Ignition Capsule Research Articles

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.

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.

Using distributions to understand neutron and x-ray production in ICF ignition capsules and other high energy density plasmas.

This paper describes how x-ray and neutron distribution functions can be useful tools to visualize the conditions measured in many types of plasma physics experiments. In particular, we model a standard inertial confinement fusion ignition capsule that consists of a Si doped plastic ablator surrounding a layer of deuterium-tritium (DT) ice as the yield varies from 18 kJ to 16.7 MJ and use the distribution functions to show that neutrons and high energy x rays (15keV) are produced under similar conditions when the yield is low. However, as the capsule starts to support a propagating burn due to alpha heating, the x rays and neutrons are produced under somewhat different conditions in different parts of the plasma. In particular, the x-ray production takes place mainly in the hot plastic ablator for the full yield ignition capsule under quite different plasma conditions from the DT region producing the 14MeV neutrons, which results in x-ray images with larger radii than the corresponding neutron images. These same distribution functions can be applied to many other plasma physics experiments.

Analytical physical models for cryogenic double-shell capsule design driven by Z-pinch dynamic Hohlraum

The Z-pinch dynamic Hohlraum (ZPDH) is a promising indirect-drive approach for inertial confinement fusion. The volume ignition capsule is more robust than the hot-spot ignition capsule for ZPDH due to the fact that the ZPDH radiation drive source has a high energy but low symmetry. Focusing on the ignition design of cryogenic double-shell volume ignition capsules using ZPDH radiation sources, three analytical physical models, including the ablation and implosion model, the shell collision model, and the burn fraction model, are established to quantitatively characterize the relation of capsule parameters. Robust capsule designs are then determined based on these analytical models together with 1D radiation hydrodynamics simulations. The results show that under the 10 ns, 308 eV radiation drive source produced by ZPDH with 50 MA load current, capsules with a large range of parameters can ignite. The fusion yield of the recommended capsule is 16.0 MJ, and the absorbed energy is 1.28 MJ.

Mechanical property improvement of B4C ceramic hollow microspheres by doping carbon nanotubes at low-temperature

Boron carbide (B4C) ceramic hollow microspheres are considered to be a potential ignition capsule for inertial confinement fusion (ICF). B4C hollow microspheres with enhanced mechanical properties were obtained by pressureless calcination at low temperature with the addition of 2 wt% carbon nanotubes (CNTs). Notably, the microstructure of as-prepared microspheres directly reveals the strengthening mechanism is bridge toughening and pullout of CNTs. The density of B4C hollow microspheres reached 73.2% T.D. at 1000 °C when the doping amount of CNTs is 2 wt%. The crush load of B4C ceramic hollow microspheres (2 wt% CNTs) calcinated at 1000 °C is 25.3 N, while the crush load of the undoped samples under the same conditions is only 8.0 N. The improvement of mechanical properties of B4C hollow microspheres reduces the sensitivity of hollow microspheres to hydrodynamic instability in the high-temperature and high-pressure environment during fusion reaction, which can achieve relatively high fuel efficiency. Meanwhile, the B4C hollow microspheres with high surface finish and high strength as ICF target pellets can greatly reduce the influence of hydrodynamics instability on implosion and effectively improve the gain of the target.

Computational study of instability and fill tube mitigation strategies for double shell implosions

Double shell capsules are an attractive alternative scheme for achieving robust alpha-heating at the National Ignition Facility due to their low convergence ratio and low predicted temperature for achieving volume ignition. Nevertheless, simulations suggest that double shell targets are more susceptible to the fill tube, used to fill the inner shell with liquid DT, than typical single-shell ignition capsule designs, due to the higher density gradient between the shell and the fill tube hole, a lower outer shell velocity, which prevents the implosion from catching up to the initial fill tube jet, and the absence of a rebounding shock through the foam to slow this jet. Double shells are also highly susceptible to the Rayleigh-Taylor instability at both interfaces with the high density inner shell. Combined, these effects are predicted by radiation-hydrodynamics simulations to reduce fuel confinement and temperature, resulting in reduced performance by a factor of ≈20–45, depending on design details, compared to idealized one-dimensional (1D) simulations. We discuss a mitigation strategy for both the interfacial instabilities and the fill tube that is predicted by simulations to decrease the yield degradation to a factor of ≈4. The mitigation strategy involves a modification of the capsule geometry as well as the use of a multishock pulse shape. The multishock pulse is required for the fill tube mitigation strategy and has the added benefit of stabilizing perturbations at the foam/pusher interface without decreasing 1D yield. In order to experimentally verify these predictions, we discuss the potential use of a hydrogrowth radiography platform that could be applied to test the proposed mitigation strategies.

Surface morphology and microstructure evolution of B4C ceramic hollow microspheres prepared by wet coating method on a pyrolysis substrate

B4C hollow microspheres have been proposed as one of the promising ignition capsules for inertial confinement fusion (ICF). It is worth noting that the selection of easier-to-remove substrate materials is the key to obtaining B4C hollow microspheres. In this work, B4C core-shell microspheres with a uniform structure are prepared by the wet coating method on a PAMS substrate. After the calcination, the complete thermal decomposition of the PAMS substrate leads to a hollow structure B4C ceramic microsphere. The effects of solid content of coating slurry on the morphology and microstructure of the B4C core-shell microspheres were investigated in detail. The result shows that the spacing of the B4C particles in the slurry gradually decreases with increasing the solid content, resulting in an increase in the surface tension of the slurry and an improved stabilization, which helps to optimize the surface roughness and sphericity of the B4C microspheres.

Progress toward a self-consistent set of 1D ignition capsule metrics in ICF

One-dimensional metrics can be considered an upper bound on the performance that can be achieved given an implosion with an imploding mass Mimp and a given adiabat α, driven to an implosion velocity V by a specified ablation pressure Pa for single shell capsules with low-opacity ablators. The quantitative value of an ignition metric depends on the definition of ignition. We review the choices that have been made by various authors before settling on a definition based on yield amplification of 30 where yield amplification is the ratio of the yield from an implosion that includes the alpha particle and neutron deposition relative to the yield obtained from PdV work alone. We then derive improved 1D ignition metrics for radiation-driven inertial confinement fusion targets that span a wide range of drive pressures, adiabats, and scales. This includes emphasizing the importance of the total imploding mass and kinetic energy inside the ablation front, including the remaining ablator mass and kinetic energy, on the 1D ignition metrics. We have also explicitly included the sensitivity to ablation pressure driving the implosion, as well as the sensitivity to the coupling efficiency between the total incoming kinetic energy and the hot spot. For implosions in which the remaining ablator mass contributes to the total stagnated mass, we have developed an approach based on defining an effective implosion adiabat which incorporates the properties and the mass of the stagnated ablator as well as the cold DT fuel. We have added a dependence on total ρr to account for the fact that the time available for self-heating increases as the total ρr increases. This extends previous work in that the value of the product of stagnation pressure times burn width required for ignition depends on the total ρr as well as on the fuel ion temperature. Additionally, we show that ignition metrics derived from a requirement on the product of the hotspot ρr and the hot spot temperature are equivalent to ignition metrics derived from a requirement on the product of stagnation pressure and burn width. Further, we discuss those ignition metrics, developed as metrics for the underlying hydrodynamics in the absence of alpha heating, which can be used when alpha heating is present.

Octahedral spherical Hohlraum for Rev. 6 NIF beryllium capsule

We have designed an octahedral spherical hohlraum with 6 laser entrance holes (LEHs) for the Rev. 6 Be ignition capsule [Simakov et al., Phys. Plasmas 21, 022701 (2014)]. With a Au spherical hohlraum of 4400 μm in radius and six LEHs of 1200 μm in radius, a laser pulse of 2.15 MJ energy and 630 TW peak power is required to deliver the radiation drive designed for the Rev. 6 Be ignition capsule. Both our 1D and 2D simulations have shown that the expansion of the Be capsule is very close to or even slightly slower than that of the CH capsule under the same radiation drive inside the spherical hohlraum, in spite of the higher ablation rate of Be. The reason why the Be and CH capsules have similar expansions is due to their similar exhaust velocities, and the reason why CH has a slightly faster expansion is that the CH capsule has a higher opacity which causes the hotter ablated plasmas and then a faster expansion of the CH ablated plasmas. The large volume of the octahedral spherical hohlraum, together with the incident angle of 55° in its laser arrangement, leaves enough room for the laser transportation, thus avoiding the laser being absorbed by Be ablated plasmas and, consequently, avoiding the high risk of laser plasma instabilities. It means that the higher mass ablation rate of Be does not affect the hohlraum energetics and the naturally high symmetry of radiation inside an octahedral spherical hohlraum. Thus, the superior ablation properties of the Be capsule can be fully exploited and hence have a higher opportunity to achieve ignition inside the octahedral spherical hohlraum.

Absolute calibration of a time-resolved high resolution x-ray spectrometer for the National Ignition Facility (invited).

A high resolution, Diagnostic Instrument Manipulator (DIM)-based x-ray Bragg crystal spectrometer has been calibrated for and deployed at the National Ignition Facility (NIF) to diagnose plasma conditions in ignition capsules near stagnation times. The spectrometer has two conical crystals in the Hall geometry focusing rays from the Kr Heα, Lyα, and Heβ complexes onto a streak camera, with the physics objectives of measuring time-resolved electron density and temperature through observing Stark broadening and the relative intensities of dielectronic satellites. A third von Hámos crystal that time-integrates the Kr Heα, Heβ and intervening energy range provides in situ calibration for the streak camera signals. The spectrometer has been absolutely calibrated using a microfocus x-ray source, an array of CCD and single-photon-counting detectors, and multiple K- and L-absorption edge filters at the Princeton Plasma Physics Laboratory (PPPL) x-ray laboratory. Measurements of the integrated reflectivity, energy range, and energy resolution for each crystal are discussed. These calibration data provide absolute x-ray signal levels for NIF measurements, enabling precise filter selection and comparisons to simulations.

Effects of asymmetry and hot-spot shape on ignition capsules

Asymmetric implosion of inertial confinement fusion capsules is known, both experimentally and computationally, to reduce thermonuclear performance. This work shows that low-mode asymmetries degrade performance as a result of a decrease in the hydrodynamic disassembly time of the hot-spot core, which scales with the minimum dimension of the hot spot. The asymmetric shape of a hot spot results in decreased temperatures and areal densities and allows more alpha particles to escape, relative to an ideal spherical implosion, thus reducing alpha-energy deposition in the hot spot. Here, we extend previous ignition theory to include the hot-spot shape and quantify the effects of implosion asymmetry on both the ignition criterion and the capsule performance. The ignition criterion becomes more stringent with increasing deformation of the hot spot. The new theoretical results are validated by comparison with existing experimental data obtained at the National Ignition Facility. The shape effects on thermonuclear performance are relatively more noticeable for capsules having self-heating and high yields. The degradation of thermonuclear burn can be as high as 45% for shots with a yield lower than 2×10^{15} and less than 30% for shots with a higher yield.

A “polar contact” tent for reduced perturbation and improved performance of NIF ignition capsules

In indirectly driven Inertial Confinement Fusion implosions conducted on the National Ignition Facility (NIF), the imploding capsule is supported in a laser-heated radiation enclosure (called a “hohlraum”) by a pair of very thin (∼15–45 nm) plastic films (referred to as a “tent”). Even though the thickness of these tents is a small fraction of that of the spherical capsule ablator (∼165 μm), both numerical simulations as well as experiments indicate that this capsule support mechanism results in a large areal density (ρR) perturbation on the capsule surface at the contact point where the tent departs from the capsule. As a result, during deceleration of the deuterium-tritium (DT) fuel layer, a jet of the dense ablator material penetrates and cools the fuel hot spot, significantly degrading the neutron yield (resulting in only ∼10%–20% of the unperturbed 1-D yield). In this article, we present a hypothesis and supporting design simulations of a new “polar contact” tent support system, which reduces the contact area between the tent and the capsule and results in a significant improvement in the capsule performance. Simulations predict a ∼70% increase in neutron yield over that for an implosion with a traditional tent support. An initial demonstration experiment was conducted on the NIF and produced highest ever recorded primary DT neutron yield among all layered DT implosions with plastic ablators on the NIF, though more experiments are needed to comprehensively study the effect of the polar tent on implosion performance.

Stable and confined burn in a Revolver ignition capsule

The main burn phase physics in a Revolver ignition capsule is analyzed and found to exhibit a new feature where pusher stagnation is persistent and burn occurs with the fuel at a fixed volume. The pressure and density gradients at the fuel-pusher interface are both positive making it stable to Rayleigh-Taylor growth. Expansion cooling and RT mixing are absent from the Revolver burn during this time. The effect is due to the massive heavy metal pusher shell being compressed during implosion and heated on an inner layer by the Marshak wave. The pusher is driven to a higher pressure than the DT fuel and becomes a fuel confining shell starting at stagnation and continuing past the time of peak burn. This period of persistent stagnation lasts for approximately 100 ps (in the baseline design) with a fuel burnup during stagnation of 40%. This behavior does not occur in any other capsule designs, including the double shell schemes that also employ a heavy metal pusher.

Design of octahedral spherical hohlraum for CH Rev5 ignition capsule

In this paper, we design an octahedral spherical Au hohlraum for CH Rev5 ignition capsule [S. W. Haan et al., Phys. Plasmas 18, 051001 (2011)] by using the initial design method and two-dimensional (2D) simulations, and we investigate its laser entrance hole (LEH) closure and laser-plasma instabilities (LPI) by using a spherical hohlraum with two different-size LEHs via 2D simulations. The designed spherical hohlraum with RH=5 RC, RL=1.2 mm, and RL*=2RL requires an ignition laser pulse of 1.92 MJ in energy and 670 TW in peak power, where RH, RC, RL, and RL* are radii of the spherical hohlraum, capsule, LEH, and the cylindrical LEH outer ring, respectively. From 2D simulations, the closure and opening up of LEH are clearly obtained. The LEH closure and its rate are strongly connected to the radiation pulse, while the LEH opening-up and its rate are strongly connected to the laser pulse. The smallest radius of LEH during closure is 0.6 mm before opening up, which leaves enough room for arranging the laser beams with a radius of 0.5 mm in our design. By using a post-process code for LPI, a relatively high stimulated Brillouin scattering fraction and a very low stimulated Raman scattering fraction are predicted, which may be due to the neglection of three-dimensional density gradients of the ablative flow along the laser transportation in 2D simulations. This work provides the energy and power references for the future ignition laser facility which uses octahedral spherical hohlraums as ignition targets.

Shock-induced mix across an ideal interface

According to particle-in-cell and multi fluid simulations, as a planar shock propagates across an unperturbed classical interface, significant amounts of rearward shocked material are predicted to advect with the shock front over distances that are much larger than an ion-ion collisional mean free path of a shocked ion. This novel mechanism of interface mixing is found to scale strongly with the Mach number (∼M4) and produces an ion population bunch that penetrates the upstream material at nearly the shock speed. Possible implications for ignition capsule designs are conjectured.

P2 asymmetry of Au's M-band flux and its smoothing effect due to high-Z ablator dopants

X-ray drive asymmetry is one of the main seeds of low-mode implosion asymmetry that blocks further improvement of the nuclear performance of “high-foot” experiments on the National Ignition Facility [Miller et al., Nucl. Fusion 44, S228 (2004)]. More particularly, the P2 asymmetry of Au's M-band flux can also severely influence the implosion performance of ignition capsules [Li et al., Phys. Plasmas 23, 072705 (2016)]. Here we study the smoothing effect of mid- and/or high-Z dopants in ablator on Au's M-band flux asymmetries, by modeling and comparing the implosion processes of a Ge-doped ignition capsule and a Si-doped one driven by X-ray sources with P2 M-band flux asymmetry. As the results, (1) mid- or high-Z dopants absorb hard X-rays (M-band flux) and re-emit isotropically, which helps to smooth the asymmetric M-band flux arriving at the ablation front, therefore reducing the P2 asymmetries of the imploding shell and hot spot; (2) the smoothing effect of Ge-dopant is more remarkable than Si-dopant because its opacity in Au's M-band is higher than the latter's; and (3) placing the doped layer at a larger radius in ablator is more efficient. Applying this effect may not be a main measure to reduce the low-mode implosion asymmetry, but might be of significance in some critical situations such as inertial confinement fusion (ICF) experiments very near the performance cliffs of asymmetric X-ray drives.

Effects of mode coupling between low-mode radiation flux asymmetry and intermediate-mode ablator roughness on ignition capsule implosions

The low-mode shell asymmetry and high-mode hot spot mixing appear to be the main reasons for the performance degradation of the National Ignition Facility (NIF) implosion experiments. The effects of the mode coupling between low-mode P2 radiation flux asymmetry and intermediate-mode L = 24 capsule roughness on the implosion performance of ignition capsule are investigated by two-dimensional radiation hydrodynamic simulations. It is shown that the amplitudes of new modes generated by the mode coupling are in good agreement with the second-order mode coupling equation during the acceleration phase. The later flow field not only shows large areal density P2 asymmetry in the main fuel, but also generates large-amplitude spikes and bubbles. In the deceleration phase, the increasing mode coupling generates more new modes, and the perturbation spectrum on the hot spot boundary is mainly from the strong mode interactions rather than the initial perturbation conditions. The combination of the low-mode and high-mode perturbations breaks up the capsule shell, resulting in a significant reduction of the hot spot temperature and implosion performance.

Asymmetric-shell ignition capsule design to tune the low-mode asymmetry during the peak drive

The low-mode radiation flux asymmetry in the hohlraum is a main source of performance degradation in the National Ignition Facility (NIF) implosion experiments. To counteract the deleterious effects of the large positive P2 flux asymmetry during the peak drive, this paper develops a new tuning method called asymmetric-shell ignition capsule design which adopts the intentionally asymmetric CH ablator layer or deuterium-tritium (DT) ice layer. A series of two-dimensional implosion simulations have been performed, and the results show that the intentionally asymmetric DT ice layer can significantly improve the fuel ρR symmetry, hot spot shape, hot spot internal energy, and the final neutron yield compared to the spherical capsule. This indicates that the DT asymmetric-shell capsule design is an effective tuning method, while the CH ablator asymmetric-shell capsule could not correct the fuel ρR asymmetry, and it is not as effective as the DT asymmetric-shell capsule design.

Effects of the P2 M-band flux asymmetry of laser-driven gold Hohlraums on the implosion of ICF ignition capsule

Low-mode asymmetries in the laser-indirect-drive inertial confinement fusion implosion experiments conducted on the National Ignition Facility [G. H. Miller et al., Nucl. Fusion 44, S228 (2004)] are deemed the main obstacles hindering further improvement of the nuclear performance of deuterium-tritium-layered capsules. The dominant seeds of these asymmetries include the P2 and P4 asymmetries of x-ray drives and P2 asymmetry introduced by the supporting “tent.” Here, we explore the effects of another possible seed that can lead to low-mode asymmetric implosions, i.e., the M-band flux asymmetry (MFA) in laser-driven cylindrical gold Hohlraums. It is shown that the M-band flux facilitates the ablation and acceleration of the shell, and that positive P2 MFAs can result in negative P2 asymmetries of hot spots and positive P2 asymmetries of shell's ρR. An oblate or toroidal hot spot, depending on the P2 amplitude of MFA, forms at stagnation. The energy loss of such a hot spot via electron thermal conduction is seriously aggravated not only due to the enlarged hot spot surface but also due to the vortices that develop and help transferring thermal energy from the hotter center to the colder margin of such a hot spot. The cliffs of nuclear performance for the two methodologies of applying MFA (i.e., symmetric flux in the presence of MFA and MFA added for symmetric soft x-ray flux) are obtained locating at 9.5% and 5.0% of P2/P0 amplitudes, respectively.

Simulations of fill tube effects on the implosion of high-foot NIF ignition capsules

Encouraging results have been obtained using a strong first shock during the implosion of carbon-based ablator ignition capsules. These “high-foot” implosion results show that capsule performance deviates from 1D expectations as laser power and energy are increased. A possible cause of this deviation is the disruption of the hot spot by jets originating in the capsule fill tube. Nominally, a 10 μm outside diameter glass (SiO2) fill tube is used in these implosions. Simulations indicate that a thin coating of Au on this glass tube may lessen the hotspot disruption. These results and other mitigation strategies will be presented.