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To achieve hotspot ignition, an inertial confinement fusion implosion must achieve high hotspot pressure that is inertially confined by a dense shell of DT fuel. This requires a symmetric implosion having high in-flight shell velocity and high areal density at stagnation. The size of the driver and scale of the capsule required can be minimized by maintaining a high efficiency of energy coupling from the imploding shell to the hotspot. Significant 3D low mode asymmetries, however, are commonly observed in indirect-drive implosions and reduce the coupling of shell kinetic energy to the hotspot. To better quantify the magnitudes and impacts of shell density asymmetries, we have developed new analysis techniques and analytic models [Hurricane et al., Phys. Plasmas 27(6), 062704 (2020)]. To build confidence in the underlying data, we have also developed an analytic neutron transport model to cross-compare two independent measurements of asymmetry, which shows excellent agreement across shots for mode-1 (l = 1). This work also demonstrates that asymmetry can introduce potential sampling bias into down-scattered ratio measurements causing the solid-angle-average and uncertainty-weighted-average down-scattered ratios to differ significantly. Diagnosing asymmetries beyond mode-1 (l > 1) presents significant challenges. Using new diagnostic instruments and analysis techniques, however, evidence of significant Legendre mode P2 (l = 2, m = 0) and additional 3D asymmetries (l > 1, m ≠ 0) are beginning to emerge from the high precision activation diagnostic data (real-time nuclear activation detectors) and down-scattered neutron imaging data.

The shaping of the drive pulse in time is a key tool in the design of fusion experiments that use inertia to confine burning plasmas. It is directly related to the adiabat and compressibility of the DT fuel and the characteristics of the laser and target that are needed to ignite. With this in mind, we have performed experiments at the National Ignition Facility that test small changes in the shape of the pulse. In contrast to theory, we find implosions at lower adiabats can have reduced yield and areal density. We discuss implications to performance and the mechanism(s) that could be responsible.

Plasma jets, such as γ-ray burst jets, Herbig–Haro jets, μ-quasar jets, and active galactic nuclei jets, are found throughout the universe [S. Mendoza et al., Rev. Mex. Astron. Astrofis. 41, 453 (2005)]. Plasma jets are also present in indirect drive inertial confinement fusion experiments originating from the capsule's fill tube and occasionally from divots and voids in the capsules, particles on the exterior of the capsule, or from the tent holding the capsule in the target. This paper looks at two different gas-filled capsule implosions containing a plasma jet resulting from a capsule fill tube and fill channel, both of which utilized high density carbon ablators. Two models were developed, a drag and a snowplow model, which use the time-dependent motion of the injected mass through the hotspot to estimate the mass injected into the hotspot from the fill tube and channel, arriving at an average injected mass of ∼84.5 ± 25.5 ng for the first experiment and 91 ± 20 ng for the second experiment. Unlike previous methods to estimate fill tube injected mass, these techniques do not assume that the mixed mass is in thermal equilibrium with the hotspot or that the x-ray emission is only coming from within the hotspot itself. This paper also discusses the features seen in these experiments which include limb brightening in the shell for undoped ablators and flattening in the ablator from shadowing by the fill tube.

This paper analyzes x-ray-driven implosions that are designed to be less sensitive to 2D and 3D effects in Hohlraum and capsule physics. Key performance metrics including the burn-averaged ion temperature, hot-spot areal density, and fusion yield are found to agree with simulations where the design adiabat (internal pressure) is multiplied by a factor of 1.4. These results motivate the development of a simple model for interpreting experimental data, which is then used to quantify how improvements in compression could help achieve ignition.

Progress in inertial confinement fusion depends on the accurate interpretation of experiments that are complex and difficult to explain with simulations. Results could depend on small changes in the laser pulse or target or physics that are not fully understood or characterized. In this paper, we discuss an x-ray-driven platform [Baker et al., Phys. Rev. Lett. 121, 135001 (2018)] with fewer sources of degradation and find the fusion yield can be described as a physically motivated function of laser energy, target scale, and implosion symmetry. This platform and analysis could enable a more experimental approach to the study and optimization of implosion physics.

For many years, low mode asymmetry in inertially confined fusion (ICF) implosions has been recognized as a potential performance limiting factor, but analysis has been limited to using simulations and searching for data correlations. Herein, an analytically solvable model based upon the simple picture of an asymmetric piston is presented. Asymmetry of the shell driving the implosion, as opposed to asymmetry in the hot-spot, is key to the model. The model provides a unifying framework for the action of mode-1 shell asymmetry and the resulting connections between various diagnostic signatures. A key variable in the model is the shell asymmetry fraction, f, which is related to the areal density variation of the shell surrounding the hot-spot. It is shown that f is simply related to the observed hot-spot mode-1 velocity and to the concept of residual energy in an implosion. The model presented in this paper yields explicit expressions for the hot-spot diameter, stagnation pressure, hot-spot energy, inertial confinement-time, Lawson parameter, hot-spot temperature, and fusion yield under the action of mode-1 asymmetry. Agreement is found between the theory scalings when compared to ICF implosion data from the National Ignition Facility and to large ensembles of detailed simulations, making the theory a useful tool for interpreting data. The theory provides a basis for setting tolerable limits on asymmetry.

We describe the overall performance of the major indirect-drive inertial confinement fusion campaigns executed at the National Ignition Facility. With respect to the proximity to ignition, we can describe the performance of current experiments both in terms of no-burn ignition metrics (metrics based on the hydrodynamic performance of targets in the absence of alpha-particle heating) and in terms of the thermodynamic properties of the hotspot and dense fuel at stagnation—in particular, the hotspot pressure, temperature, and areal density. We describe a simple 1D isobaric model to derive these quantities from experimental observables and examine where current experiments lie with respect to the conditions required for ignition.

Computer simulations of high energy density science experiments are computationally challenging, consisting of multiple physics calculations including radiation transport, hydrodynamics, atomic physics, nuclear reactions, laser–plasma interactions, and more. To simulate inertial confinement fusion (ICF) experiments at high fidelity, each of these physics calculations should be as detailed as possible. However, this quickly becomes too computationally expensive even for modern supercomputers, and thus many simplifying assumptions are made to reduce the required computational time. Much of the research has focused on acceleration techniques for the various packages in multiphysics codes. In this work, we explore a novel method for accelerating physics packages via machine learning. The non-local thermodynamic equilibrium (NLTE) package is one of the most expensive calculations in the simulations of indirect drive inertial confinement fusion, taking several tens of percent of the total wall clock time. We explore the use of machine learning to accelerate this package, by essentially replacing the physics calculation with a deep neural network that has been trained to emulate the physics code. We demonstrate the feasibility of this approach on a simple problem and perform a side-by-side comparison of the physics calculation and the neural network inline in an ICF Hohlraum simulation. We show that the neural network achieves a 10× speed up in NLTE computational time while achieving good agreement with the physics code for several quantities of interest.

This work details a model used to infer the 3-D structure of the stagnated hot-spot and shell of inertial confinement fusion implosion experiments at the National Ignition Facility. The model assumes that 3-D low-mode drive perturbations can account for the majority of stagnation asymmetries experimentally observed. It uses an adaptive sampling algorithm to navigate the 24-D input parameter space to find a 3-D x-ray flux asymmetry whose application to an otherwise symmetric implosion results in a consistent match between synthetic and experimental diagnostic observables. The model is applied to a series of experiments and is able to achieve a consistent match for over 41 different observables, providing a high-fidelity reconstruction of the stagnation hot-spot and shell profile.

The Bigfoot approach to indirect-drive inertial confinement fusion has been developed as a compromise trading high convergence and areal densities for high implosion velocities, large adiabats, and hydrodynamic stability. Shape control and predictability are maintained by using relatively short laser pulses and merging the shocks within the deuterium-tritium-ice layer. These design choices ultimately limit the theoretically achievable performance, and one strategy to increase the 1D performance is to reduce the shell adiabat by extending the pulse shape. However, this can result in the loss of low-mode symmetry control, as the hohlraum “bubble,” the high-Z material launched by the outer-cone beams during the early part of the laser pulse, has more time to expand and will eventually intercept inner-cone beams preventing them from reaching the hohlraum waist, thus losing an equatorial capsule drive. Experiments were performed to study the shape control and predictability with extended pulse shapes in Bigfoot implosions, reducing the adiabat from nominally α ∼ 4 to α ∼ 3 and otherwise very similar experimental parameters. The implosion shape was measured both in-flight and at stagnation, with near-round implosions and low levels of P2 asymmetry throughout, indicating a maintained symmetry control with extended pulse shapes.

Computer models of inertial confinement fusion (ICF) implosions play an essential role in experimental design and interpretation as well as our understanding of fundamental physics under the most extreme conditions that can be reached in the laboratory. Building truly predictive models is a significant challenge, with the potential to greatly accelerate progress to high yield and ignition. One path to more predictive models is to use experimental data to update the underlying physics in a way that can be extrapolated to new experiments and regimes. We describe a statistical framework for the calibration of ICF simulations using data collected at the National Ignition Facility (NIF). We perform Bayesian inferences for a series of laser shots using an approach that is designed to respect the physics simulation as much as possible and then build a second model that links the individual-shot inferences together. We show that this approach is able to match multiple X-ray and neutron diagnostics for a whole series of NIF “BigFoot” shots. Within the context of 2D radiation hydrodynamic simulations, our inference strongly favors a significant reduction in fuel compression over other known degradation mechanisms (namely, hohlraum issues and engineering perturbations). This analysis is expanded using a multifidelity technique to pick fuel-ablator mix from several candidate causes of the degraded fuel compression (including X-ray preheat and shock timing errors). Finally, we use our globally calibrated model to investigate the extra laser drive energy that would be required to overcome the inferred fuel compression issues in NIF BigFoot implosions.

Machine learning is finding increasingly broad applications in the physical sciences. This most often involves building a model relationship between a dependent, measurable output, and an associated set of controllable, but complicated, independent inputs. We present a tutorial on current techniques in machine learning—a jumping-off point for interested researchers to advance their work. We focus on deep neural networks with an emphasis on demystifying deep learning. We begin with background ideas in machine learning and some example applications from current research in plasma physics. We discuss supervised learning techniques for modeling complicated functions, beginning with familiar regression schemes, and then advancing to more sophisticated deep learning methods. We also address unsupervised learning and techniques for reducing the dimensionality of input spaces. Along the way, we describe methods for practitioners to help ensure that their models generalize from their training data to as-yet-unseen test data. We describe classes of tasks—predicting scalars, handling images, and fitting time-series—and prepare the reader to choose an appropriate technique. We finally point out some limitations to modern machine learning and speculate on some ways that practitioners from the physical sciences may be particularly suited to help.

A comprehensive model is developed to study alpha-heating in inertially confined plasmas. It describes the time evolution of a central low-density hot spot confined by a compressible shell, heated by fusion alphas, and cooled by radiation and thermal losses. The model includes the deceleration, stagnation, and burn phases of inertial confinement fusion implosions, and is valid for sub-ignited targets with ≤10× amplification of the fusion yield from alpha-heating. The results of radiation-hydrodynamic simulations are used to derive realistic initial conditions and dimensionless parameters for the model. It is found that most of the alpha energy (∼90%) produced before bang time is deposited within the hot spot mass, while a small fraction (∼10%) drives mass ablation off the inner shell surface and its energy is recycled back into the hot spot. Of the bremsstrahlung radiation emission, ∼40% is deposited in the hot spot, ∼40% is recycled back in the hot spot by ablation off the shell, and ∼20% leaves the hot ...

This paper presents the spectroscopic aspects of using Krypton as a dopant in NIF capsule implosions through simulation studies and the first set of NIF experiments. Using a combination of 2D hohlraum and 1D capsule simulations with comprehensive spectroscopic modeling, the calculations focused on the effect of dopant concentration on the implosion, and the impact of gradients in the electron density and temperature to the Kr line features and plasma opacity. Experimental data were obtained from three NIF Kr-dopant experiments, performed with varying Kr dopant concentrations between 0.01% and 0.03%. The implosion performance, hotspot images, and detailed Kr spectral analysis are summarized relative to the predictions. Data show that fuel-dopant spectroscopy can serve as a powerful and viable diagnostic for inertial confinement fusion implosions.

Doppler broadening of the 14 MeV DT and 2.45 MeV DD fusion neutron lines has long been our best measure of temperature in a burning plasma. At the National Ignition Facility (NIF), yields are high enough and our neutron spectrometers accurate enough that we see finer details of the peak shape. For example, we can measure the shift of the peak due to the bulk motion of the plasma, and we see indications of non-thermal broadening, skew, and kurtosis of the peak caused by the variations of temperature and fluid velocity during burn. We can also distinguish spectral differences among several lines of sight. This paper will review the theory of fusion neutron line shape, show examples of non-Gaussian line shapes and directional variations in NIF data, and describe detailed spectral shapes we see in radiation-hydrodynamics simulations of implosions.

A supervised machine learning algorithm trained on a multi-petabyte dataset of inertial confinement fusion simulations has identified a class of implosions that robustly achieve high yield, even in the presence of drive variations and hydrodynamic perturbations. These implosions are purposefully driven with a time-varying asymmetry, such that coherent flow generation during hotspot stagnation forces the capsule to self-organize into an ovoid, a shape that appears to be more resilient to shell perturbations than spherical designs. This new class of implosions, whose configurations are reminiscent of zonal flows in magnetic fusion devices, may offer a path to robust inertial fusion.

Radiation-driven, layered deuterium-tritium (DT) implosions were carried out using 3-shock and 4-shock “adiabat-shaped” drives and plastic ablators on the National Ignition Facility (NIF) [E. M. Campbell et al., AIP Conf. Proc. 429, 3 (1998)]. The purpose of these shots was to gain further understanding on the relative performance of the low-foot implosions of the National Ignition Campaign [M. J. Edwards et al., Phys. Plasmas 20, 070501 (2013)] versus the subsequent high-foot implosions [T. Doppner et al., Phys. Rev. Lett. 115, 055001 (2015)]. The neutron yield performance in the experiment with the 4-shock adiabat-shaped drive was improved by factors ∼3 to ∼10, compared to five companion low-foot shots despite large low-mode asymmetries of DT fuel, while measured compression was similar to its low-foot companions. This indicated that the dominant degradation source for low-foot implosions was ablation-front instability growth, since adiabat shaping significantly stabilized this growth. For the experiment with the low-power 3-shock adiabat-shaped drive, the DT fuel compression was significantly increased, by ∼25% to ∼36%, compared to its companion high-foot implosions. The neutron yield increased by ∼20%, lower than the increase of ∼50% estimated from one-dimensional scaling, suggesting the importance of residual instabilities and asymmetries. For the experiment with the high-power, 3-shock adiabat-shaped drive, the DT fuel compression was slightly increased by ∼14% compared to its companion high-foot experiments. However, the compression was reduced compared to the lower-power 3-shock adiabat-shaped drive, correlated with the increase of hot electrons that hypothetically can be responsible for reduced compression in high-power adiabat-shaped experiments as well as in high-foot experiments. The total neutron yield in the high-power 3-shock adiabat-shaped shot N150416 was 8.5 × 1015 ± 0.2 × 1015, with the fuel areal density of 0.90 ± 0.07 g/cm2, corresponding to the ignition threshold factor parameter IFTX (calculated without alpha heating) of 0.34 ± 0.03 and the yield amplification due to the alpha heating of 2.4 ± 0.2. The performance parameters were among the highest of all shots on NIF and the closest to ignition at this time, based on the IFTX metric. The follow-up experiments were proposed to continue testing physics hypotheses, to measure implosion reproducibility, and to improve quantitative understanding on present implosion results.

A technique for measuring residual motion during the stagnation phase of an indirectly driven inertial confinement experiment has been implemented. This method infers a velocity from spatially and temporally resolved images of the X-ray emission from two orthogonal lines of sight. This work investigates the accuracy of recovering spatially resolved velocities from the X-ray emission data. A detailed analytical and numerical modeling of the X-ray emission measurement shows that the accuracy of this method increases as the displacement that results from a residual velocity increase. For the typical experimental configuration, signal-to-noise ratios, and duration of X-ray emission, it is estimated that the fractional error in the inferred velocity rises above 50% as the velocity of emission falls below 24 μm/ns. By inputting measured parameters into this model, error estimates of the residual velocity as inferred from the X-ray emission measurements are now able to be generated for experimental data. Details...

Integrated radiation hydrodynamic modeling in two dimensions, including the hohlraum and capsule, of layered cryogenic HighFoot Deuterium-Tritium (DT) implosions on the NIF successfully predicts important data trends. The model consists of a semi-empirical fit to low mode asymmetries and radiation drive multipliers to match shock trajectories, one dimensional inflight radiography, and time of peak neutron production. Application of the model across the HighFoot shot series, over a range of powers, laser energies, laser wavelengths, and target thicknesses predicts the neutron yield to within a factor of two for most shots. The Deuterium-Deuterium ion temperatures and the DT down scattered ratios, ratio of (10–12)/(13–15) MeV neutrons, roughly agree with data at peak fuel velocities

A series of indirectly driven capsule implosions has been performed on the National Ignition Facility to assess the relative contributions of ablation-front instability growth vs. fuel compression on implosion performance. Laser pulse shapes for both low and high-foot pulses were modified to vary ablation-front growth and fuel adiabat, separately and controllably. Three principal conclusions are drawn from this study: (1) It is shown that reducing ablation-front instability growth in low-foot implosions results in a substantial (3-10X) increase in neutron yield with no loss of fuel compression. (2) It is shown that reducing the fuel adiabat in high-foot implosions results in a significant (36%) increase in fuel compression together with a small (10%) increase in neutron yield. (3) Increased electron preheat at higher laser power in high-foot implosions, however, appears to offset the gain in compression achieved by adiabat-shaping at lower power. These results taken collectively bridge the space between the higher compression low-foot results and the higher yield high-foot results.

High Density Carbon (or diamond) is a promising ablator material for use in near-vacuum hohlraums, as its high density allows for ignition designs with laser pulse durations of

By increasing the velocity in “high foot” implosions [Dittrich et al., Phys. Rev. Lett. 112, 055002 (2014); Park et al., Phys. Rev. Lett. 112, 055001 (2014); Hurricane et al., Nature 506, 343 (2014); Hurricane et al., Phys. Plasmas 21, 056314 (2014)] on the National Ignition Facility laser, we have nearly doubled the neutron yield and the hotspot pressure as compared to the implosions reported upon last year. The implosion velocity has been increased using a combination of the laser (higher power and energy), the hohlraum (depleted uranium wall material with higher opacity and lower specific heat than gold hohlraums), and the capsule (thinner capsules with less mass). We find that the neutron yield from these experiments scales systematically with a velocity-like parameter of the square root of the laser energy divided by the ablator mass. By connecting this parameter with the inferred implosion velocity ( v), we find that for shots with primary yield >1 × 1015 neutrons, the total yield ∼ v9.4. This incre...

We simulate in 3D both the hydrodynamics and, simultaneously, the X-ray and neutron diagnostic signatures of National Ignition Facility (NIF) implosions. We apply asymmetric radiation drive to study the impact of low mode asymmetry on diagnostic observables. We examine X-ray and neutron images as well as neutron spectra for these perturbed implosions. The X-ray images show hot spot evolution on small length scales and short time scales, reflecting the incomplete stagnation seen in the simulation. The neutron images show surprising differences from the X-ray images. The neutron spectra provide additional measures of implosion asymmetry. Flow in the hot spot alters the neutron spectral peak, namely, the peak location and width. The changes in the width lead to a variation in the apparent temperature with viewing angle that signals underlying hot spot asymmetry. We compare our new expectations based on the simulated data with NIF data. We find that some recent cryogenic layered experiments show appreciable temperature anisotropy indicating residual flow in the hot spot. We also find some trends in the data that do not reflect our simulation and theoretical understanding.

Charged-particle spectroscopy is used to assess implosion symmetry in ignition-scale indirect-drive implosions for the first time. Surrogate D3He gas-filled implosions at the National Ignition Facility produce energetic protons via D+3He fusion that are used to measure the implosion areal density (ρR) at the shock-bang time. By using protons produced several hundred ps before the main compression bang, the implosion is diagnosed in-flight at a convergence ratio of 3–5 just prior to peak velocity. This isolates acceleration-phase asymmetry growth. For many surrogate implosions, proton spectrometers placed at the north pole and equator reveal significant asymmetries with amplitudes routinely ≳10%, which are interpreted as l=2 Legendre modes. With significant expected growth by stagnation, it is likely that these asymmetries would degrade the final implosion performance. X-ray self-emission images at stagnation show asymmetries that are positively correlated with the observed in-flight asymmetries and compar...

Gas-filled capsules imploded with indirect drive on the National Ignition Facility have been employed as symmetry surrogates for cryogenic-layered ignition capsules and to explore interfacial mix. Plastic capsules containing deuterated layers and filled with tritium gas provide a direct measure of mix of ablator into the gas fuel. Other plastic capsules have employed DT or D3He gas fill. We present the results of two-dimensional simulations of gas-filled capsule implosions with known degradation sources represented as in modeling of inertial confinement fusion ignition designs; these are time-dependent drive asymmetry, the capsule support tent, roughness at material interfaces, and prescribed gas-ablator interface mix. Unlike the case of cryogenic-layered implosions, many observables of gas-filled implosions are in reasonable agreement with predictions of these simulations. Yields of TT and DT neutrons as well as other x-ray and nuclear diagnostics are matched for CD-layered implosions. Yields of DT-filled capsules are over-predicted by factors of 1.4–2, while D3He capsule yields are matched, as well as other metrics for both capsule types.

In an indirectly driven implosion, non-radial translational motion of the compressed fusion capsule is a signature of residual kinetic energy not coupled into the compressional heating of the target. A reduction in compression reduces the peak pressure and nuclear performance of the implosion. Measuring and reducing the residual motion of the implosion is therefore necessary to improve performance and isolate other effects that degrade performance. Using the gated x-ray diagnostic, the x-ray Bremsstrahlung emission from the compressed capsule is spatially and temporally resolved at x-ray energies of >8.7 keV, allowing for measurements of the residual velocity. Here details of the x-ray velocity measurement and fitting routine will be discussed and measurements will be compared to the velocities inferred from the neutron time of flight detectors.

The effects of shock dynamics on compressibility of indirect-drive ignition-scale surrogate implosions, CH shells filled with D3He gas, have been studied using charged-particle spectroscopy. Spectral measurements of D3He protons produced at the shock-bang time probe the shock dynamics and in-flight characteristics of an implosion. The proton shock yield is found to vary by over an order of magnitude. A simple model relates the observed yield to incipient hot-spot adiabat, suggesting that implosions with rapid radiation-power increase during the main drive pulse may have a 2× higher hot-spot adiabat, potentially reducing compressibility. A self-consistent 1-D implosion model was used to infer the areal density (ρR) and the shell center-of-mass radius (Rcm) from the downshift of the shock-produced D3He protons. The observed ρR at shock-bang time is substantially higher for implosions, where the laser drive is on until near the compression bang time (“short-coast”), while longer-coasting implosions have lowe...

The “High-Foot” platform manipulates the laser pulse-shape coming from the National Ignition Facility laser to create an indirect drive 3-shock implosion that is significantly more robust against instability growth involving the ablator and also modestly reduces implosion convergence ratio. This strategy gives up on theoretical high-gain in an inertial confinement fusion implosion in order to obtain better control of the implosion and bring experimental performance in-line with calculated performance, yet keeps the absolute capsule performance relatively high. In this paper, we will cover the various experimental and theoretical motivations for the high-foot drive as well as cover the experimental results that have come out of the high-foot experimental campaign. At the time of this writing, the high-foot implosion has demonstrated record total deuterium-tritium yields (9.3×1015) with low levels of inferred mix, excellent agreement with implosion simulations, fuel energy gains exceeding unity, and evidence for the “bootstrapping” associated with alpha-particle self-heating.

In order to achieve ignition using inertial confinement fusion it is important to control the growth of low-mode asymmetries as the capsule is compressed. Understanding the time-dependent evolution of the shape of the hot spot and surrounding fuel layer is crucial to optimizing implosion performance. A design and experimental campaign to examine sources of asymmetry and to quantify symmetry throughout the implosion has been developed and executed on the National Ignition Facility (NIF) [E. I. Moses et al., Phys. Plasmas 16, 041006 (2009)]. We have constructed a large simulation database of asymmetries applied during different time intervals. Analysis of the database has shown the need to measure and control the hot-spot shape, areal density distribution, and symmetry swings during the implosion. The shape of the hot spot during final stagnation is measured using time-resolved imaging of the self-emission, and information on the shape of the fuel at stagnation can be obtained from Compton radiography [R. Tommasini et al., Phys. Plasmas 18, 056309 (2011)]. For the first time on NIF, two-dimensional inflight radiographs of gas-filled and cryogenic fuel layered capsules have been measured to infer the symmetry of the radiation drive on the capsule. These results have been used to modify the hohlraum geometry and the wavelength tuning to improve the inflight implosion symmetry. We have also expanded our shock timing capabilities by the addition of extra mirrors inside the re-entrant cone to allow the simultaneous measurement of shock symmetry in three locations on a single shot, providing asymmetry information up to Legendre mode 4. By diagnosing the shape at nearly every step of the implosion, we estimate that shape has typically reduced fusion yield by about 50% in ignition experiments.

We investigate yield degradation due to applied low mode P2 and P4 asymmetries in layered inertial confinement fusion implosions. This study has been performed with a large database of >600 2D simulations. We show that low mode radiation induced drive asymmetries can result in significant deviation between the core hot spot shape and the fuel ρR shape at peak compression. In addition, we show that significant residual kinetic energy at peak compression can be induced by these low mode asymmetries. We have developed a metric, which is a function of the hot spot shape, fuel ρR shape, and residual kinetic energy at peak compression, that is well correlated to yield degradation due to low mode shape perturbations. It is shown that the ρR shape and residual kinetic energy cannot, in general, be recovered by inducing counter asymmetries to make the hot core emission symmetric. In addition, we show that the yield degradation due to low mode asymmetries is well correlated to measurements of time dependent shape throughout the entire implosion, including early time shock symmetry and inflight fuel symmetry.

Mode 1 radiation drive asymmetry (pole-to-pole imbalance) at significant levels can have a large impact on inertial confinement fusion implosions at the National Ignition Facility (NIF). This asymmetry distorts the cold confining shell and drives a high-speed jet through the hot spot. The perturbed hot spot shows increased residual kinetic energy and reduced internal energy, and it achieves reduced pressure and neutron yield. The altered implosion physics manifests itself in observable diagnostic signatures, especially the neutron spectrum which can be used to measure the neutron-weighted flow velocity, apparent ion temperature, and neutron downscattering. Numerical simulations of implosions with mode 1 asymmetry show that the resultant simulated diagnostic signatures are moved toward the values observed in many NIF experiments. The diagnostic output can also be used to build a set of integrated implosion performance metrics. The metrics indicate that P1 has a significant impact on implosion performance a...

The National Ignition Facility (NIF) at Lawrence Livermore National Laboratory includes a precision laser system now capable of delivering 1.8 MJ at 500 TW of 0.35-μm light to a target. NIF has been operational since March 2009. A variety of experiments have been completed in support of NIF's mission areas: national security, fundamental science, and inertial fusion energy. NIF capabilities and infrastructure are in place to support its missions with nearly 60 X-ray, optical, and nuclear diagnostic systems. A primary goal of the National Ignition Campaign (NIC) on the NIF was to implode a low-Z capsule filled with ∼0.2 mg of deuterium-tritium (DT) fuel via laser indirect-drive inertial confinement fusion and demonstrate fusion ignition and propagating thermonuclear burn with a net energy gain of ∼5–10 (fusion yield/input laser energy). This requires assembling the DT fuel into a dense shell of ∼1000 g/cm3 with an areal density (ρR) of ∼1.5 g/cm2, surrounding a lower density hot spot with a temperature of ∼10 keV and a ρR ∼0.3 g/cm2, or approximately an α-particle range. Achieving these conditions demand precise control of laser and target parameters to allow a low adiabat, high convergence implosion with low ablator fuel mix. We have demonstrated implosion and compressed fuel conditions at ∼80–90% for most point design values independently, but not at the same time. The nuclear yield is a factor of ∼3–10× below the simulated values and a similar factor below the alpha dominated regime. This paper will discuss the experimental trends, the possible causes of the degraded performance (the off-set from the simulations), and the plan to understand and resolve the underlying physics issues.

Indirectly driven capsule implosions on the National Ignition Facility (NIF) [Moses et al., Phys. Plasmas 16, 041006 (2009)] are being performed with the goal of compressing a layer of cryogenic deuterium-tritium (DT) fuel to a sufficiently high areal density (ρR) to sustain the self-propagating burn wave that is required for fusion power gain greater than unity. These implosions are driven with a temporally shaped laser pulse that is carefully tailored to keep the DT fuel on a low adiabat (ratio of fuel pressure to the Fermi degenerate pressure). In this report, the impact of variations in the laser pulse shape (both intentionally and unintentionally imposed) on the in-flight implosion adiabat is examined by comparing the measured shot-to-shot variations in ρR from a large ensemble of DT-layered ignition target implosions on NIF spanning a two-year period. A strong sensitivity to variations in the early-time, low-power foot of the laser pulse is observed. It is shown that very small deviations (∼0.1% of the total pulse energy) in the first 2 ns of the laser pulse can decrease the measured ρR by 50%.

First results from the analysis of neutron image data collected on implosions of cryogenically layered deuterium-tritium capsules during the 2011-2012 National Ignition Campaign are reported. The data span a variety of experimental designs aimed at increasing the stagnation pressure of the central hotspot and areal density of the surrounding fuel assembly. Images of neutrons produced by deuterium–tritium fusion reactions in the hotspot are presented, as well as images of neutrons that scatter in the surrounding dense fuel assembly. The image data are compared with 1D and 2D model predictions, and consistency checked using other diagnostic data. The results indicate that the size of the fusing hotspot is consistent with the model predictions, as well as other imaging data, while the overall size of the fuel assembly, inferred from the scattered neutron images, is systematically smaller than models' prediction. Preliminary studies indicate these differences are consistent with a significant fraction (20%–25%) of the initial deuterium-tritium fuel mass outside the compact fuel assembly, due either to low mode mass asymmetry or high mode 3D mix effects at the ablator-ice interface.

Measurements have been made of the in-flight dynamics of imploding capsules indirectly driven by laser energies of 1–1.7 MJ at the National Ignition Facility [Miller et al., Nucl. Fusion 44, 228 (2004)]. These experiments were part of the National Ignition Campaign [Landen et al., Phys. Plasmas 18, 051002 (2011)] to iteratively optimize the inputs required to achieve thermonuclear ignition in the laboratory. Using gated or streaked hard x-ray radiography, a suite of ablator performance parameters, including the time-resolved radius, velocity, mass, and thickness, have been determined throughout the acceleration history of surrogate gas-filled implosions. These measurements have been used to establish a dynamically consistent model of the ablative drive history and shell compressibility throughout the implosion trajectory. First results showed that the peak velocity of the original 1.3-MJ Ge-doped polymer (CH) point design using Au hohlraums reached only 75% of the required ignition velocity. Several capsule, hohlraum, and laser pulse changes were then implemented to improve this and other aspects of implosion performance and a dedicated effort was undertaken to test the sensitivity of the ablative drive to the rise time and length of the main laser pulse. Changing to Si rather than Ge-doped inner ablator layers and increasing the pulse length together raised peak velocity to 93% ± 5% of the ignition goal using a 1.5 MJ, 420 TW pulse. Further lengthening the pulse so that the laser remained on until the capsule reached 30% (rather than 60%–70%) of its initial radius, reduced the shell thickness and improved the final fuel ρR on companion shots with a cryogenic hydrogen fuel layer. Improved drive efficiency was observed using U rather than Au hohlraums, which was expected, and by slowing the rise time of laser pulse, which was not. The effect of changing the Si-dopant concentration and distribution, as well as the effect of using a larger initial shell thickness were also examined, both of which indicated that instabilities seeded at the ablation front are a significant source of hydrodynamic mix into the central hot spot. Additionally, a direct test of the surrogacy of cryogenic fuel layered versus gas-filled targets was performed. Together all these measurements have established the fundamental ablative-rocket relationship describing the dependence of implosion velocity on fractional ablator mass remaining. This curve shows a lower-than-expected ablator mass at a given velocity, making the capsule more susceptible to feedthrough of instabilities from the ablation front into the fuel and hot spot. This combination of low velocity and low ablator mass indicates that reaching ignition on the NIF will require >20 μm (∼10%) thicker targets and laser powers at or beyond facility limits.

The National Ignition Campaign (NIC) uses non-igniting “tritium hydrogen deuterium (THD)” capsules to study and optimize the hydrodynamic assembly of the fuel without burn. These capsules are designed to simultaneously reduce DT neutron yield and to maintain hydrodynamic similarity with the DT ignition capsule. We will discuss nominal THD performance and the associated experimental observables. We will show the results of large ensembles of numerical simulations of THD and DT implosions and their simulated diagnostic outputs. These simulations cover a broad range of both nominal and off-nominal implosions. We will focus on the development of an experimental implosion performance metric called the experimental ignition threshold factor (ITFX). We will discuss the relationship between ITFX and other integrated performance metrics, including the ignition threshold factor (ITF), the generalized Lawson criterion (GLC), and the hot spot pressure (HSP). We will then consider the experimental results of the recent NIC THD campaign. We will show that we can observe the key quantities for producing a measured ITFX and for inferring the other performance metrics. We will discuss trends in the experimental data, improvement in ITFX, and briefly the upcoming tuning campaign aimed at taking the next steps in performance improvement on the path to ignition on NIF.

A detailed simulation-based model of the June 2011 National Ignition Campaign cryogenic DT experiments is presented. The model is based on integrated hohlraum-capsule simulations that utilize the best available models for the hohlraum wall, ablator, and DT equations of state and opacities. The calculated radiation drive was adjusted by changing the input laser power to match the experimentally measured shock speeds, shock merger times, peak implosion velocity, and bangtime. The crossbeam energy transfer model was tuned to match the measured time-dependent symmetry. Mid-mode mix was included by directly modeling the ablator and ice surface perturbations up to mode 60. Simulated experimental values were extracted from the simulation and compared against the experiment. Although by design the model is able to reproduce the 1D in-flight implosion parameters and low-mode asymmetries, it is not able to accurately predict the measured and inferred stagnation properties and levels of mix. In particular, the measured yields were 15%–40% of the calculated yields, and the inferred stagnation pressure is about 3 times lower than simulated.

Collection of representative samples of debris following inertial confinement fusion implosions in order to diagnose implosion conditions and efficacy is a challenging endeavor because of the unique conditions within the target chamber such as unconverted laser light, intense pulse of x-rays, physical chunks of debris, and other ablative effects. We present collection of gas samples following an implosion for the first time. High collection fractions for noble gases were achieved. We also present collection of solid debris samples on flat plate collectors. Geometrical collection efficiencies for Au hohlraum material were achieved and collection of capsule debris (Be and Cu) was also observed. Asymmetric debris distributions were observed for Au and Be samples. Collection of Be capsule debris was higher for solid collectors viewing the capsule through the laser entrance hole in the hohlraum than for solid collectors viewing the capsule around the waist of the hohlraum. Collection of Au hohlraum material showed the opposite pattern: more Au debris was collected around the waist than through the laser entrance hole. The solid debris collectors were not optimized for minimal Cu backgrounds, which limited the conclusions about the symmetry of the Cu debris. The quality of the data limited conclusions on chemical fractionation effects within the burning, expanding, and then cooling plasma.

Ignition requires precisely controlled, high convergence implosions to assemble a dense shell of deuterium-tritium (DT) fuel with ρR>∼1 g/cm2 surrounding a 10 keV hot spot with ρR ∼ 0.3 g/cm2. A working definition of ignition has been a yield of ∼1 MJ. At this yield the α-particle energy deposited in the fuel would have been ∼200 kJ, which is already ∼10 × more than the kinetic energy of a typical implosion. The National Ignition Campaign includes low yield implosions with dudded fuel layers to study and optimize the hydrodynamic assembly of the fuel in a diagnostics rich environment. The fuel is a mixture of tritium-hydrogen-deuterium (THD) with a density equivalent to DT. The fraction of D can be adjusted to control the neutron yield. Yields of ∼1014−15 14 MeV (primary) neutrons are adequate to diagnose the hot spot as well as the dense fuel properties via down scattering of the primary neutrons. X-ray imaging diagnostics can function in this low yield environment providing additional information about the assembled fuel either by imaging the photons emitted by the hot central plasma, or by active probing of the dense shell by a separate high energy short pulse flash. The planned use of these targets and diagnostics to assess and optimize the assembly of the fuel and how this relates to the predicted performance of DT targets is described. It is found that a good predictor of DT target performance is the THD measurable parameter, Experimental Ignition Threshold Factor, ITFX ∼ Y × dsf 2.3, where Y is the measured neutron yield between 13 and 15 MeV, and dsf is the down scattered neutron fraction defined as the ratio of neutrons between 10 and 12 MeV and those between 13 and 15 MeV.

Point design targets have been specified for the initial ignition campaign on the National Ignition Facility [G. H. Miller, E. I. Moses, and C. R. Wuest, Opt. Eng. 443, 2841 (2004)]. The targets contain D-T fusion fuel in an ablator of either CH with Ge doping, or Be with Cu. These shells are imploded in a U or Au hohlraum with a peak radiation temperature set between 270 and 300 eV. Considerations determining the point design include laser-plasma interactions, hydrodynamic instabilities, laser operations, and target fabrication. Simulations were used to evaluate choices, and to define requirements and specifications. Simulation techniques and their experimental validation are summarized. Simulations were used to estimate the sensitivity of target performance to uncertainties and variations in experimental conditions. A formalism is described that evaluates margin for ignition, summarized in a parameter the Ignition Threshold Factor (ITF). Uncertainty and shot-to-shot variability in ITF are evaluated, and...

Capsule performance optimization campaigns will be conducted at the National Ignition Facility [G. H. Miller, E. I. Moses, and C. R. Wuest, Nucl. Fusion 44, 228 (2004)] to substantially increase the probability of ignition. The campaigns will experimentally correct for residual uncertainties in the implosion and hohlraum physics used in our radiation-hydrodynamic computational models using a variety of ignition capsule surrogates before proceeding to cryogenic-layered implosions and ignition experiments. The quantitative goals and technique options and down selections for the tuning campaigns are first explained. The computationally derived sensitivities to key laser and target parameters are compared to simple analytic models to gain further insight into the physics of the tuning techniques. The results of the validation of the tuning techniques at the OMEGA facility [J. M. Soures et al., Phys. Plasmas 3, 2108 (1996)] under scaled hohlraum and capsule conditions relevant to the ignition design are shown ...

The velocity and remaining ablator mass of an imploding capsule are critical metrics for assessing the progress toward ignition of an inertially confined fusion experiment. These and other convergent ablator performance parameters have been measured using a single streaked x-ray radiograph. Traditional Abel inversion of such a radiograph is ill-posed since backlighter intensity profiles and x-ray attenuation by the ablated plasma are unknown. To address this we have developed a regularization technique which allows the ablator density profile ρ(r) and effective backlighter profile I0(y) at each time step to be uniquely determined subject to the constraints that ρ(r) is localized in radius space and I0(y) is delocalized in object space. Moments of ρ(r) then provide the time-resolved areal density, mass, and average radius (and thus velocity) of the remaining ablator material. These results are combined in the spherical rocket model to determine the ablation pressure and mass ablation rate during the implos...

The velocity and remaining ablator mass of an imploding capsule are critical metrics for assessing the progress toward ignition of an inertially confined fusion experiment. These and other ablator rocket parameters have been measured using a single streaked x-ray radiograph. A regularization technique has been used to determine the ablator density profile ρ(r) at each time step; moments of ρ(r) then provide the areal density, average radius, and mass of the unablated, or remaining, ablator material, with the velocity determined from the time derivative of the average radius. The technique has been implemented on experiments at the OMEGA laser facility.

Inertial confinement fusion (ICF) capsule performance can be negatively impacted by the presence of hydrodynamic instabilities. To perform a gas fill on an ICF capsule current plans involve drilling a small hole and inserting a fill tube to inject the gas mixture into the capsule. This introduces a perturbation on the capsule, which can seed hydrodynamic instabilities. The small hole can cause jetting of the shell material into the gas, which might adversely affect the capsule performance. We have performed simulations and experiments to study the hydrodynamic evolution of jets from high-aspect ratio holes, such as the fill tube hole. Although simulations using cold materials over predict the amount of mass in the jet, when a reasonable amount of preheat (< 1 eV) is introduced, the simulations are in better agreement with the experiment.

The physics of thermonuclear ignition in inertial confinement fusion (ICF) is presented in the familiar frame of a Lawson-type criterion. The product of the plasma pressure and confinement time Pτ for ICF is cast in terms of measurable parameters and its value is estimated for cryogenic implosions. An overall ignition parameter χ including pressure, confinement time, and temperature is derived to complement the product Pτ. A metric for performance assessment should include both χ and Pτ. The ignition parameter and the product Pτ are compared between inertial and magnetic-confinement fusion. It is found that cryogenic implosions on OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] have achieved Pτ∼1.5 atm s comparable to large tokamaks such as the Joint European Torus [P. H. Rebut and B. E. Keen, Fusion Technol. 11, 13 (1987)] where Pτ∼1 atm s. Since OMEGA implosions are relatively cold (T∼2 keV), their overall ignition parameter χ∼0.02–0.03 is ∼5× lower than in JET (χ∼0.13), where the average temp...

A capsule performance optimization campaign will be conducted at the National Ignition Facility [G. H. Miller et al., Nucl. Fusion 44, 228 (2004)] to substantially increase the probability of ignition by laser-driven hohlraums [J. D. Lindl et al., Phys. Plasmas 11, 339 (2004)]. The campaign will experimentally correct for residual uncertainties in the implosion and hohlraum physics used in our radiation-hydrodynamic computational models before proceeding to cryogenic-layered implosions and ignition attempts. The required tuning techniques using a variety of ignition capsule surrogates have been demonstrated at the OMEGA facility under scaled hohlraum and capsule conditions relevant to the ignition design and shown to meet the required sensitivity and accuracy. In addition, a roll-up of all expected random and systematic uncertainties in setting the key ignition laser and target parameters due to residual measurement, calibration, cross-coupling, surrogacy, and scale-up errors has been derived that meets the required budget.

A streaked radiography diagnostic has been proposed as a technique to determine the ablator mass remaining in an inertial confinement fusion ignition capsule at peak velocity. This instrument, the "HXRI-5," has been designed to fit within a National Ignition Facility Diagnostic Instrument Manipulator. The HXRI-5 will be built at Sandia National Laboratories (SNL), and initial testing will be done at the SNL Z-Beamlet Facility. In this paper, we will describe the National Ignition Campaign requirements for this diagnostic, the instrument design, and the planned test experiments.