How numerical simulations helped to achieve breakeven on the NIF

Nuclear fusion offers the possibility of a nearly unlimited, reliable source of energy that makes minimal demands on land and natural resources. A fusion plant could be designed with a very small inventory of radioactivity and would produce no long lived highly radioactive waste. There exist fusion reactions that would produce zero radioactive waste. A fusion industry would produce almost no carbon emissions.

The first fusion reactions produced in a laboratory were made in 1933 by Oliphant.¹ Then, Lawson in 1957 first published the fundamental requirements for fusion ignition.² He analyzed both pulsed and steady state systems and determined that both required n $τ > 10 20$ sec/m³ and sufficiently high $T ion$ in the range of keV. Over many decades, a wide range of fusion concepts have been researched around the world with the goal of producing a net energy gain in the plasma. Steady state systems include magnetically confined tokamaks, stellarators, magnetic mirrors, and spheromaks. Pulsed systems include inertially confined systems and z pinches. After the laser was invented in 1960, several authors proposed methods to use lasers to create fusion reactions^3–5 Nuckolls at Lawrence Livermore National Laboratory (LLNL) proposed a method to use high powered lasers to implode and ignite a fusion plasma.⁶ Indirect drive, direct drive, and magnetic drive approaches to ICF are being actively pursued.

An indirect drive implosion on the National Ignition Facility (NIF)^7–10 involves illuminating the interior of a high-Z element cylindrical hohlraum with 1–2.2 MJ of a 351 nm laser light, which is converted into x-rays. The resulting radiation drive on the capsule eliminates all but the lowest asymmetry modes (⁠ $ℓ < 10$⁠). These x-rays ablate the outer layer of the ablator with a frozen deuterium–tritium (DT) fuel layer inside in equilibrium with DT gas. The shell is accelerated to speeds of 380–400 km/s, and the cold fuel is compressed to hundreds of times the density of water. The central gas region is heated to 4–6 keV at stagnation when it reaches minimum volume. If the central hotspot ignites, and the rate of energy deposition from fusion product alpha particles exceeds other losses, the burn wave can propagate into the surrounding cold dense fuel. Lawson's n $τ$ requirement is directly related to areal density $ρ r$ in inertial confinement fusion (ICF). Here, $ρ r$ is the average of the integral of mass density in the radial direction. Lawson's criterion for ICF generalizes to a hotspot $ρ r ∼$ 0.3 g/cm², and a central ion temperature of 10 keV for hotspot ignition. There is also an additional critical total $ρ r ∼$ 1.3 g/cm² (fuel + ablator) required for ignition determined from numerical simulations.^11,12 The first $ρ r$ criterion corresponds to the requirement that charged particle fusion products deposit their energy in sufficiently hot plasma to enable bootstrapping of the fusion reaction rate. The second $ρ r$ criterion is what is required to hold the capsule together long enough that it can ignite and burn.

The first laboratory plasma to surpass Lawson's ignition criterion was demonstrated on the NIF on August 8, 2021.^13–15 This target was the result of many design optimizations, guided by simulations, theory, and experimental observations. Following this result, a set of five similar implosions showed variations in yield, ranging from factors of 2–5, which can be explained in simulations as being caused by low mode asymmetries and mix.¹⁶ Variations in laser delivery and target quality between the shots correlated with the types of degradations applied in the simulations.

Simulations performed with the multiphysics radiation hydrodynamic codes Lasnex¹⁷ and HYDRA,¹⁸ backed by theory, indicated that a modest increase in laser energy driving a thicker capsule could decrease the design's sensitivities to low mode and mix degradations and increase the yield.¹⁹ A several year effort enabled the laser to increase delivered energy from 1.9 to 2.05 MJ by September 2022.^20,21 In December 2022, a slightly modified target design, with a thicker ablator, was driven by a 2.05 MJ laser pulse. This experiment N221204 marked the first time a laboratory plasma achieved breakeven, where the fusion energy produced was greater than the laser energy on the target by a factor of 1.5. There is evidence that this higher energy design is in fact rather more robust than the N210808 design, as we will discuss later.

This paper will describe how Livermore's ICF codes have helped to guide LLNL's ICF program to ignition and breakeven. Before starting that discussion, we give in Sec. II a brief overview of the many different approaches to ICF ignition pursued at laboratories around the world, along with other codes used to model them. Section III presents a historical view of codes in LLNL's ICF program and how they are employed. Section IV discusses the Lasnex multiphysics radiation hydrodynamic code and its development starting from the early days of the program. Section V discusses the development and application of the pF3D code used to simulate and understand LPI. Section VI describes the development and capabilities of the 2D/3D multiphysics ICF code HYDRA. Section VII describes code advances and first-of-a-kind simulations performed with HYDRA. Section VIII discusses examples of how simulations helped to guide the program to ignition. Section IX describes the role codes played in optimizing most recent target designs.

This paper focuses on indirectly-driven ignition targets, which employ a single high density carbon (HDC) ablator shell enclosing a cryogenic fuel layer. Many different approaches to ICF ignition have been and continue to be examined at various laboratories around the world. Here, we give a brief overview of these along with other simulation tools that have been employed to model them.

Designers at Los Alamos National Laboratory (LANL) played an instrumental role in advocating for advantages of Be ablator capsules²² and studying the performance of various Be ablator designs.²³ LANL designers were leaders in designing and executing experiments with double shell capsules.²⁴ More recently, an innovative triple shell design was the focus of LANL's Revolver campaign.²⁵ Scientists for Sandia National Laboratory, Albuquerque, and LANL studied a concept that used an alternative hotspot formation technique with a liquid deuterium–tritium layer.²⁶ Certain ICF capsule designs intentionally create low areal densities, where kinetic effects can become pronounced. At LANL, an approximate model for the ion kinetic regime was formulated for such targets.²⁷ The iFP 1D-2V multi-species Vlasov–Fokker–Planck code developed at LANL has also been employed to study such capsules.²⁸ An analytic model was developed to study the dynamics of hotspot formation and implications for ignition.²⁹ LANL simulations performed with the Eulerian adaptive mesh refinement (AMR) code xRAGE enable comparing results of calculations obtained using distinctly different methods, such as arbitrary Lagrange Eulerian (ALE) hydrodynamics. Challenging fill tube simulations have been compared between xRAGE and HYDRA.³⁰ Likewise, xRAGE simulations of a void inside the ablator³¹ have been compared to HYDRA simulations of a void in a related capsule.³² The similarity of the results obtained using two very different numerical methods increased confidence in the simulations. More recently, the xRAGE code has been used to simulate signatures of failure mechanisms for indirect drive ignition capsules.³³ 

The Laser Megajoule facility at CEA in France has started operation with 48 beams. They have recently performed their first indirect drive campaign using rugby-shaped hohlraums, which are illuminated highly asymmetrically due to the limited number of beams currently available. Integrated 3D hohlraum simulations performed with the Troll ALE code have captured many features of these highly asymmetric experiments when an absorption multiplier is employed.³⁴ 

Naval Research Laboratory scientists studied the relative advantages of using different laser wavelengths to drive capsules directly using NRL's Fastrad3D radiation hydrodynamics code.^35,36 The effects of cross beam energy transfer (CBET) are generally quite pronounced in direct drive capsules. The University of Rochester, Laboratory for Laser Energetics (LLE) Draco code, was a pioneer in including inline CBET in its laser package. Detailed studies of the effect of CBET in direct drive and how to mitigate it have been performed at LLE.³⁷ This includes the interplay between CBET and target offset.³⁸ A wavelength detuning approach to reduce the impact of CBET was successfully applied in Draco modeling of NIF polar direct drive experiments.³⁹ The impact of beam speckle and polarization smoothing on CBET have been studied using the 3D wave-based-plasma interaction code LPSE.⁴⁰ 

A hybrid method that combines indirect drive and direct drive using a spherical hohlraum has been proposed at the Institute of Applied Physics and Computational Mathematics in China.⁴¹ It has been explored with 1D and 2D simulations using their LARED-S code. Capsule simulations combined with viewfactor calculations show reduced growth of hydrodynamic instabilities. Initial results from experiments performed with hemispherical and planar ablator targets in a semicylindrical hohlraum demonstrated increased pressures.⁴² 

The MagLIF concept, pioneered at Sandia National Laboratory (SNL), Albuquerque, employs a novel hybrid magnetic and laser drive system. Sandia modeling of MagLIF has included studies of the optimum density of the hydrogen layers⁴³ and how the laser beam preheat varies with target size.⁴⁴ A comprehensive design effort at Sandia has studied the parameter space of MagLIF, making use of similarity scaling.⁴⁵ 

The effect of an external magnetic field applied to ICF capsule implosions has been studied using several codes. In a recent paper, the impact of imposed B-fields on capsule performance and implosion shape was examined using the Gorgon code developed at Imperial College.⁴⁶ A separate effort, at the University of York, studied the effect of externally applied magnetic fields on the conduction zone in laser-produced plasmas using 2D Vlasov–Fokker–Planck simulations performed with the IMPACT code.⁴⁷ It was found that magnetized transport terms Righi–Leduc heat flow and thermoelectric heat flow are strongly enhanced by non-locality.

ILE Osaka researchers have presented optimized designs for fast ignition targets based upon 2D radiation hydrodynamics simulations performed with their PINOCO code.⁴⁸ 

Heavy ion beam fusion approaches are driven by heavy ion accelerator concepts, which have often been designed using the WARPX particle-in-cell (PIC) code.⁴⁹ 

PIC codes are also used to study a variety of kinetic plasma effects, including plasma interpenetration, wave damping, interaction of speckles with Raman backscatter, as well as particle spectra produced by short pulse lasers. The VPIC code developed at LANL,^50,51 the OSIRIS code developed at UCLA,⁵² and the PSC code at LLNL⁵³ are well known PIC tools.

Simulations play an essential role in ICF, helping to guide the program and helping to understand the physics the occurs in the targets. Since the beginning of LLNL's modern ICF program in 1972, the program has supported an effort to develop dedicated ICF codes. John Nuckolls, who led the formation of the modern ICF program, understood the essential role simulations played in ICF and the special challenges it posed. He believed that these dedicated ICF codes were essential to the progress of his program.⁵⁴ In fact, in the earlier years, a full 30% of the LLNL ICF theory budget was committed to code development.

ICF codes must handle a range of challenging and unique physics problems. Simulating hydrodynamic instabilities in ICF presents several numerical challenges. The presence of ablative stabilization and x-ray preheat requires multigroup radiation transport. Different surfaces are unstable to Richtmyer–Meshkov and Rayleigh–Taylor instabilities at different times of the implosion. These multiple unstable interfaces continuously interact through acoustic gravity waves. Simulating high convergence ratio implosions (CR 35 on NIF) presents numerical challenges. High convergence ratio results in higher growth factors, which are more challenging. In a 3D simulation that high convergence ratio must be simulated on a mesh which has non-uniform spacing in angle. For the high densities required for ICF, electron degeneracy must be accounted for in various physics. Hohlraum simulations must handle a variety of unusual and challenging physics, including detailed nonlocal thermal equilibrium (NLTE) atomic kinetics. For an NIF hohlraum, the $P 2$ Legendre mode drive asymmetry must be controlled to approximately 1 percent. Self-generated or imposed magnetic fields generate forces and impact other physics in a complex manner. Another challenge is simulating laser plasma interactions (LPI), which impact energy flow and drive symmetry in the hohlraum. Cross beam energy transfer (CBET) transfers energy between overlapping laser beams. Stimulated Brillouin Scattering (SBS) reflects laser energy back out of hohlraum. Stimulated Raman Scattering (SRS) reflects laser light and generates hot electron preheat.

Lasnex was already in development two years before the modern LLNL ICF program was formed. Simulations performed with Lasnex helped to demonstrate an understanding of the physics of ICF and produced quantitative target designs. This helped to justify making the investment in the rest of the program, including the first laser, Janus, associated diagnostics as well as target fabrication.

Today, LLNL's ICF program relies upon simulations for a wide range of design activities. Simulations are used before the experiment to design targets. They are used after the experiment to produce simulated diagnostics to interpret experimental results. They are also used to examine sensitivities or improve designs through individual simulations or ensembles of simulations. We will outline in more detail the advances in simulation capabilities made in LLNL codes over several decades and describe first of a kind simulations that these enabled.

The 2D axisymmetric Lasnex code¹⁷ has been under development since 1970. Early target designs were direct drive,⁶ drops of liquid DT, and gas filled glass microspheres. So, the Lasnex models first concentrated on laser light absorption, electron thermal conduction, hydrodynamics, and thermonuclear burn. Various methods for transporting x-rays, neutrons, and alphas soon followed. In 1975, Lasnex simulated the first proof of laser induced thermonuclear burn, a DT gas filled microsphere irradiated by Livermore's Janus two-beam Nd laser.⁵⁵ 

Meanwhile, theoretical work showed that assuming a Maxwell distribution for the electrons was not justified both due to numerous plasma instabilities and because electron transport itself would generate non-thermal distributions. This core-corona decoupling⁵⁶ motivated a model using two electron temperatures and eventually multi-group diffusion models for suprathermal and non-local electrons. Difficulties designing viable targets under these conditions, led to requirements for shorter wavelength lasers and to indirect drive targets.

Indirect drive's requirement to simulate high-Z hohlraum walls soon revealed the need for non-LTE atomic physics processes. Lasnex incorporated several models including average atom, statistical configuration accounting, and detailed configuration accounting (DCA)⁵⁷ modifying them for high density effects like continuum lowering and electron degeneracy. More recently, expensive DCA models have been captured in steady-state tables providing efficient and accurate high-Z non-LTE models.⁵⁸ By 1993 the Lasnex coupled models of laser light, atomic physics, x-ray transport, electron conduction, hydrodynamics, and thermonuclear burn were advanced enough to perform the first 2D integrated hohlraum-capsule simulation.

In addition to general boundary conditions and energy sources, physics-based ray tracing sources handle the 3D propagation and deposition of lasers and ion beams. Laser beams smoothly refract in a continuous electron density profile as they are absorbed by classical inverse bremsstrahlung and parametrized formulas representing various non-linear plasma processes. Cross beam energy transfer, which can affect hohlraum symmetry by moving energy between laser beams, uses reduced laser–plasma interactions models to consistently couple the fully 3D laser intensity pattern and create backward stimulated Raman scattered light.⁵⁹ 

The Lasnex hydrodynamics is Lagrange with optional second order remap to a user-controlled ALE mesh. It includes material strength, elastic-plastic flow, sub-zonal mix models, momentum deposition from all transported particles and slide lines that allow discontinuous tangential velocities and flexibility in zone resolution. In our 2D cylindrical geometry magnetic fields about the symmetry axis can be self-generated by electron temperature and pressure gradients. Fields in the RZ plane can also be imposed initially or generated by external circuit sources making it possible to simulate many pulsed power experiments. Lasnex includes magnetic effects on electron and ion conductivity and viscosity as well as most other extended magnetohydrodynamic (MHD) terms⁶⁰ and uses orbit following methods to account for the effects of both magnetic and electric fields on alpha particle transport. To simulate ion species separation/diffusion when ion mean-free-paths are not small, and normal MHD breaks down, Lasnex recently implemented a 13 moment multi-fluid hydrodynamics model and may eventually replace all electron magnetic terms with a generalized Ohm's law.

Lasnex was always a leader in allowing its users to interactively inspect and modify their simulations, but in 1990 it adopted the Basis interface⁶¹ providing a fully functional programming language. This allows Basis users to create generally useful problem specifications, modify databases such as equation of state and opacity, and develop their own diagnostics. It also enables them to inspect and guide simulations toward optimized solutions, for example controlling the mesh used for ALE remap.⁶² In fact, it was a user in 1996 that made Lasnex an ALE code by calling the remap function every time step. Going forward, the Basis interface and moderate parallelization (dozens to hundreds of CPUs) makes Lasnex an ideal research tool for asking new questions and getting quick answers.

The 3D laser plasma interaction (LPI) code pF3D has existed in some form since the early 1990s. Over the years, many physics upgrades and structural improvements have been made. Early code versions coupled a paraxial laser model to a linear hydrodynamic plasma response to study filamentation and forward Brillouin scattering of the laser.⁶³ Subsequently, plasma wave models that allowed for the treatment of backward Brillouin scattering (SBS) and both backward and forward Raman scattering (SRS) were added, and the hydrodynamic response of the plasma was made nonlinear. Models of heat transport were included to treat thermal enhancement of instabilities, and a great deal of effort was expended to precisely reproduce the various laser spot conditioning and smoothing techniques (including polarization smoothing, phase plates, and smoothing by spectral dispersion) employed at multiple laser facilities. More recently, the capabilities of the code have been expanded to include a foam model,⁶⁴ a new causal explicit heat transport algorithm applicable to nonlocal heat conduction,⁶⁵ a nonparaxial wave solver for wide-angle laser beam propagation,⁶⁶ and inverse bremsstrahlung momentum deposition to investigate the effect of laser beam angular momentum on LPI.

Initially a serial code, the desire to model LPI over ever larger scales while resolving the finely speckled structure of the laser beams used at facilities such as the NIF motivated enabling the code to run distributed memory parallel using MPI.⁶⁷ This permitted very large scale simulations, such as those of multiple interacting quads of laser beams simultaneously undergoing cross-beam energy transfer (CBET) and SRS in cm-scale length plasma^68,69 in early NIF designs where SRS was a major implosion performance degradation. Today, various modules have been made compatible with graphical processing unit (GPU) hardware and development is ongoing to efficiently leverage GPU-based architectures at massively parallel scales. pF3D users have for much of its existence guided simulations using code written in the interpreted language Yorick.⁷⁰ This interpreted environment has facilitated rapid model development and testing and gives the user great control and diagnostic capabilities. The code is currently undergoing a full restructuring to be steered in a Python environment.

In indirect-drive ICF targets, LPI can scatter laser energy back out of the hohlraum or modify its spatial deposition, impacting implosion symmetry in a time-dependent fashion. It can also preheat the fuel, impeding compression. In the current low gas fill density (0.3 mg/cm³) ignition designs, SRS is typically energetically insignificant. SBS reduces drive by up to a few percent but remains a process of concern, primarily because of its ability to damage optics. pF3D simulations explained experimentally observed patterns of optics damage caused by SBS at the NIF.⁷¹ Simulations of SBS reproduce measurements made by the SBS diagnostics at the NIF across a range of experiments, capturing both time dependence as well as total energy.⁷² Efforts at the NIF to mitigate SBS have included mixed-ion hohlraum liners, such as AuB and Ta2O5, where the intent is to increase the ion Landau damping experienced by the ion acoustic waves driven during SBS. pF3D simulations that include the linear multi-ion Landau damping in such plasmas have guided and informed experimental efforts,⁷³ while the limitations of describing the plasma with a static (Maxwellian) distribution function shape typically employed in pF3D have been explored using the fully kinetic Vlasov–Fokker–Planck code LOKI.⁷⁴ SBS mitigation remains an area of active development at the NIF.

As NIF was in the planning stages, LLNL's ICF program became interested in a 3D code. 3D simulations are necessary for a variety of reasons. The Rayleigh–Taylor (RT) instability grows larger in 3D than in 2D. This is because nonlinear saturation occurs at a higher amplitude and the nonlinear growth rate is also higher. The laser drive asymmetry is also 3D. The NIF illumination pattern in the hohlraum, with perfect pointing and power balance, has various m = 4 and m = 8 3D spherical harmonic modes. The inclusion of laser pointing and power balance errors create various modes with (⁠ $ℓ$⁠,m) = 1–3. In addition, engineered features such as the fill tube, tent, and hohlraum windows are 3D. Various asymmetries can combine more disruptively in 3D than 2D. So, a more realistic and accurate simulation, which includes all asymmetry sources, requires 3D simulations.

In 1994, we began the development of HYDRA as a 2D/3D ICF code. Bob Tipton of LLNL had started work on a 3D hydrodynamics package. At that point, when Marty Marinak began collaborating with Bob, HYDRA consisted of 50 000 lines of code. Years later as the team grew, under the leadership of Marinak, a broad range of physics and simulation capabilities developed. Today, HYDRA consists of 1.3 × 10⁶ lines of code. HYDRA has been extensively tested against a wide variety of test problems, and experiments, many of the latter published in journals.^75–79 HYDRA is used to design and simulate a wide range of ICF targets (laser indirect drive, laser direct drive, magnetic drive, and heavy ions) and high energy density (HED) physics at LLNL, SNL, LANL, LLE, and universities.

HYDRA simulates a wide range of physical process, with several physics models available for almost every one of these. Laser light transport and deposition are modeled with 3D ray tracing and inverse bremsstrahlung deposition. The laser package includes inline semi-empirical models for cross beam energy transfer (CBET),⁵⁹ for stimulated Raman scattering, and stimulated Brillouin scattering. There are two models for direct drive laser deposition, including a method of inverse point projection for low noise, and two methods for CBET, developed in conjunction with LLE.⁸⁰ Several options for electron transport are available, including flux limited conduction, which is anisotropic in the presence of magnetic fields, multigroup non-local electron transport, and relativistic PIC, through linking to a kinetic code Zuma.⁸¹ The nonlocal model is an extension of the method of Schurtz⁸² extended to treat inverse cascade for accurate electron slowing down range and to enable implicit time stepping. Ion thermal conduction is treated as well as electron–ion coupling. Several methods for radiation transport are available, including multigroup diffusion, 1D/2D multigroup Polar $S N$^83,84 and implicit Monte Carlo transport.⁸⁵ Ion beams are treated either with a 3D ray tracing method or Monte Carlo particle transport, with a choice of stopping power models. Magnetic fields are treated with 2D/3D resistive MHD, which includes all of the terms of Ohm's law.^60,86 A generalized circuit model is available, including a Spice network and Hutsel circuit elements, used for example in simulating targets on the Z machine^87,88 An interface to MFEM⁸⁹ allows consistent treatment of the MHD equations in regions where multi-resolution advection is used. Thermonuclear burn is treated by one of two models. Full relativistic Monte Carlo transport of neutrons, gammas, and charged particles is available, including in-flight reactions. The package tracks the orbits of charged particles in magnetic fields. A second multi-group diffusion burn model of charged particle transport is available, along with free streaming neutron transport. Momentum deposition is accounted for all particles transported. Radiochemistry is available either inline or through post processing.

A wide range of atomic physics models and EOS are available. Analytic EOS's and the Quotidian EOS (QEOS) are available inline.⁹⁰ In addition, the tabular Livermore EOS system is available. Tabular LTE opacities can be generated on demand. Also available are inline LTE and non-LTE opacities and EOS from DCA⁵⁷ and XSN.⁹¹ HYDRA is a Lagrange ALE code with automatic mesh motion and a wide range of mesh control options. These range from very localized controls to remapping the problem to an entirely new mesh. HYDRA uses a block structured mesh with a multi-resolution capability to avoid issues with mesh singularities. Reduced and enhanced connectivity are supported at block boundaries to enable flexible conformal meshing. An inline shape generation library is available to generate complex shapes on arbitrary meshes using material interface reconstruction. HYDRA offers many models for isotropic strength, including the elastic–plastic flow. There are a range of atomic mix models, including through the RANSBox library.⁹² Inline tracer particles are available to track material elements. HYDRA is fully parallelized to generate problems and run them on distributed memory platforms, using a combination of distributed and thread-based parallelism. HYDRA has run an individual 3D capsule simulation on 262 000 processors using 2.6 × 10⁹ zones on LLNL's Sequoia machine. It also has a set of capabilities that take advantage of GPU processors on hybrid architectures such as LLNL's Sierra and El Capitan machines. HYDRA includes a flexible Python interface offering a fully capable programming interface. This gives users a wide range of capabilities to control the problem, introduce their own physics modules, and develop their own diagnostics. It also allows them to write out various additional quantities from the code for inspection and use.

Unprecedented increases in computing power along with improved radiation hydrodynamic code algorithms have enabled more realistic and accurate solutions. Back in 1994 HYDRA was routinely running problems on a Cray Y/MP, which had a peak processor capability of 250 MFlops, when using vectorization. A long series of improvements to platforms deployed by the advanced simulation and computing (ASC) program have increased the aggregate computing power available to us by many orders of magnitude. The El Capitan machine scheduled to be delivered to LLNL during 2024 will have a peak theoretical capability of two exaflops. This represents a factor of 10 × 10⁹ increase in theoretical computing power available to us over 30 years. It is possible that such a huge proportional increase in computing power will never again be replicated over a 30-year period. The combination of the aforementioned factors enabled HYDRA to achieve a long series of first-of-a-kind simulations. We will briefly describe a number of these.

HYDRA performed the first 3D simulations of RT growth on indirectly driven planar foils in the 1990s. These examined shape effects and multimode coupling and saturation, as will be described in Sec. VIII.

HYDRA performed the first 3D simulations of Nova⁹³ and NIF capsules,^94,95 as will be described in Sec. VIII.

The first high resolution (⁠ $ℓ ∼ 1000$⁠) simulations of a double shell capsule were performed using HYDRA.⁹⁶ These underlined the necessity of including high mode numbers and pointed to various methods of reducing overall RT growth.

HYDRA performed the first 3D integrated simulations of NIF hohlraums, run with full 3D laser transport and Monte Carlo photonics.⁹⁷ 

HYDRA performed groundbreaking 3D simulations of the Be grain structures on NIF capsules, considering overall growth of structures seeded.⁹⁸ 

HYDRA also performed the first full sphere high resolution (⁠ $ℓ ∼$ 100, 200) NIF capsule simulations as will be described in Sec. VIII. Improvements in simulation capabilities enabled HYDRA to simulate the full set of NIF nuclear diagnostics on implosion experiments.

HYDRA performed a number of integrated simulations of fast ignition designs with a hohlraum having the capsule mounted on a reentrant cone. These helped to clarify the requirements for short pulse laser energy.

More recently, LLNL's inline DCA package was restructured to make efficient use of GPUs on LLNL's ASC Sierra machine. We have constructed a set of NLTE models for gold with increasing complexity going as their names progress alphabetically from model A to H.⁹⁹ This results from including photo-ionization term splitting and extending to doubly, triply, and quadruply excited states in the successively more complex models. Compared to our 2010 baseline model, the most complex, model H, tracks 100 times as many levels and requires a similar ratio of computing power. LLNL's Sierra machine enables us to use the highly complex DCA NLTE models in-line for integrated hohlraum simulations. The highest resolution model tracks 20 × 10⁶ configurations per zone per species. Improved DCA models bring opacity and emissivity into better agreement with detailed codes.

The set of inline models of CBET, SRS, and SBS in HYDRA's raytrace package brings important advantages. These include the consistent treatment of dynamic state variables, inclusion of ray refraction, and less designer interaction with the simulation, compared with when these are treated by postprocessing results. LPI has fundamentally important effects on laser energy flow and hot electron production in a hohlraum. For example, energy on a given laser beam entering the laser entrance hole (LEH) can be transferred to another beam by CBET. Then, some may be backscattered out of the hohlraum from that beam by SRS and SBS.

Let us consider how the inline package was applied to an extended series of experiments with CH capsules. These were performed to examine the ability to model and control symmetry. Figures 1(a) and 1(b) show the Hybrid-C target, which used a full-scale CH capsule in a large low gas-fill hohlraum at full NIF energy. The goal of this series of experiments was to test the efficacy of small amounts of wavelength detuning $Δ λ$ between the inner and outer beams to control $P 2$ and symmetry swings. Figure 2 shows the resulting $P 2$ amplitude for integrated simulations using inline CBET and a consistent set of drive adjustments. Modest multipliers are required on the laser power in the integrated simulations to match the in-flight symmetry, in-flight capsule velocity, and shock velocities along two lines of sight (pole and equator). These were determined for a given shot and held fixed over all the simulations. The set of shots includes various plastic ablator capsules from the high foot campaign, and different scale hohlraums, including one from Hybrid-C. These low gas fill hohlraums with plastic capsules had varying target scale sizes, difference capsule sizes, different drive pulses, and different wavelength detuning between 0 and 1 Å. The black symbols show the $P 2$ from hotspot data. The red symbols show the hotspot $P 2$ from the simulations. At $Δ λ = 0 − 1 Å$ simulations using inline CBET capture $P 2$ symmetry trends of low gas-fill CH data. The inline CBET mode has substantially improved our modeling of symmetry effects in NIF hohlraums.

We are now using cognitive simulation to study the probability of possible experimental outcomes. These involve ensembles of many runs. A prerequisite is code improvements that have enabled simulations to run fast enough and robust enough to perform large, automated scans. Here greater than 98% of the simulations run to completion with no human intervention. Figure 3 shows 30 000 2D HYDRA simulations with varying drive, asymmetry, and mix. These are drawn from a set of 150 000 simulations. Each of these represents a possible outcome.¹⁰⁰ The orange and blue curves show the boundary of the 50% most probable region. Recent shot data are generally falling within the most likely probability contours predicted from the analysis. This helps support that the simulations are operating in the correct location in phase space.

Having covered some of the more recent simulation advances, let us consider the bigger picture of how simulations helped to guide the ICF program to breakeven.

The high convergence required in ICF sets very strict demands on the uniformity of the implosion. The Rayleigh–Taylor (RT) instability, along with Richtmyer Meshkov (RM) instabilities are centrally important in these implosions. The RT instability is the most damaging as it grows exponentially vs time in the linear growth regime. Linear growth factors of several hundred to over one thousand can occur in the ablation front of an NIF capsule implosion. We have spent much effort developing good ways to calculate this growth. The simulations of hydrodynamic instabilities have been extensively validated against experiments. Much of this early work was done in the HEP2 and HEP4 campaigns on the Nova laser.¹⁰¹ These studied all aspects of ablation front RT and RM in the weakly nonlinear regime. NIF Ignition targets are designed to remain in the weakly nonlinear regime, in which the final perturbation is directly related to the initial surface or volumetric perturbation.¹³⁴ This occurs when the initial perturbation amplitude is sufficiently small, enabling the instability growth and evolution into the nonlinear regime to avoid a turbulent state.

The presence of ablative stabilization distinguishes the RT on the ablating surfaces of an NIF capsule from RT, which occurs in most other physical systems. Ablative stabilization fundamentally changes the nature of the Rayleigh–Taylor instability in the ablators of indirectly-driven targets. Ablative stabilization reduces the RT growth rates of various modes, while completely stabilizing sufficiently high modes,^102,103 playing a centrally important role in enabling weakly nonlinear behavior. Only a limited set of modes need be simulated in ablatively stabilized surfaces. This makes it possible to resolve essentially the full range of important modes in 3D on modern computers. Operating in the weakly nonlinear regime enables one to specify detailed limits on surface roughness spectra in order to limit the final perturbation amplitudes. The ability to model a range of single mode wavelength perturbations on planar foils was demonstrated in the HEP2 campaign for polystyrene and beryllium ablators.^104–106 This included the evolution of single mode perturbations through the linear regime and into nonlinear saturation. Further experiments studied the evolution of mode coupling in targets with 2D perturbations consisting of two modes and eight modes, respectively.^107,108

Planar experiments examined the dependence of the nonlinear saturation amplitude of a single mode 3D perturbation upon the perturbation shape, which agreed well with simulations.⁷⁹ An experiment with a prescribed 3D multimode perturbation on a foil tested our ability to model 3D multimode coupling and nonlinear saturation relevant to NIF ablators.¹⁰⁹ The perturbation spanned a decade in Fourier space over a range of modes expected to be the most important on an NIF ablator, with initial amplitudes designed to give a similar degree of nonlinear saturation as an NIF capsule ablator. The perturbation was designed with reflection symmetries so as to facilitate numerical simulation with the limited computer power available at the time. The foil was mounted on the side of a Nova hohlraum to produce indirectly driven instability growth. This also enabled 2D images of the instability growth to be obtained using face on radiography. Figure 4 compares the experimental radiographs with the simulated images. The experimental images show the perturbation growth emerging from the microchannel plate noise. The broad light areas are bubbles surrounded by dark interconnecting spike sheets. The bubbles are in a hexagonally close packed geometry characteristic of weakly nonlinear RT evolution. The simulations show a strikingly similar evolution of the perturbations. Figure 5 shows the quantitative comparison of the experimental data points and the curves from simulation vs mode number at different times. The 3D HYDRA simulation is in quantitative agreement with measured evolution into multimode nonlinear saturation.¹⁰⁹ 

Experiments performed on Nova capsules as part of the HEP4 campaign examined the effects of two distinct perturbations, a regular soccer ball pattern and randomly located Gaussian perturbations. 3D simulations showed a similar sensitivity in the yield degradation vs perturbation amplitudes as the experimental measurements.⁹³ More recent hydro growth radiography (HGR) experiments tested the ability to model surface perturbations on imploding spheres using face on radiography.⁷⁷ These dedicated experiments enabled us gradually to gain confidence of the numerical algorithms in HYDRA and Lasnex to simulate the various aforementioned physical effects important in NIF capsules, for specific ablators.

NIF ignition capsules utilize a fill tube to fill the interior with fuel. They are supported in the hohlraum using a pair of 50 nm thick membranes called the tent. Both of these engineered capsule features generate important perturbations. Because they are extremely small features compared to the scale of the capsule they pose particular challenges to simulate. A major effort went into developing methods to simulate capsule engineered features. Simulating them with the required resolution and solid angle requires such computing power that it only became possible around 10 years ago. Prior to this, the tent was approximated crudely as a step change in the thickness of the ablator where the tent contacted the capsule. Early in the operation of NIF, improved diagnostics enabled a more detailed view of capsule perturbations during the implosion, showing large scars visible at the tent contact locations.¹¹⁰ So making use of the increased computing power ab initio simulations of the capsule with the tent were then performed.^111,112 These challenging simulations resolved the tenuous 50 nm tent structure. Simulated x-ray images showing similar scars at the tent contact location.^110,113 These simulations correctly predicted a strong dependence of the tent scar upon the tent liftoff angle. They also showed a dependence upon the tent thickness. In simulations, these scars launched rings of material into the hotspot of the early plastic ablator capsules in the low and high foot campaigns, substantially reducing the yields by itself. These simulations provided many valuable insights regarding the ultimate impact of the tent perturbation and how it could be minimized.

Resolving the effect of the fill tube requires very fine zoning, in HYDRA equal to 12 000 zones in angle across the capsule. The fill tube generates a jet that injects material with impurities into the center of the hotspot. X ray diagnostics show the motion of the impurities into the center. Since the vortex generated by the fill tube during the implosion entrains material into the hotspot in a highly nonlinear manner, including other perturbation sources in the simulation, such as low mode asymmetry and surface roughnesses, is required. For the more recent implosions on NIF, which use tungsten doped diamond, the hotspot x-ray emission due to tungsten impurities is correlated with the mass of tungsten injected into the hotspot.¹¹⁴ As shown in Fig. 6, the emission and reduction in capsule yield due to this injected tungsten mass agrees reasonably well between the simulations and experiments. Early cryogenic capsules shot on NIF had 30  $μ$m diameter fill tubes. As shown in Fig. 7, simulations indicated that in addition to improving symmetry and stability, reducing fill tube to 2  $μ$m was important for achieving high yield. A major effort in target fabrication went into reducing the size of the fill tubes to 2  $μ$m. Developing methods for attaching these to the capsules and hohlraum have required a dedicated effort. Simulations indicated that the fill tube stood out from all other perturbation sources in terms of its impact and importance, particularly for diamond ablator capsules. These fill tube simulations were also compared with results from Lasnex and the LANL xRAGE code.³⁰ The simulations, and favorable comparisons to the emission data, helped underscore the importance of reducing their impact to the program and provide a definite, quantitative goal for reduced size.

In addition to the jet of impurities introduced into the hotspot from the fill tube, simulations predicted that similar jets of impurities would be created by discrete features, such as divots, voids, and inclusions, that are large enough. These meteors were first predicted in 2D high resolution HYDRA capsule simulations first performed in 2006, indicating the presence of a new mix mechanism for NIF capsule implosions.^116,117 As this was determined years before NIF first went into operation, a special x-ray spectrometer was developed and fielded for NIF to enable the composition of these meteors to be determined. This is an example of simulations helping to set future requirements for diagnostics. After NIF began experiments, the meteors were observed as expected. The x-ray spectrometer was able to confirm that these originated in the ablator.¹¹⁸ Simulations of meteors created by various discrete defects have been used to set a specification on the allowable volume in cubic micrometers for these features. This limit approximately corresponds to what is seen experimentally. So, these simulations help provide guidance as to the allowable volume of features, and their depth in the ablator.¹¹⁹ 

NIF ignition capsules require precise timing of each shock. An absolute drive accuracy of approximately one percent is required to maintain the required adiabat of the capsule fuel and ablator with the desired implosion velocity. We did not expect our codes to be able to calculate the absolute drive to that level of accuracy without adjustments. So given the essential importance of shock timing, a method had to be devised to measure the shock timing experimentally. This presented a major challenge for a variety of reasons. The measurement had to work for opaque ablators such as HDC and beryllium.¹²⁰ All viable methods required very significant changes to the hohlraum geometry. The shock timing had to be tuned in the surrogate hohlraum. This leaves the question of how can one have confidence the shock timing is the same in the actual hohlraum? An elegant solution was devised to allow a measurement of the timing of shocks transiting the shell.¹²¹ This employed a “keyhole” hohlraum which has a line of site pipe attached to a mock capsule. The dimensions of the conical pipe were designed so that the estimated albedo times surface area was equal to the estimated albedo times area of the lost wall and capsule areas. However, there are a number of differences not addressed by this geometric equivalence. For example, the laser beams which strike the light pipe do so at a very different angle than the wall they miss as shown in Fig. 8. The laser spot pattern on the wall is modified. If these differences were enough to change the timing in the surrogate target relative to the actual target by some 2%, that detuning could be enough to prevent the capsule from igniting.

To assess the quality of surrogacy of the keyhole target 3D HYDRA simulations were conducted for both geometries. These employed HYDRA's multiblock structured mesh capability to allow seamless zoning of ablating surfaces. As shown in Fig. 9(b), the keyhole mesh uses reduced and enhanced connectivity points at block boundaries. This allows it to employ best practices ablative zoning on all surfaces. A volume averaged drive was extracted at pole and equator locations for both simulations. The drive temperature histories, shown in Fig. 10, show close agreement with and without the keyhole.¹²² Thus the shock timing method for all NIF cryogenic capsule implosions relies upon the equivalence of keyhole targets established previously with 3D HYDRA simulations.

One of the most significant impediments to obtaining ignition on the NIF was the appearance of sizeable random low mode asymmetries. These had the geometry of a spherical harmonic $ℓ$ = 1, m = 1 perturbation, which varied randomly in amplitude and direction from shot to shot. The amplitudes were large enough to prevent ignition by itself.¹³⁰ To understand the origins of these asymmetries a series of 3D integrated hohlraum simulations were performed with HYDRA. These included the dominant sources for the m = 1 asymmetry: laser power imbalance, capsule thickness variations and diagnostic windows.¹²³ The diagnostic window is very small. It is a gold coated HDC window with a 120 μm gap. These were treated separately using best practices HYDRA simulations which resolved the ablating material around the gap and allowed it to close with ablation, as shown in Fig. 11. This small (nearly point) source was included in the full integrated simulation as a reduced model. Figure 12 compares experimental data with simulation results for shot N180226. The colors show the areal density variation over solid angle, which are closely matched by the simulation. Also listed are the apparent m = 1 hotspot velocity magnitude and direction angles. These are well matched by the simulation. We can match these reasonably well in most shots. In addition to the detailed simulations, a simplified semi-analytic model by Brian MacGowan yielded similar conclusions.¹²⁴ Drive asymmetry due to laser power imbalance and capsule shell thickness variations were the main sources of the asymmetry. As a result, tighter specifications were placed upon the m = 1 in the capsule ablator and ice layers. To reduce the low mode laser power imbalance, the front end of the NIF laser was rebuilt. Finally, the diagnostic window was responsible for a much smaller and consistent contribution to m = 1. A design modification to the hohlraum eliminated the intrinsic m = 1 contribution from diagnostic windows.

High resolution full sphere 3D capsule simulations have improved our understanding of implosion performance, and the relative importance of factors that limit it. These simulations are regularly run resolving all spherical harmonics up to $ℓ$ = 100.^125,126 A comparison simulation has been run at $ℓ$ = 200, and the results were “nearly identical” to the case resolving $ℓ$ = 100. In these 3D simulations, surface roughness is represented “as shot.” These include effects of the tent, fill tube, high-mode mix at the embedded interfaces, and drive asymmetries. In these simulations, multi-group diffusion radiation transport is applied, including NLTE (non local thermodynamics equilibrium) hotspot emissivities. The x-ray drives are constrained by VISAR,¹²⁷ ConA,¹²⁶ and bang time data. Plasma viscosity is included in the hotspot. Monte Carlo methods are used to transport fusion products, neutrons, charged particles and gamma rays.

Full sphere high resolution 3D capsule simulations greatly enhanced our understanding of NIF capsule implosions. Eliminating any artificial symmetries from the simulations resulted in substantially lower stagnation pressures in the hotspot, due to greater residual kinetic energy. Unlike the simplified models with artificial symmetries, the plasma at the center of the capsule is never truly stagnant. These 3D simulations produced markedly improved agreement with various diagnostics, especially important nuclear diagnostics. The various 3D asymmetry sources combine in complex ways not seen in 2D simulations. Also, the nonlinear RT saturation amplitudes are larger in 3D, leading to greater degradation of capsule performance.

Earlier 3D simulations that included most sources of asymmetry were able to describe the performance of the NIF low foot and high foot CH ablator capsule implosions, including neutron yields, neutron downscattered ratio, and ion temperature¹²⁵ generally close to or within error bars. Simulations of the low foot capsules showed the combined effects of a range of 3D asymmetries, with their larger saturation amplitudes, resulted in a high degree of cold fuel and shell material mixing into the core, reducing the hotspot into small isolated pockets of warm fuel. The fraction of clean 1D yield of these implosions was around one percent in the simulations and experimental data.¹²⁵ The simulations were able to match the various experimental measurements reasonably well without introducing any additional physical explanations. Simulations of capsules in the subsequent high foot campaign showed greater capsule stability particularly against high mode perturbations, resulting in improved capsule performance. Again, the simulations were able to match the various experimental measurements reasonably well. Overall agreement has since improved as more complete models of the physics and the initial perturbations have been incorporated.

The Bigfoot and Hybrid-B campaigns utilized HDC capsule ablators and were designed for greater stability, learning from the previous campaigns and simulations. A simulation of one of these HDC ablator capsules N170601 is illustrated in Figs. 13(a) through 13(d). As the implosion advances the visualization zooms with the capsule to maintain the same overall size. High mode growth in the ablation front is apparent, along with the growth of the fill tube jet near the equator on the right side cut away view.¹²⁶ These high modes are less able to feedthrough and grow on the inner capsule shell surface during deceleration. Only mode numbers less than 30 are able to grow on the inner cold fuel surface due to conductive ablation stabilization. It is these lower mode features inside of the capsule, along with discrete features, such as the fill tube and meteors, that have the major impact on the hotspot's ability to ignite and propagate into the dense fuel.

In preparation for the NNSA 2020 review, a series of 3D capsule simulations was performed on significant capsule implosions that include the highest yield at the time, performance cliffs, and experiments that assessed repeatability or hydrodynamic scaling. Simulation results are plotted in Figs. 14(a) and 14(d) for neutron yield, neutron downscattered ratio (DSR), ion temperature and burn width. The diagonal line marks where data and simulation exactly match. The blue triangles are 2D simulations whereas the red squares are 3D simulations. The high-fidelity 3D HYDRA capsule simulations capture the global trends in NIF implosion data, giving better agreement than 2D. The close level of agreement for this set of highly significant implosions gave us confidence that these simulations were capturing the important implosion physics including the burn.

Some 5–6 years ago, we were trying to understand what was standing between our implosions and obtaining ignition. There was a line of thought that by “fixing” the various asymmetry sources, including the fill tube and tent, that we would be able to achieve ignition. The 3D simulations performed indicated various asymmetry sources were acting in concert to degrade capsule yields. Simulations indicated that fixing just one or two of these would not result in a measurable improvement in capsule performance. These indicated that even if we fixed all of them to within the abilities of target fabrication and the laser the capsule would still not ignite. These made it clear that while we needed to work on all the asymmetry sources, it was imperative that we needed to develop more robust target designs.

Theory indicates that a larger target is more robust everything else equal.^{12,128,129,131,132} However, with fixed laser energy, there are tradeoffs. This is where simulations play an indispensable role. Simulations evaluate designs allowing for optimizing overall performance. Approaching the task of optimizing a larger target, computer simulations were used to converge on the design.¹⁴ The design choices were also informed by semi-analytic models.¹³³ The simulations indicated that improved robustness could be achieved with a somewhat larger hohlraum and lower case-to-capsule ratio. Figure 15 shows the HYBRID-E design, which compared to a HDC (BigFoot) target has a much bigger capsule in a slightly larger hohlraum. Both HYDRA and Lasnex simulations indicated this design would be more robust.

The challenge of increasing initial capsule radius with fixed available laser energy is the potential loss of energy density. To avoid loss of energy density, the Hybrid-E design also balanced key metrics important for maintaining high hotspot pressure such as the compressibility of the fuel (“adiabat” = plasma pressure/Fermi pressure), $v imp$⁠, implosion symmetry, and hydrodynamic stability.¹⁴ The N210808 design used a thicker DT ice layer compared to a hydrodynamic scaling of Bigfoot (⁠ $∼$30% increase in DT thickness for a $∼$10% increase in scale), which can protect the “hotspot” from high-Z ablator mixing, translating to better implosion quality, but also had a lower design fuel adiabat.¹⁴ Maintaining sufficient ablator mass is also important for stability and confinement.

Simulations¹⁴ and theory¹³¹ indicated sizeable benefits to robustness from reducing the coast time for this design. The coast time is defined as the time interval from when the laser turns off to when the capsule reaches peak convergence/compression. To reduce the coast time, the hohlraum was made even more efficient by reducing the laser entrance hole (LEH) diameter.¹⁴ It was reduced by 27% by reducing the radius from 3.65 to 3.1 mm. The reduced radiation loss means one can get the same drive (⁠ $T rad$⁠) with lower laser power. The design added the energy to the back end of the pulse to reduce the coast time. This modification to the HYBRID-E design would change the drive symmetry. Simulations were used, along with data driven models, to re-tune the symmetry successfully for the smaller LEH on the first DT shot.

There were also other improvements for N210808 that simulations indicated were important. The fill tube diameter was reduced from 5  $μ$m to 2  $μ$m, as described previously. There were accumulated laser improvements, some of which were described here previously. The shot used the highest quality diamond capsule ever produced. Also, subtle modifications were made to the drive pulse to reduce instability growth at the fuel ablator interface. This is the set of changes that enabled N210808 to surpass Lawson's ignition criterion for the first time.

Improvements to the NIF laser enabled it to increase its deliverable energy to 2.05 MJ, compared with 1.9 MJ used in the N210808 experiment.^20,21 Additional design modifications were made to enable effective use of the additional laser energy. Simulations indicated that using a longer laser pulse with a 6  $μ$m thicker ablator would enable the capsule shell to make efficient use of the extra laser energy.¹⁹ It would provide higher-energy coupling of the radiation drive to the hotspot, higher total areal density at peak compression, and improved stability. The percentage of W dopant in the diamond was also increased compared to N210808. The simulations also indicated these changes would make the design more robust and enable higher yield. Specifically, the changes were predicted to increase a key ignition metric EP² by approximately 25% compared to N210808, using radiation hydrodynamic simulations, where E is the hotspot internal energy and P is the hotspot pressure at bang time with $α$-off simulations.¹⁹ Increasing the ignition margin enables igniting the hotspot in the presence of various asymmetries and ablator mixing. There is experimental evidence to support this increased robustness. The very first shot with this design N220919 produced greater than 1 MJ yield, even with worse capsule quality and worse implosion symmetry than N210808.¹⁹ The symmetry of N221204 was optimized using a combination of integrated simulation for the early and middle parts of the pulse, benchmarked to shock timing data after N220919, and experimentally measured playbooks.¹⁹ Preshot HYDRA simulations predicted the second shot with symmetry improvements (N221204) would achieve energy breakeven with a greater than 2.5 times yield increase. The subsequent experimental yield fell within the preshot predicted range.

The postshot HYDRA simulation for N221204 captured the burn physics for this new higher yield regime fairly well. As is routinely done, an integrated 2D hohlraum simulation was run. A frequency dependent x-ray source was extracted and then applied to a high resolution 2D capsule only simulation using the methodology described in reference.¹⁴ This simulation represents all known asymmetry sources that can be treated in 2D, resolving modes up to $ℓ ∼ 250$⁠. Figure 16 shows the simulated values compared with data. The neutron yield is well matched. The simulated ion temperature increased from 11 to 14 keV relative to N210808 and the burn width decreased from 75 to 60 ps (approximately). The same relative changes were seen in the data, consistent with the model, showing the higher yield N221204 burned hotter and faster than N210808. The areal density was well matched. It is a principal indicator of how well the shell confines the burning plasma.

With the higher laser energy used in this design ignition is reproducible and predictable. Preshot simulations correctly predicted ignition for both N221204 and the first attempt at repeating it with a high-quality capsule, N230729. While there were small changes in N230729, the yield of 3.88 MJ was similar to N221204.

In summary, the December 5 NIF shot N221204 achieved ignition by all definitions and was the first laboratory plasma to achieve energy breakeven. Simulations performed using LLNL's multiphysics ICF codes HYDRA and Lasnex and the specialized LPI code pF3D played important roles in helping to guide LLNL's ICF program to these accomplishments. They were relied upon to perform detailed simulations used to design targets and interpret experimental results. They were also used to examine sensitivities and improve designs through individual simulations and ensembles.

Over 1 × 10⁶ person hours were expended by code developers to create the most complete set of physics models, and add a range of new code capabilities which enabled various first-of-a-kind simulations. Vast increases in computing power, enabled by succeeding ASC platforms, combined with these algorithmic advances, enabled more realistic and accurate simulations. This has enabled simulations to treat all known asymmetry sources. These simulations helped to guide the program, to understand the impediments to breakeven, and optimize every aspect of target design. Examples presented included understanding hydrodynamic instabilities from various sources including engineered features. They include underpinning the method for timing shocks in capsules. Simulations helped to explain “random” low mode drive asymmetries and what was needed to mitigate them. High resolution 3D HYDRA capsule simulations captured the global trends in NIF implosion data, giving better agreement than 2D. Several years ago these showed that a variety of asymmetry sources was preventing ignition and made clear the need to develop more robust designs. Codes were employed to optimize the designs, helping to enable more robust implosions and increased yields, leading to N221204.

We acknowledge Art Pak for the analysis of emission from experiments with varying fill tube diameters. Gail Glendinning performed the analysis of the planar foil experiments with multimode perturbations. Ryan Nora performed the simulation scan used in the cognitive simulation analysis figure. The contours shown on that figure were developed with a neural network developed by Eugene Kur. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

The authors have no conflicts to disclose.

Michael M. Marinak: Methodology (equal); Project administration (equal); Software (equal); Validation (equal); Writing—original draft (equal). Judith Alice Harte: Methodology (supporting); Software (supporting); Validation (supporting). David Bailey: Methodology (supporting); Software (supporting); Validation (supporting). Lee A. Taylor: Methodology (supporting); Software (supporting). Steven Langer: Methodology (supporting); Software (supporting); Validation (supporting). Mikhail Alexander Belyaev: Methodology (supporting); Software (supporting); Validation (supporting). Daniel S. Clark: Formal analysis (equal); Methodology (supporting); Validation (supporting). Jim A. Gaffney: Formal analysis (equal); Methodology (supporting); Validation (supporting). B.A. Hammel: Formal analysis (equal); Methodology (supporting); Validation (supporting). Denise Hinkel: Formal analysis (equal); Methodology (supporting); Validation (supporting). Andrea L. Kritcher: Formal analysis (equal); Methodology (supporting); Validation (supporting). George Zimmerman: Conceptualization (equal); Methodology (supporting); Resources (supporting); Software (supporting); Validation (equal); Writing—original draft (supporting). Jose L. Milovich: Formal analysis (equal); Methodology (supporting); Validation (supporting). Harry F. Robey: Formal analysis (equal); Methodology (supporting); Validation (supporting). Christopher Weber: Formal analysis (equal); Methodology (supporting); Validation (supporting). Thomas Chapman: Methodology (supporting); Software (supporting); Validation (supporting); Writing—original draft (supporting). Gary D. Kerbel: Software (supporting); Validation (supporting). Mehul Vasant Patel: Methodology (supporting); Software (supporting); Validation (supporting). Joseph Koning: Methodology (supporting); Software (supporting); Validation (supporting). Scott Michael Weber Sepke: Methodology (supporting); Software (supporting); Validation (supporting). Britton Chang: Methodology (supporting); Software (supporting); Validation (supporting). Christopher Schroeder: Methodology (supporting); Software (supporting); Validation (supporting).

The data that support the findings of this study are available within the article.