capsules

The performance of fusion capsules on the National Ignition Facility (NIF) is strongly affected by the physical properties of the hot deuterium–tritium (DT) fuel, such as the mass, areal density, and pressure of the hot spot at the stagnation time. All of these critical quantities depend on one measured quantity, which is the ratio of the specific peak implosion energy to the specific internal energy of the hot spot. This unique physical quantity not only can measure the incremental progress of the inertial confinement fusion capsules towards ignition but also measures the conversion of the peak implosion kinetic energy of the pusher shell into the internal energy of the hot fuel in a capsule. Analysis of existing NIF shots to date are performed. The ratio metric is compared quantitatively with the ignition criterion. Results provide new perspectives on the NIF experiments by which the performance of the burning plasma can be determined and controlled through the fine tune of the implosion parameters, which improves future designs and predictions of the ignition capsules.

Validating methods for modeling composition gradients in planar shock experiments

An interface is Rayleigh–Taylor (RT) unstable when acceleration pushes a less dense material into a more dense one, and the growth of the instability is governed partly by the Atwood number gradient. Double-shell inertial confinement fusion capsules have a foam spacer layer pushing on an inner capsule composed of a beryllium tamper and high-Z inner shell, and so have RT unstable interfaces that require benchmarking. To this end, the results of a planar shock experiment with beryllium/tungsten targets are presented. One target had the normal bilayer construction of beryllium and tungsten in two distinct layers; the second target had the beryllium grading into tungsten with a quasi-exponential profile, motivated by the potential for reduced RT growth with the gradient profile. Simulations mimic the shock profiles for both targets and match the shock velocity to within 5%. These results validate the ability of our simulations to model double-shell capsules with bilayer or graded layer Be/W inner shells, which are needed to design future experiments at the National Ignition Facility.

Simulated impact of fill tube geometry on recent high-yield implosions at the National Ignition Facility

Inertial confinement fusion capsules fielded at the National Ignition Facility are filled with deuterium and tritium fuel by means of a fill tube. The fill tube introduces a low-density pathway into the fuel region of the capsule that allows high Z contaminant to invade the hot spot during the course of the implosion. A recent series of nominally identical high-yield implosions on the NIF has exhibited significant variability in performance. We evaluate the impact of the fill tube in these implosions computationally to determine whether variations in fill tube geometry could have contributed to this variability. The main contrast between the fill tube geometry in the six shots was the outer diameter of the capsule bore hole, a conical hole into which the fill tube is inserted. In our simulations, the geometry of the bore hole can play a significant role in the development of nonlinear flows seeded by the fill tube. We find that the amount of space between the bore hole and the fill tube is the primary factor that determines the amount of contaminant jetted into the hot spot by the fill tube and, in turn, the level of yield reduction due to the fill tube in our simulations. As a consequence, some capsules with 5 μm fill tubes are predicted to outperform capsules with 2 μm fill tubes. We also find that micrometer-scale changes to bore hole size can impact fusion yields by up to four times near the ignition threshold. Nevertheless, simulation trends do not reproduce experimental yield trends, suggesting that the fill tube geometry was not the primary factor contributing to the observed variability in performance and that the fill tube could be masking sensitivity to other asymmetries such as other micrometer-scale capsule defects like voids that were not included in our simulations.

Properties of superconducting MgB2 spherical shells deposited on 2 mm and 1 mm diameter Si3N4 spheres

Superconducting spherical shells may not only provide an appealing platform for exploring superconductivity in three-dimensional (3D) geometries with curved surfaces, but also be practically applied in important fields, such as in gyroscopes and gravimeters. In inertial confinement fusion (ICF), the perturbation on the target capsule caused by traditional contact support methods is recognized as one of the major contributors to performance degradation in ICF implosions. It was proposed recently that coating the capsule with a thin superconducting MgB2 spherical shell to realize non-contact support by means of magnetic levitation at the required temperatures K might offer a promising solution to this longstanding problem. To simulate the coating of ICF capsules, we deposited MgB2 spherical shells onto polycrystalline Si3N4 spheres (diameter d = 2 mm and 1 mm) via a hybrid physical–chemical vapour deposition technique. For both diameters, the spherical shells, of about 1 µm in thickness and covering the whole spheres completely, were polycrystalline with thin plate-shaped MgB2 crystallites oriented randomly and closely connected. The spherical shells exhibited superconducting transition at a zero resistance temperature of 38.5–39.4 K in four-probe resistance measurements and ideal diamagnetism at low temperatures in magnetization measurements, suggesting the good crystallinity and homogeneity of the shells. The upper critical field , the irreversibility field and the lower critical field were characterized and showed similar magnitudes and temperature dependencies for the d = 2 mm and 1 mm shells, yielding of 7–8 T and of 7–12 mT at 20 K. The superconducting critical current density values, evaluated from the magnetization hysteresis loops, were A cm−2 and A cm−2 at 20 K under zero and 2 T applied field, respectively, for the d = 1 mm shell. The occurrence of small flux jumps was observed at low temperatures up to 12 K and in low fields below 0.3 T. The results demonstrate the feasibility of fabricating MgB2 spherical shells with properties applicable to potential areas employing magnetic levitation such as in ICF and that MgB2 spherical shells may be exploited as an experimental system to study superconductivity in 3D curvilinear geometry.

What Machine Learning Can and Cannot Do for Inertial Confinement Fusion

Machine learning methodologies have played remarkable roles in solving complex systems with large data, well-defined input–output pairs, and clearly definable goals and metrics. The methodologies are effective in image analysis, classification, and systems without long chains of logic. Recently, machine-learning methodologies have been widely applied to inertial confinement fusion (ICF) capsules and the design optimization of OMEGA (Omega Laser Facility) capsule implosion and NIF (National Ignition Facility) ignition capsules, leading to significant progress. As machine learning is being increasingly applied, concerns arise regarding its capabilities and limitations in the context of ICF. ICF is a complicated physical system that relies on physics knowledge and human judgment to guide machine learning. Additionally, the experimental database for ICF ignition is not large enough to provide credible training data. Most researchers in the field of ICF use simulations, or a mix of simulations and experimental results, instead of real data to train machine learning models and related tools. They then use the trained learning model to predict future events. This methodology can be successful, subject to a careful choice of data and simulations. However, because of the extreme sensitivity of the neutron yield to the input implosion parameters, physics-guided machine learning for ICF is extremely important and necessary, especially when the database is small, the uncertain-domain knowledge is large, and the physical capabilities of the learning models are still being developed. In this work, we identify problems in ICF that are suitable for machine learning and circumstances where machine learning is less likely to be successful. This study investigates the applications of machine learning and highlights fundamental research challenges and directions associated with machine learning in ICF.

Application of the HeliosX ICF Advanced Propulsion Mission Analysis Code to Perturbed Interstellar Design Models

HeliosX is a system integrated programming design tool which has the purpose of calculating spacecraft mission profile and propulsion performance for inertial confinement fusion (ICF) driven designs. This code uses the vehicle configuration input and capsule assumptions and then calculates the likely mission profile for a given destination target. The key technology is the inclusion of the fusion propulsion system and an adequate modelling of its likely energy outputs. This paper discusses calculations for perturbed design concepts from a baseline model in both series and parallel thrust mode. These new concepts are collectively known as the advanced baseline models which are presented in preliminary form under the names Resolution, Endeavour and Pegasus. These are for missions to 4.3 ly in trip times of less than 100 years for flyby and rendezvous configurations carrying a 150 tons payload. The designs utilise an ICF capsule mass of 0.288 g filled with D-3He fuel detonated at a pulse frequency in the range 100-150 Hz. The calculations show that the propulsion systems are characterised by thrusts 0.3-2 MNkg-1, jet powers 1.2-9.2 TW and specific powers 2.9-5.1 MWkg-1 for interstellar missions at 0.045-0.049c. In addition to the preliminary mission performance calculations we also discuss the philosophy and methodology used in the design evolution. Keywords: Interstellar Studies, Fusion Propulsion, HeliosX, Project Icarus

Thermal transport in warm dense matter revealed by refraction-enhanced x-ray radiography with a deep-neural-network analysis

Transport properties of high energy density matter affect the evolution of many systems, ranging from the geodynamo in the Earth’s core, to hydrodynamic instability growth in inertial confinement fusion capsules. Large uncertainties of these properties are present in the warm dense matter regime where both plasma models and condensed matter models become invalid. To overcome this limit, we devise an experimental platform based on x-ray differential heating and time-resolved refraction-enhanced radiography coupled to a deep neural network. We retrieve the first measurement of thermal conductivity of CH and Be in the warm dense matter regime and compare our measurement with the most commonly adopted models. The discrepancies observed are related to the estimation of a correction term from electron-electron collisions. The results necessitate improvement of transport models in the warm dense matter regime and could impact the understanding of the implosion performance for inertial confinement fusion.

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.

Vorticity screening by dense layers

We investigate variable density layers in the presence of vortices, by analogy to line charges in the presence of a dielectric slab. We adapt solutions for dielectric layers from the literature to the variable density fluid case, obtaining exact hypergeometric expressions for flow velocities induced everywhere by a vortex in the vicinity of a finite-thickness slab of different densities. The dimensionless Atwood number, which appears naturally in other variable density phenomena, such as the Rayleigh–Taylor instability, reappears here as the natural ordering parameter for the influence of the slab, which acts primarily to screen the influence of vorticity across the slab to a lower effective circulation. The solution takes the form of scaling correction factors that might be applied to computational models or evaluated directly. Extensions, where vorticity is localized within the dense layer itself and amplified outside of it, are considered, as well as some speculative applications such as inertial confinement fusion capsule designs.

Benchmarking solid-to-plasma transition modeling for inertial confinement fusion laser-imprint with a pump-probe experiment

For laser direct-drive (LDD) fusion implosions, intense laser beams are used to directly illuminate the inertial confinement fusion (ICF) capsule. The laser beams' intensity nonuniformity (due to speckles) on the target can impose perturbation seeds which are subsequently amplified by Rayleigh-Taylor instability growth, thereby leading to degradation of ICF implosion performance. To devise methods to mitigate this issue, adequate understanding of the underlying so-called laser-imprinting process is required. Here, we report measurements and modeling of the initial plasma formation process which has been shown to affect the laser imprint. Specifically, we measured the transient transmission of a femtosecond probe pulse through a polystyrene target for different 100-picosecond pump pulse intensities pertaining to ICF conditions. The experimental data are used to benchmark a microphysics model of initial plasma formation that overall describes the observed dynamics, thus providing a validated solid-to-plasma modeling for laser-imprinting purposes in radiation-hydrodynamic codes to accurately simulate and design LDD targets.

Interstellar Propulsion Using Laser-Driven Inertial Confinement Fusion Physics

To transport a spacecraft to distances far beyond the solar heliosphere and around the planets of other stars will require advanced space propulsion systems that go beyond the existing technological state of the art. The release of fusion energy from the interaction of two low mass atomic nuclei that are able to overcome the Coulomb barrier offers the potential for ∼1011J/g specific energy release and implies that robotic missions to the nearby stars to distances of ∼5–10 ly may be possible in trip durations of the order of ∼50–100 years, travelling at cruise speeds of the order of ∼0.05–0.15 c. Such missions would be characterised with ∼kN-MN thrust levels, ∼GW-TW jet powers, ∼kW/kg-MW/kg specific powers. One of the innovative methods by which fusion reactions can be ignited is via the impingement of laser beams onto an inertial confinement fusion capsule, imploding it to a thermonuclear state. This paper gives an overview of the physics of inertial confinement fusion and the interaction of a laser beam with a capsule to include the simulation of a 1D particle-in-cell code calculation to illustrate the effects. In the application to deep space missions, various spacecraft concepts from the literature are discussed, and the range of values assumed for the pulse frequency, burn fraction and areal density appropriate for the mission are presented. It is concluded that advanced space propulsion via inertial confinement fusion is a plausible part of our future, provided that experimental validation of ignition is on the horizon and numerical models for feasibility concepts are developed to high fidelity and on a consistent basis.

The development of a high-resolution Eulerian radiation-hydrodynamics simulation capability for laser-driven Hohlraums

Hohlraums are hollow cylindrical cavities with high-Z material walls used to convert laser energy into uniform x-ray radiation drives for inertial confinement fusion capsule implosions and high energy density physics experiments. Credible computational modeling of hohlraums requires detailed modeling and coupling of laser physics, hydrodynamics, radiation transport, heat transport, and atomic physics. We report on improvements to Los Alamos National Laboratory's xRAGE radiation-hydrodynamics code in order to enable hohlraum modeling. xRAGE's Eulerian hydrodynamics and adaptive mesh refinement make it uniquely well suited to study the impacts of multiscale features in hohlraums. In order to provide confidence in this new modeling capability, we demonstrate xRAGE's ability to produce reasonable agreement with data from several benchmark hohlraum experiments. We also use xRAGE to perform integrated simulations of a recent layered high density carbon capsule implosion on the National Ignition Facility in order to evaluate the potential impacts of the capsule support tent, mixed cell conductivity methodologies, plasma transport, and cross-beam energy transfer (XBT). We find that XBT, seeded by plasma flows in the laser entrance hole (LEH), causes a slight decrease in energy coupling to the capsule and that all of these impact the symmetry of the x-ray drive such that they have an appreciable impact on the capsule implosion shape.

First graded metal pushered single shell capsule implosions on the National Ignition Facility

Graded metal pushered single shell (PSS) capsules are predicted to be a viable alternative to low-Z capsule indirect drive inertial confinement fusion (ICF) implosions for achieving high fusion yields [MacLaren et al., Phys. Plasmas 28, 122710 (2021)]. The first experiments with Be/Cr-graded metal PSS capsules indicate that the implementation of the principle design feature, the graded density inner metal layer, has succeeded in producing a stable implosion with performance in agreement with predictions. With 50% Cr concentration in the pusher, PSS capsules have greater than ∼2× higher shell densities during stagnation for enhanced core confinement and radiation trapping at ∼35% lower shell implosion velocities than low-Z capsules. High-energy >30 keV inflight shell radiography recorded 215 km/s implosion velocities and show that implosion Legendre mode P2 asymmetry can be tuned via inner-to-outer beam wavelength separation, similar to other implosions. Shell radiographs and neutron core images show similar P2 asymmetry, suggesting no symmetry swings between peak implosion velocity and stagnation times. Despite the modest implosion velocities, gas-filled deuterium–tritium capsule implosions generate 1015 neutron yields at relatively modest core ion temperatures of 2.75 keV, indicating that in spite of the high-density inner layer, the implosions have been stabilized by the design density gradient. When compared with hydrodynamic simulations, the measured yield-over-simulated is 35% due to fuel–pusher mix and other perturbations such as the capsule fill tube. Simple analytical scalings of hot spot pressure and neutron yield show that PSS implosions reach similar performance at lower implosion velocities and higher shell densities to low-Z ICF capsules.

Double cylinder target design for study of hydrodynamic instabilities in multi-shell ICF

Cylindrical implosions are used to study hydrodynamic instability growth for inertial confinement fusion (ICF) applications, as the cylindrical geometry allows for easier diagnostic access while retaining convergence effects. In this work, we use the established cylindrical implosion platform [Palaniyappan et al., Phys. Plasmas 27, 042708 (2020)] to inform the double shell ICF campaign [Montgomery et al., Phys. Plasmas 25, 092706 (2018)]. We present a design for a double cylindrical target as an analogue to the double shell ICF capsule in order to study hydrodynamic instability growth on the high-Z inner shell. Our design work is done with two-dimensional (2D) Eulerian radiation-hydrodynamics simulations, considering the axial uniformity of the implosion and feasibility of measuring the instability growth of pre-seeded single mode sinusoidal perturbations. We discuss in depth the design for a target to be directly driven at the OMEGA laser facility [Boehly et al., Opt. Commun. 133, 495 (1997)]. We evaluate the design for axial implosion symmetry and visibility of instability growth using synthetic radiographs constructed from the simulations, as the instability growth on the inner cylinder is experimentally measured using x-ray radiography of the implosion. We find that the seeded perturbation growth on the inner cylinder should be visible in an experiment, even with axial implosion asymmetry and preheat. We compare our 2D simulations with linear theory predictions for perturbation growth and show that a cylinder with lower azimuthal mode number (mode-20) perturbations compares more favorably with linear theory, while a cylinder with higher azimuthal mode number (mode-40) perturbations at the same starting amplitude saturates and is over-predicted by linear theory.

Interferometric microscope with a confocal focusing for inner surface defect detection of ICF capsule.

Inner surface defects of inertial confinement fusion (ICF) capsule are a key factor leading to ignition failure; however, there are still no effective and non-destructive detection methods available. To solve this problem, we propose the first interferometric microscope with confocal focusing (CFIM). CFIM first uses confocal technology to achieve accurate axial positioning of both capsule and the camera, thereby ensuring that the inner surface of the capsule is precisely and clearly imaged at the camera. Then, phase-shifting interferometry based on a short-coherence source and a spherical reference is applied to obtain inner defects result from null inner surface interferograms. In addition, in-situ focusing is realized by the axial adjustment of camera, but not by the capsule, to ensure that the outer defects and the fake inner defects caused by it have the same pixel coordinates, thereby solving the confusion of fake inner defects. The comparative experimental results of the CFIM and the scanning electron microscope (destructive detection) prove the feasibility of the proposed method. With unique precision confocal focusing and in-situ focusing ability, CFIM provides the first approach for non-destructive detection of inner surface defects of ICF capsule to the best of our knowledge.

Surface defect measurement of ICF capsules under a limited depth of field

A surface defect detection device based on null interferometric microscopy (NIM) enables the measurement of surface defects in inertial confinement fusion (ICF) capsules. However, the microscope objective with a large numerical aperture in NIM causes the depth of field (DOF) of the system to be shallow, limiting the field of view (FOV) of the measurement. To expand the measurement FOV, a reconstruction method for the defocused surface defects in the FOV is presented, the angular spectrum diffraction model from the surface to the tilted plane is established, and the phase recovery method of the defocused surface defects is proposed by the theory of angular spectrum diffraction. Both the simulated and experimental results show that the proposed method can achieve the phase recovery of the surface defects in the defocused state and expand the measurement FOV, which improves the measurement accuracy and efficiency of the surface defects of the ICF capsules.

Combined effects of viscosity and a vertical magnetic field on Rayleigh–Taylor instability

The utilization of an external magnetic field greatly enhances the ion temperature and neutron yield from inertial confinement fusion capsule implosions, and viscosity is important in damping the small-scale mixing. In this paper, we present a linear analysis on Rayleigh–Taylor instability in the presence of viscosity and a vertical magnetic field. Unexpectedly, we find that the combined effects may strongly suppress the instability when the ratio S between the viscosity and the magnetic field strength is equal to 0.1, but enhance the instability for sufficiently large S, particularly for perturbations with high wave numbers. Moreover, the growth rate for S = 10 is broadly the same as when the magnetic field is absent, namely, S = 0. Therefore, the suppression or enhancement of the growth rates is greatly dependent on the ratio S. This phenomenon may play an essential role in the dynamics of intracluster gas in astrophysics and the uniformity of the compression target in magnetic inertial fusion. At last, we confirm that the viscosity instead of the electric resistivity plays a more important role to determine the interface motion in relation to inertial confinement fusion.

Impact of areal-density asymmetries on the loss of confinement and ignition threshold in inertial confinement fusion capsules

In inertial confinement fusion implosion experiments, variations in the shell areal density reduce the shell's inertia to confine the core pressure. Distorted capsules with large areal-density modulations decompress faster than uniform capsules in the disassembly phase. A simple 3D analytic hot-spot model is derived to include the effects of low-mode areal-density modulations in the ignition criterion. The generalized 3D ignition criterion for low modes is shown to depend on both the harmonic mean and the arithmetic mean of the areal density. The “thin spots” in the shell are shown to dominate the loss of confinement as reflected by the harmonic mean definition of areal densities.

Characterization of Doping Distribution of ICF Capsules by X-Ray Tomography

A technique has been developed to characterize the doping concentration distribution of inertial confinement fusion capsules based on a method combining absorption retrieval, computerized tomography, and a gradient doping absorption model. The doping concentration distribution in a reconstructed slice of Si-doped capsules was obtained using this method and on average is in good agreement with contact radiography by comparison experiments. The established technique has been used to obtain a three-dimensional point cloud of the doping concentration distribution by reconstructing all of the slices for the doping capsules. Uncertainty of the doping concentration was analyzed, and the expanded uncertainty is approximately 0.1 at. % (K = 2).