Low-mode Asymmetries Research Articles

Thermonuclear performance variability near ignition at the National Ignition Facility

We describe our current understanding of the variability and degradation mechanisms observed through a series of five indirectly driven inertial fusion implosions fielded at the National Ignition Facility in the fall of 2021, four of which attempted to reproduce the first experiment to achieve Lawson's criterion for ignition with a thermonuclear yield of 1.35 MJ on August 8, 2021. A large number of absolutely calibrated (imaging, time-resolved, and spectrally resolved) x-ray and neutron diagnostics are fielded on the NIF along multiple lines of sight for each experiment. This allows for a reconstruction of the DT fuel and ablator mix injected into the hotspot around peak burn. We show that nuclear yield variations are well reproduced by numerical modeling when the measured low mode asymmetries and mix mass are included. Furthermore, these observed perturbations during burn are linked to small variations in laser delivery and capsule defects. Stringent specifications are then set to achieve robust ignition with the implosion design studied in this paper.

Evolution of low-mode asymmetries introduced by x-ray P2 drive asymmetry during double shell implosions on the SG facility

Abstract Double shell capsule can provide a potential low-convergence to fusion ignition at relatively low temperature (∼3 keV). One of the main sources of degrading double shell implosion performance is the low-mode asymmetries. Recently, the experiments on the evolution of low-mode asymmetries introduced by x-ray P2 drive asymmetry during double shell implosions were carried out on the SG facility, where the outer shell and inner shell shapes were measured through the backlit radiography, and the fuel shape near stagnation was measured by core x-ray self-emission imaging. The time-dependent x-ray flux symmetry was controlled by varying the inner cone fraction, defined as the ratio of the inner cone power to the total laser power, while keeping the drive temperature histories same across experiments. Both the hohlraum radiation and the capsule implosions were analyzed using a two-dimensional radiation-hydrodynamics code. Comparing the experimental radiographs and self-emission images to the simulations, it is found that the simulated outer shell, inner shell and hot spot shapes are in qualitative agreement with experiments, especially, the symmetry swings of the hot spot shape near stagnation are observed from both experimental and simulation results. Further, the effect of x-ray drive asymmetries on double shell implosion performance is preliminarily investigated using numerical simulations. We find that the azimuthal variations in radial velocity caused by drive asymmetries can generate azimuthal mass flow of the inner shell, thus kinetic energy of the inner shell would be not converted into fuel internal energy with high efficiency, and the mass-averaged ion temperature of the fuel at stagnation would be reduced.

Demonstration of low-mode shape control in indirect-drive double shell implosions at the NIF

Double shell inertial confinement fusion is a concept for achieving robust thermonuclear burn that uses dense metal shells to compress deuterium-tritium (DT) fuel to fusion conditions. Double shell implosions are typically indirectly driven and involve a target that consists of a low-Z ablator, a foam layer, and a high-Z pusher surrounding the DT fuel. The goal of the campaign is to achieve a volumetric burn as radiation losses from the DT fuel are trapped by the opaque high-Z shell. The overall performance of double shell implosions relies on the efficient collisional transfer of kinetic energy between layers. The efficiency of this transfer (and therefore the overall performance of a given implosion) is degraded by the presence of low-mode asymmetries. P2 asymmetries are often observed in spatially resolved 2D radiographs of nominal double shell implosions. This work discusses three such experiments: one with an oblate P2 asymmetry, one with a prolate P2 asymmetry, and one with an approximate spherical symmetry. After performing a shape analysis of the oblate and prolate implosions to quantify asymmetries, these experimental results were compared with the results of hydrodynamic simulations for the two experiments. Differences between the experiment and simulation were then used to design an approximately spherical implosion by altering the incident laser cone fraction. Radiographs from the experiment that implemented the modified cone fraction show evidence of an implosion that is approximately spherical until bang time. This design is intended to serve as a point design for future studies that will seek to optimize various aspects of the double shell target.

Design of the first fusion experiment to achieve target energy gain G>1.

In this work we present the design of the first controlled fusion laboratory experiment to reach target gain G>1 N221204 (5 December 2022) [Phys. Rev. Lett. 132, 065102 (2024)10.1103/PhysRevLett.132.065102], performed at the National Ignition Facility, where the fusion energy produced (3.15 MJ) exceeded the amount of laser energy required to drive the target (2.05 MJ). Following the demonstration of ignition according to the Lawson criterion N210808, experiments were impacted by nonideal experimental fielding conditions, such as increased (known) target defects that seeded hydrodynamic instabilities or unintentional low-mode asymmetries from nonuniformities in the target or laser delivery, which led to reduced fusion yields less than 1 MJ. This Letter details design changes, including using an extended higher-energy laser pulse to drive a thicker high-density carbon (also known as diamond) capsule, that led to increased fusion energy output compared to N210808 as well as improved robustness for achieving high fusion energies (greater than 1 MJ) in the presence of significant low-mode asymmetries. For this design, the burnup fraction of the deuterium and tritium (DT) fuel was increased (approximately 4% fuel burnup and a target gain of approximately 1.5 compared to approximately 2% fuel burnup and target gain approximately 0.7 for N210808) as a result of increased total (DT plus capsule) areal density at maximum compression compared to N210808. Radiation-hydrodynamic simulations of this design predicted achieving target gain greater than 1 and also the magnitude of increase in fusion energy produced compared to N210808. The plasma conditions and hotspot power balance (fusion power produced vs input power and power losses) using these simulations are presented. Since the drafting of this manuscript, the results of this paper have been replicated and exceeded (N230729) in this design, together with a higher-quality diamond capsule, setting a new record of approximately 3.88MJ of fusion energy and fusion energy target gain of approximately 1.9.

Point design of octahedral spherical Hohlraum with HDC–CH capsule for a predictable inertial confinement fusion at/beyond ignition

Fusion ignition has been successfully achieved at the National Ignition Facility, but the main obstacles of low-mode asymmetries, laser-plasma instabilities (LPIs), and hydrodynamic instabilities (HIs) still remain in the path toward a predictable yield for fusion ignition, especially at high gain. A recently proposed octahedral spherical Hohlraum, i.e., a spherical Hohlraum with six laser entrance holes of octahedral symmetry [Lan et al., Phys. Plasmas 21, 010704 (2014); Phys. Rev. Lett. 127, 245001 (2021)], was demonstrated to have the advantages of a naturally high radiation symmetry without any symmetry tuning technology and a high energy coupling efficiency from the drive laser to the capsule hotspot. In addition, a novel HDC–CH (here, HDC and CH refer to high density carbon and glow discharge plastic, respectively) capsule design was proposed to have the advantages in both low LPIs and low HIs by using two different ablators [Qiao and Lan, Phys. Rev. Lett. 126, 185001 (2021)]. For the first time, here we proposed a point design target composed of an octahedral spherical Hohlraum and an HDC–CH capsule to suppress the above-mentioned obstacles and presented the 2D simulation of the effect of symmetry and hydrodynamic instabilities on implosion performances. Our work provides a novel target design for a more predictable fusion ignition in experiment.

Diagnosing the origin and impact of low-mode asymmetries in ignition experiments at the National Ignition Facility.

Inertial confinement fusion ignition requires high inflight shell velocity, good energy coupling between the hotspot and shell, and high areal density at peak compression. Three-dimensional asymmetries caused by imperfections in the drive symmetry or target can grow and damage the coupling and confinement. Recent high-yield experiments have shown that low-mode asymmetries are a key degradation mechanism and contribute to variability. We show the experimental signatures and impacts of asymmetry change with increasing implosion yield given the same initial cause. This letter has implications for improving robustness to a key degradation in ignition experiments.

Correlations between asymmetric compression, burn amplification, and hot-spot velocities in inertial confinement fusion implosions

This manuscript examines the correlations between the hot-spot velocity (an observable signature of residual kinetic energy), low-mode implosion asymmetries, and burn amplification in inertial confinement fusion implosions on the National Ignition Facility (NIF). Using a combination of two-dimensional axis-symmetric and three-dimensional radiation-hydrodynamic simulations coupled to neutronics, we find that for typical NIF implosions, the stagnation asymmetry multiplies the observed hot-spot velocity anywhere from 80% to 120%, while burn amplification always increases it. Additionally, we find stagnation asymmetry typically deflects the observed hot-spot flow. The two mechanisms (low-mode implosion asymmetries and burn amplification) can be decoupled, and application of a simple model to a database of cryogenic implosions on the NIF infers the total hot-spot velocity amplification. This finding modifies the interpretation of data collected from inertial confinement fusion experiments and impacts the magnitude and origin of low-mode asymmetries.

Correcting Hohlraum Drive Asymmetry with Glow Discharge Polymerization Coated Capsule Shims

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

Diagnosing low-mode (ℓ < 6) and mid-mode (6 ≤ ℓ ≤ 60) asymmetries in the post-stagnation phase of laser-direct-drive deuterium-tritium cryogenic implosions on OMEGA.

Low- and mid-mode perturbations are possible candidates for performance limitations in cryogenic direct-drive implosions on the OMEGA laser at the Laboratory of Laser Energetics. Simulations with a 3D hydrocode demonstrated that hotspot imagers do not show evidence of the shell breakup in the dense fuel. However, these same simulations revealed that the low- and mid-mode perturbations in the dense fuel could be diagnosed more easily in the post-stagnation phase of the implosion by analyzing the peak in the x-ray emission limb at the coronal-fuel interface than before or at the stagnation phase. In experiments, the asymmetries are inferred from gated images of the x-ray emission of the implosion by using a 16-pinhole array imager filtered to record x-ray energies >800eV and an x-ray framing camera with 40-ps time integration and 20-μm spatial resolution. A modal analysis is applied to the spatial distribution of the x-ray emission from deuterium and tritium cryogenic implosions on OMEGA recorded after the bang time to diagnose the low- and mid-mode asymmetries, and to study the effect that the beam-to-target ratio (Rb/Rt) has on the shell integrity.

X-ray-imaging spectrometer (XRIS) for studies of residual kinetic energy and low-mode asymmetries in inertial confinement fusion implosions at OMEGA (invited).

A system of x-ray imaging spectrometer (XRIS) has been implemented at the OMEGA Laser Facility and is capable of spatially and spectrally resolving x-ray self-emission from 5 to 40keV. The system consists of three independent imagers with nearly orthogonal lines of sight for 3D reconstructions of the x-ray emission region. The distinct advantage of the XRIS system is its large dynamic range, which is enabled by the use of tantalum apertures with radii ranging from 50 μm to 1mm, magnifications of 4 to 35×, and image plates with any filtration level. In addition, XRIS is capable of recording 1-100's images along a single line of sight, facilitating advanced statistical inference on the detailed structure of the x-ray emitting regions. Properties such as P0 and P2 of an implosion are measured to 1% and 10% precision, respectively. Furthermore, Te can be determined with 5% accuracy.

Measurements of low-mode asymmetries in the areal density of laser-direct-drive deuterium-tritium cryogenic implosions on OMEGA using neutron spectroscopy.

Areal density is one of the key parameters that determines the confinement time in inertial confinement fusion experiments, and low-mode asymmetries in the compressed fuel are detrimental to the implosion performance. The energy spectra from the scattering of the primary deuterium-tritium (DT) neutrons off the compressed cold fuel assembly are used to investigate low-mode nonuniformities in direct-drive cryogenic DT implosions at the Omega Laser Facility. For spherically symmetric implosions, the shape of the energy spectrum is primarily determined by the elastic and inelastic scattering cross sections for both neutron-deuterium and neutron-tritium kinematic interactions. Two highly collimated lines of sight, which are positioned at nearly orthogonal locations around the OMEGA target chamber, record the neutron time-of-flight signal in the current mode. An evolutionary algorithm is being used to extract a model-independent energy spectrum of the scattered neutrons from the experimental neutron time-of-flight data and is used to infer the modal spatial variations (l = 1) in the areal density. Experimental observations of the low-mode variations of the cold-fuel assembly (ρL0 + ρL1) show good agreement with a recently developed model, indicating a departure from the spherical symmetry of the compressed DT fuel assembly. Another key signature that has been observed in the presence of a low-mode variation is the broadening of the kinematic end-point due to the anisotropy of the dense fuel conditions.

Analysis of core asymmetries in inertial confinement fusion implosions using three-dimensional hot-spot reconstruction

Three-dimensional effects play a crucial role during the hot-spot formation in inertial confinement fusion (ICF) implosions. A data analysis technique for 3D hot-spot reconstruction from experimental observables has been developed to characterize the effects of low modes on 3D hot-spot formations. In nuclear measurements, the effective flow direction, governed by the maximum eigenvalue in the velocity variance of apparent ion temperatures, has been found to agree with the measured hot-spot flows for implosions dominated by mode ℓ=1. Asymmetries in areal-density (ρR) measurements were found to be characterized by a unique cosine variation along the hot-spot flow axis. In x-ray images, a 3D hot-spot x-ray emission tomography method was developed to reconstruct the 3D hot-spot plasma emissivity using a generalized spherical-harmonic Gaussian function. The gradient-descent algorithm was used to optimize the mapping between the projections from the 3D hot-spot emission model and the measured x-ray images along multiple views. This work establishes a platform to analyze 3D low-mode core asymmetries in ICF.

Analytical model for viscous and elastic Rayleigh–Taylor instabilities in convergent geometries at static interfaces

Great attention has been attracted to study the viscous and elastic Rayleigh–Taylor instability in convergent geometries, especially for their low mode asymmetries that behave distinctively from the planar counterparts. However, most analyses have focused on the instability at static interfaces that excludes the studies of the Bell–Plesset effects and the elastic–plastic transition since they involve too complex mathematics. Herein, we perform detailed analyses on the dispersion relations by applying the viscous and elastic potential flow method to obtain their approximate growth rates compared with the exact ones to demonstrate: (i) The approximate growth rates based on potential flow method generally coincide with the exact ones. (ii) An alternative expression is proposed to overcome the discrepancy for the low mode asymmetries at fluid/fluid interface. (iii) Extra care must be taken in solids since the maximum discrepancies occur at the n = 1 mode and at the mode proximate to the cutoff. This analytical method of great simplicity is essential to describe the dynamic interface by including the overall motion of the interface based on the static construction, while the exact analysis involves too complex mathematics to be extended by including the Bell–Plesset effects and the elastic–plastic properties. To sum up, the approximate analytical dispersion relations derived in convergent geometries, have the potential for dealing with dynamic interfaces where Bell–Plesset effects are combined with elastic–plastic transition.

Mechanisms of shape transfer and preheating in indirect-drive double shell collisions

Implosions of Hohlraum-driven double shell targets as an alternative inertial confinement fusion concept are underway at the National Ignition Facility. The double shell system relies on a series of energy transfer processes starting from thermal x-ray absorption by the outer shell, followed by collisional transfer of kinetic energy to a heavy metal inner shell, and finally, conversion to the internal energy of the deuterium-tritium fuel. During each of these energy transfer stages, low-mode asymmetries can act to reduce the ideal transfer efficiency degrading double shell performance. Mechanisms, such as hard x-ray preheat from the Hohlraum, not only decrease the efficiency of kinetic energy transfer but may also be a source of low-mode asymmetry. In this article, we evaluate the shape transfer processes through the time of shell collision using two-dimensional integrated Hohlraum and capsule computations. We find that the dominant mode of the shape transfer is well described using a “radial impulse” model from the shape of the foam pressure reservoir. To evaluate the importance of preheat on inner shell shape, we also report on first measurements of Au L-shell preheat asymmetry in a double shell with a tungsten pusher. These measurements showed a 65% higher preheat velocity at the pole of the capsule relative to the equator. We also found that the experiments provided rigorous constraints by which to test the Hohlraum model settings that impact the amount and symmetry of Au L-shell preheat via the plasma conditions inside the outer cone Au bubble.

Extensions of a classical mechanics “piston-model” for understanding the impact of asymmetry on ICF implosions: The cases of mode 2, mode 2/1 coupling, time-dependent asymmetry, and the relationship to coast-time

As long suspected, low mode asymmetry in inertially confined fusion (ICF) implosions has been implicated as a performance limiting factor [Casey et al., “Evidence of three-dimensional asymmetries seeded by high-density carbon-ablator nonuniformity in experiments at the national ignition facility,” Phys. Rev. Lett. 126, 025002 (2021)]. Recently a non-linear, but solvable, theory [Hurricane et al., “An analytic asymmetric-piston model for the impact of mode-1 shell asymmetry on ICF implosions,” Phys. Plasmas 27, 062704 (2020)] based upon the simple picture of a pair of asymmetric pistons has generated new insights and provided some practical formulas for estimating the degradation of an implosion due to mode-1 asymmetry and demonstrated a previously unrecognized connection between measured hot-spot drift velocity, nuclear down-scatter ratio asymmetry, and the concept of residual kinetic energy (RKE). Asymmetry of the implosion “shell,” as opposed to asymmetry of the hot-spot, was key to the classical mechanics model because the majority of the kinetic energy in an implosion is carried by the shell. Herein, the two-piston model is extended to a six-piston model in order to capture mode-2 asymmetry and coupling between mode-1 and mode-2. A key result of this new six-piston model is that the weighted harmonic mean of shell areal density is the fundamental quantity that determines the RKE and performance degradations for a three-dimensional implosion. Agreement is found between the scalings coming from the theory and ICF implosion data from the National Ignition Facility and to large ensembles of detailed simulations. The connection between the piston model's dependence upon the radius of peak velocity and coast-time is also highlighted in this paper. Finally, by extending the two-piston model to include time-dependent “swing,” it is shown in the Appendix that the shell asymmetry at the time of stagnation dominates the solution for RKE.

Effects of viscosity and elasticity on Rayleigh–Taylor instability in a cylindrical geometry

In this paper, we present a linear analysis of the Rayleigh–Taylor instability (RTI) in cylindrical geometry to investigate the effects of viscosity and elasticity on growth rates using a decomposition method. This method decomposes the fourth-order differential equations into two coupled second-order differential equations to easily obtain the dispersion relations. The motions of the interfaces are analyzed for the instability at liquid/liquid, solid/liquid, and solid/solid interfaces, and the results retrieve those previously obtained for inviscid fluids. Generally, the planar growth rates recover those in the cylindrical geometry when the dimensionless radius Br or mode number n is large enough. The RTI for different cylindrical geometries is particularly investigated to study the effects of viscosity, elasticity, and curvature. It is found that the n = 1 mode will always survive and dominate the motion of the interfaces when the dimensionless radius is significantly small. We believe that this method will provide the possibility of investigating the behaviors of different types of interfaces based on their driven conditions. Furthermore, this will help to find a way to study the evolution of low-mode asymmetries that is essential for controlling the integrity of a fusion target under study during implosion processes in high energy-density physical experiments. This method provides basic guidance for exploration of Bell–Plesset effects and of the transition from elasticity to plasticity in cylindrical geometry.

Interpolating individual line-of-sight neutron spectrometer measurements onto the "sky" at the National Ignition Facility (NIF).

Nuclear diagnostics provide measurements of inertial confinement fusion implosions used as metrics of performance for the shot. The interpretation of these measurements for shots with low mode asymmetries requires a way of combining the data to produce a "sky map" where the individual line-of-sight values are used to interpolate to other positions in the sky. These interpolations can provide information regarding the orientation of the low mode asymmetries. We describe the interpolation method, associated uncertainties, and correlations between different metrics, e.g., Tion, down scatter ratio, and hot-spot velocity direction. This work is also related to recently reported studies [H. G. Rinderknecht et al., Phys. Rev. Lett. 124, 145002 (2020) and K. M. Woo et al., Phys. Plasmas 27, 062702 (2020)] of low mode asymmetries. We report an analysis that makes use of a newly commissioned line of sight, a scheme for incorporating multiple neutron spectrum measurement types, and recent work on the sources of implosion asymmetry to provide a more complete picture of implosion performance.

Three dimensional low-mode areal-density non-uniformities in indirect-drive implosions at the National Ignition Facility

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 &amp;gt; 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 &amp;gt; 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.

Neural network for 3D inertial confinement fusion shell reconstruction from single radiographs.

In inertial confinement fusion (ICF), x-ray radiography is a critical diagnostic for measuring implosion dynamics, which contain rich three-dimensional (3D) information. Traditional methods for reconstructing 3D volumes from 2D radiographs, such as filtered backprojection, require radiographs from at least two different angles or lines of sight (LOS). In ICF experiments, the space for diagnostics is limited, and cameras that can operate on fast timescales are expensive to implement, limiting the number of projections that can be acquired. To improve the imaging quality as a result of this limitation, convolutional neural networks (CNNs) have recently been shown to be capable of producing 3D models from visible light images or medical x-ray images rendered by volumetric computed tomography. We propose a CNN to reconstruct 3D ICF spherical shells from single radiographs. We also examine the sensitivity of the 3D reconstruction to different illumination models using preprocessing techniques such as pseudo-flatfielding. To resolve the issue of the lack of 3D supervision, we show that training the CNN utilizing synthetic radiographs produced by known simulation methods allows for reconstruction of experimental data as long as the experimental data are similar to the synthetic data. We also show that the CNN allows for 3D reconstruction of shells that possess low mode asymmetries. Further comparisons of the 3D reconstructions with direct multiple LOS measurements are justified.

Elastic Rayleigh–Taylor and Richtmyer–Meshkov instabilities in spherical geometry

An exact theoretical analysis is presented, mainly concerning linearly elastic Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities at spherical interfaces by using the decomposition method. A stability analysis is performed to investigate the growth rates of instability with the degree of spherical harmonics n, dimensionless radius Br, Atwood number At, and elastic ratio T. Generally, spherical RT and RM instabilities resemble their planar counterparts when Br or n is large. However, low mode perturbations behave quite differently from planar ones, which is also observed in experiments in inertial confinement fusion and in theoretical analysis in geophysics. An analytical expression is obtained to study the dependence of the cutoff radius. There exist two kinds of it: a small one at which the most-active mode cannot be activated and a larger one that is similar to the planar one. In addition, the elastic parameter strongly affects the evolution of a mode with a lower number. The method is extended to study the RT instability at the interface between an elastic solid and a viscous fluid, which is relevant to some situations encountered experimentally. Finally, RM instability in elastic solids is also investigated, in particular, with regard to the evolution of RM instability with low-mode asymmetries. This method is able to provide guidelines for further studying spherical RT and RM instabilities in complex situations, including the finite thickness effects, elastoplastic properties, and Bell–Plesset effects.