We present an analytic thick shell model for indirect-drive ICF implosions that starts by using the Rocket equation to evaluate peak fuel kinetic energy and hence by energy balance, stagnated fuel internal energy. We then use the approximation of the hot spot decelerating adiabatically to an isobaric stagnated state coupled to a self-consistently calculated fuel aspect ratio. The model, validated by 1D radiation-hydrodynamics simulations, provides sensitivities of indirect-drive yield, DSR and ignition metrics to a host of initial and final state capsule and hohlraum parameters, applicable to the current relevant regime of igniting implosions. The model is used to highlight parameter trade-offs and estimate expected sensitivity in 1D compression, stagnated areal density and yield at current and higher performance levels. Several new insights are presented. Of note, we explain the weak dependence of ablator thickness on implosion velocity for designs with buried dopant layers, the uncertainty in performance improvement when adding fuel or reducing initial hot spot density, and the role of ionization energy and albedo in setting ablator efficiency.

Indirect Drive Inertial Confinement Fusion Experiments on the National Ignition Facility (NIF) have achieved a burning plasma state with neutron yields exceeding 170 kJ, roughly 3 times the prior record and a necessary stage for igniting plasmas. The results are achieved despite multiple sources of degradations that lead to high variability in performance. Results shown here, for the first time, include an empirical correction factor for mode-2 asymmetry in the burning plasma regime in addition to previously determined corrections for radiative mix and mode-1. Analysis shows that including these three corrections alone accounts for the measured fusion performance variability in the two highest performing experimental campaigns on the NIF to within error. Here we quantify the performance sensitivity to mode-2 symmetry in the burning plasma regime and apply the results, in the form of an empirical correction to a 1D performance model. Furthermore, we find the sensitivity to mode-2 determined through a series of integrated 2D radiation hydrodynamic simulations to be consistent with the experimentally determined sensitivity only when including alpha-heating. Recent improvements in the indirect-drive inertial confinement fusion experiments include the achievement of burning plasma state. Here the authors report the scaling of neutron yield in a burning plasma of Deuterium-Tritium fusion reaction by including the mode-2 asymmetry.

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. (C) 2024 Author(s).

An indirect -drive inertial fusion experiment on the National Ignition Facility was driven using 2.05 MJ of laser light at a wavelength of 351 nm and produced 3.1 +/- 0.16 MJ of total fusion yield, producing a target gain G = 1.5 +/- 0.1 exceeding unity for the first time in a laboratory experiment [Phys. Rev. E 109, 025204 (2024)]. Herein we describe the experimental evidence for the increased drive on the capsule using additional laser energy and control over known degradation mechanisms, which are critical to achieving high performance. Improved fuel compression relative to previous megajoule-yield experiments is observed. Novel signatures of the ignition and burn propagation to high yield can now be studied in the laboratory for the first time.

On December 5, 2022, an indirect drive fusion implosion on the National Ignition Facility (NIF) achieved a target gain G_{target} of 1.5. This is the first laboratory demonstration of exceeding "scientific breakeven" (or G_{target}>1) where 2.05 MJ of 351 nm laser light produced 3.1 MJ of total fusion yield, a result which significantly exceeds the Lawson criterion for fusion ignition as reported in a previous NIF implosion [H. Abu-Shawareb et al. (Indirect Drive ICF Collaboration), Phys. Rev. Lett. 129, 075001 (2022)PRLTAO0031-900710.1103/PhysRevLett.129.075001]. This achievement is the culmination of more than five decades of research and gives proof that laboratory fusion, based on fundamental physics principles, is possible. This Letter reports on the target, laser, design, and experimental advancements that led to this result.

Fusion ignition by inertial confinement requires compression and heating of the fusion fuel to temperatures in excess of 5 keV and densities exceeding hundreds of g/cc. In August 2021, this scientific milestone was surpassed at the National Ignition Facility (NIF), when the Lawson criterion for ignition was exceeded generating 1.37MJ of fusion energy (Abu-Shawareb et al 2022 Phys. Rev. Lett. 129 075001), and then in December 2022 target gain >1 was realized with the production of 3.1MJ of fusion energy from a target driven by 2.0MJ of laser energy (Abu-Shawareb et al 2024 Phys. Rev. Lett. 132 065102). At the NIF, inertial confinement fusion research primarily uses a laser indirect drive in which the fusion capsule is surrounded by a high-Z enclosure ('hohlraum') used to convert the directed laser energy into a symmetric x-ray drive on the capsule. Precise measurements of the plasma conditions, x-rays, gamma-rays and neutrons produced are key to understanding the pathway to higher performance. This paper discusses the diagnostics and measurement techniques developed to understand these experiments, focusing on three main topics: (1) key diagnostic developments for achieving igniting plasmas, (2) novel signatures related to thermonuclear burn and (3) advances to diagnostic capabilities in the igniting regime with a perspective toward developments for intertial fusion energy.

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.

We present findings from an experimental tuning campaign aimed at igniting larger DT cryogenic layered implosions using a dual frustum shaped hohlraum, denoted "frustraum". The frustraum's distinctive shape reduces hohlraum wall losses while concurrently enhancing minimum capsule clearance with the hohlraum wall and sensitivity to pointing changes. Compared to current cylindrical hohlraum (6.4 x 11.24 mm), the frustraum has a wall area approximately 20 % smaller, resulting in a measured improvement in efficiency of around 12 %. Consequently, 12 % less laser energy is required to implode a capsule within the same acceleration timeframe. Conversely, directing the same laser energy into the frustraum yields higher ion temperatures within symmetry capsules, along with increased radiation temperatures and reduced implosion acceleration times compared to current cylindrical hohlraums.

We present quantitative motivations and assessments of various proposed and ongoing directions to further improving yields and target gain of igniting indirect-drive implosions at the National Ignition Facility (NIF). These include increasing compression and confinement time, improving hohlraum and ablator efficiency, and further increasing peak power and laser energy. 1D hydroscaled simulations, augmented by analytic 1D theory, have been used to project yield improvements for each of these implosion optimization tracks, normalized to the best current performing 4 MJ shot. At current NIF capabilities of 2.2 MJ, 450 TW, we project several paths could reach 15 MJ yield levels. We also expect several key implosion physics questions will be addressed in attempting to reach this yield level. These include demonstrating to what extent lower adiabat designs leading to higher compression will increase gain and efficiency, and whether we can reduce residual kinetic energy and ablator-fuel mix that is probably limiting the current burn-up fraction. For an envisaged NIF upgrade to EL = 3 MJ at fixed 450 TW peak power, scaling capsule size and fuel thicknesses faster than pure hydroscaling should allow for yields that could reach up to 60–80 MJ, depending on the efficiency gains realized in increasing deuterium-tritium fuel thickness, reducing hohlraum losses, and switching to lower Z ablators. The laser-plasma instability and beam transmission scaling in these larger hohlraums is shown to be favorable if the spot size is increased with hohlraum scale.

At the National Ignition Facility, inertial confinement fusion experiments aim to burn and ignite a hydrogen plasma to generate a net source of energy through the fusion of deuterium and tritium ions. The energy deposited by α-particles released from the deuterium–tritium fusion reaction plays the central role in heating the fuel to achieve a sustained thermonuclear burn. In the hydrodynamic picture, α-heating increases the temperature of the plasma, leading to increased reactivity because the mean ion kinetic energy increases. Therefore, the ion temperature is related to the mean ion kinetic energy. Here we use the moments of the neutron spectrum to study the relationship between the ion temperature (measured by the variance in the neutron kinetic energy spectrum) and the ion mean kinetic energy (measured by the shift in the mean neutron energy). We observe a departure from the relationship expected for plasmas where the ion relative kinetic energy distribution is Maxwell–Boltzmann, when the plasma begins to burn. Understanding the cause of this departure from hydrodynamic behaviour could be important for achieving robust and reproducible ignition. Inertial confinement fusion experiments reveal a departure from the expected hydrodynamic behaviour of a plasma when the fusion reactions become the primary source of plasma heating.

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.

The change in the power balance, temporal dynamics, emission weighted size, temperature, mass, and areal density of inertially confined fusion plasmas have been quantified for experiments that reach target gains up to 0.72. It is observed that as the target gain rises, increased rates of self-heating initially overcome expansion power losses. This leads to reacting plasmas that reach peak fusion production at later times with increased size, temperature, mass and with lower emission weighted areal densities. Analytic models are consistent with the observations and inferences for how these quantities evolve as the rate of fusion self-heating, fusion yield, and target gain increase. At peak fusion production, it is found that as temperatures and target gains rise, the expansion power loss increases to a near constant ratio of the fusion self-heating power. This is consistent with models that indicate that the expansion losses dominate the dynamics in this regime.

An investigation of twenty two-shock campaign indirectly driven capsules on the National Ignition Facility was conducted using the xRAGE computer code. The two-shock platform was developed to look at the sensitivity of fuel–ablator mix with shock timing, asymmetry, surface roughness, and convergence on roughly ignition size scale capsules. This platform used CH/CD (plastic/deuterated plastic) shell capsules that were about 685-μm outer radius and filled with D2 or hydrogen-tritium (HT) gas. The experimental radius and velocity vs time, neutron yield, burn averaged ion temperature (Tion), burn width, and self-emission image size were compared to one-dimensional (1D) and two-dimensional (2D) simulations. Our 2D simulations suggest that the mixing of glass from the fill tube was the dominant source of impurity in the gas region of the capsule during burn, along with fuel–ablator mix. The mass of glass mixed in is about 5–10 ng. Our 2D simulations capture most of the yield trends from different degradation mechanisms, and they match the observed burn width and Tion measurements. Our 2D models match all the available data to within 2.5 times the normalized experimental error for 19 of 20 capsules.

An inertial fusion implosion on the National Ignition Facility, conducted on August 8, 2021 (N210808), recently produced more than a megajoule of fusion yield and passed Lawson's criterion for ignition [Phys. Rev. Lett. 129, 075001 (2022)10.1103/PhysRevLett.129.075001]. We describe the experimental improvements that enabled N210808 and present the first experimental measurements from an igniting plasma in the laboratory. Ignition metrics like the product of hot-spot energy and pressure squared, in the absence of self-heating, increased by ∼35%, leading to record values and an enhancement from previous experiments in the hot-spot energy (∼3×), pressure (∼2×), and mass (∼2×). These results are consistent with self-heating dominating other power balance terms. The burn rate increases by an order of magnitude after peak compression, and the hot-spot conditions show clear evidence for burn propagation into the dense fuel surrounding the hot spot. These novel dynamics and thermodynamic properties have never been observed on prior inertial fusion experiments.

A new additional wavelength-tuning capability has been implemented on the National Ignition Facility (NIF) laser allowing for unprecedented control of crossed-beam energy transfer (CBET) between all groups of beams for better performance of indirect-drive inertial confinement fusion (ICF) ignition experiments. In particular, this advance allows for negation and reversal of flow-induced CBET and the rebalancing of the intensity of different groups of beams within an indirect-drive (ICF) hohlraum. Experiments conducted at the NIF using a 1.1 MJ laser pulse with peak power of 390 TW demonstrate this high level of control through measurements of the precise changes to stimulated Brillouin scattering, typically driven by flow-induced CBET at the end of the pulse. Additionally, this new capability is shown to be able to predictably control gold-wall plasma expansion in the target driven by early-time flow-induced CBET. Estimates of early-time CBET from the wall expansion are shown to be consistent with simulation expectations. This new additional capability to control symmetry and backscatter expands the design space of current experiments and provides extra margin for increased laser energy in near-future experiments.

Obtaining a burning plasma is a critical step towards self-sustaining fusion energy 1 . A burning plasma is one in which the fusion reactions themselves are the primary source of heating in the plasma, which is necessary to sustain and propagate the burn, enabling high energy gain. After decades of fusion research, here we achieve a burning-plasma state in the laboratory. These experiments were conducted at the US National Ignition Facility, a laser facility delivering up to 1.9 megajoules of energy in pulses with peak powers up to 500 terawatts. We use the lasers to generate X-rays in a radiation cavity to indirectly drive a fuel-containing capsule via the X-ray ablation pressure, which results in the implosion process compressing and heating the fuel via mechanical work. The burning-plasma state was created using a strategy to increase the spatial scale of the capsule 2 , 3 through two different implosion concepts 4 – 7 . These experiments show fusion self-heating in excess of the mechanical work injected into the implosions, satisfying several burning-plasma metrics 3 , 8 . Additionally, we describe a subset of experiments that appear to have crossed the static self-heating boundary, where fusion heating surpasses the energy losses from radiation and conduction. These results provide an opportunity to study α-particle-dominated plasmas and burning-plasma physics in the laboratory.

We present the design of the first igniting fusion plasma in the laboratory by Lawson's criterion that produced 1.37 MJ of fusion energy, Hybrid-E experiment N210808 (August 8, 2021) [Phys. Rev. Lett. 129, 075001 (2022)10.1103/PhysRevLett.129.075001]. This design uses the indirect drive inertial confinement fusion approach to heat and compress a central "hot spot" of deuterium-tritium (DT) fuel using a surrounding dense DT fuel piston. Ignition occurs when the heating from absorption of α particles created in the fusion process overcomes the loss mechanisms in the system for a duration of time. This letter describes key design changes which enabled a ∼3-6× increase in an ignition figure of merit (generalized Lawson criterion) [Phys. Plasmas 28, 022704 (2021)1070-664X10.1063/5.0035583, Phys. Plasmas 25, 122704 (2018)1070-664X10.1063/1.5049595]) and an eightfold increase in fusion energy output compared to predecessor experiments. We present simulations of the hot-spot conditions for experiment N210808 that show fundamentally different behavior compared to predecessor experiments and simulated metrics that are consistent with N210808 reaching for the first time in the laboratory "ignition."