Fusion "scientific breakeven" (i.e., unity target gain G(target), total fusion energy out > laser energy input) has been achieved for the first time (here, G(target) similar to 1.5). This Letter reports on the physics principles of the design changes that led to the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce target gain greater than unity and exceeded the previously obtained conditions needed for ignition by the Lawson criterion. Key elements of the success came from reducing "coast time" (the time duration between the end of the laser pulse and implosion peak compression) and maximizing the internal energy delivered to the "hot spot" (the yield producing part of the fusion fuel). The link between coast time and maximally efficient conversion of kinetic energy into internal energy is explained. The energetics consequences of asymmetry and hydrodynamic-induced mixing were part of high-yield big radius implosion design experimental and design strategy. Herein, it is shown how asymmetry and mixing consolidate into one key relationship. It is shown that mixing distills into a kinetic energy cost similar to the impact of implosion asymmetry, shifting the threshold for ignition to higher implosion kinetic energy-a factor not normally included in most statements of the generalized Lawson criterion, but the key needed modifications clearly emerge.

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.

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.

Laser-driven Hohlraums filled with gas at lower densities (<0.6 mg/cc) have higher efficiency compared to original ≥ 0.96 mg/cc fill because of reduced backscatter losses [Hall et al., Phys. Plasmas 24, 052706 (2017)]. However, using low-density filled Hohlraums with longer drive required for lower adiabat implosions, and hence potentially higher inertial confinement fusion gain designs, has been challenging since the Hohlraum wall blow-off is less tamped, thus altering the laser beam absorption regions and drive symmetry. A series of NIF experiments using optimized pulse shaping, beam pointing, and temporal phasing have demonstrated, through imaging of the Hohlraum and capsule dynamics, that a symmetric implosion using a 14-ns low-adiabat drive pulse {2× longer than high-density-carbon ablator designs using low gas-fill density Hohlraums [Divol et al., Phys. Plasmas 24, 056309 (2017)]} is possible in a low backscatter loss 0.45 mg/cc He-filled Hohlraum. The ingress of the Hohlraum walls was mitigated by revisiting the adiabat-shaped design [Clark et al., Phys. Plasmas 21, 112705 (2014)] that uses a low-power (1 TW) trough that delays the wall expansion. Low-mode P2 and P4 drive asymmetry swings caused by the drift of the laser spots were essentially zeroed out by employing temporal beam phasing between cones of beams [Turner et al., Phys. Plasmas 7, 333 (2000)]. The results also indicate an improved coupling efficiency of ∼30% compared to an earlier design using higher density filled Hohlraums and pave the way for revisiting low-adiabat, high convergence drives using CH ablators.

In indirect-drive implosions, the final core hot spot energy and pressure and, hence, neutron yield attainable in 1D increase with increasing laser peak power and, hence, radiation drive temperature at the fixed capsule and Hohlraum size. We present simple analytic scalings validated by 1D simulations that quantify the improvement in performance and use this to explain existing data and simulation trends. Extrapolating to the 500 TW National Ignition Facility peak power limit in a low gas-fill 5.4 mm diameter Hohlraum based on existing high adiabat implosion data at 400 TW, 1.3 MJ and 1 × 1016 yield, we find that a 2–3 × 1017 yield (0.5–0.7 MJ) is plausible using only 1.8 MJ of laser energy. Based on existing data varying deuterium–tritium (DT) fuel thickness and dopant areal density, further improvements should be possible by increasing DT fuel areal density, and hence confinement time and yield amplification.

In order to understand how close current layered implosions in indirect-drive inertial confinement fusion are to ignition, it is necessary to measure the level of alpha heating present. To this end, pairs of experiments were performed that consisted of a low-yield tritium-hydrogen-deuterium (THD) layered implosion and a high yield deuterium-tritium (DT) layered implosion to validate experimentally current simulation-based methods of determining yield amplification. The THD capsules were designed to reduce simultaneously DT neutron yield (alpha heating) and maintain hydrodynamic similarity with the higher yield DT capsules. The ratio of the yields measured in these experiments then allowed the alpha heating level of the DT layered implosions to be determined. The level of alpha heating inferred is consistent with fits to simulations expressed in terms of experimentally measurable quantities and enables us to infer the level of alpha heating in recent high-performing implosions.

bypass venting of the internal helium into the second chamber adjacent to the capsule is needed to prevent rupture of the membranes. The bypass flow is cooled by the hohlraum during this venting. However, the experiments suggest that our internal heat flow calculations may be low by about a factor of 2. Further studies need to be conducted to investigate the differences between the experiment and the numerical analysis. Future studies could also possibly bring the test conditions closer to those expected in the fusion chamber to better validate the results. A sacrificial layer will probably be required on the LEH window of the target and this can be used to mitigate any unexpected target heating.

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.

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.

With NIF shot N210808, we now have an existence proof of ignition (i.e. Lawson-like criteria exceeded and capsule gain well exceeding unity) in the laboratory and it has generated renewed interest in IFE. However, it is important to recognize that ignition on the NIF has been much more difficult than what was originally envisioned. Moreover, the design for the target that actually obtained burning plasma (Kritcher, Young, Robey, et al., Nature Phys. 2022; Zylstra, Hurricane, Callahan, et al., Nature, 601, 542, 2022) and ignition conditions is much different than the high gain design originally planned in the National Ignition Campaign (NIC; e.g. Lindl, Phys. Plasmas, 2, 3933, 1995; Lindl, Amendt, Berger, et al., Phys. Plasmas, 11, 339, 2004). In order to avoid squandering time and resources, the IFE community must learn the lessons of what happened on the NIF over the past decade.

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.

A goal of the laser-based National Ignition Facility (NIF) is to increase the liberated fusion energy “yield” in inertial confinement fusion experiments well past the ignition threshold and the input laser energy. One method of increasing the yield, hydrodynamic scaling of current experiments, does not rely on improving compression or implosion velocity, but rather increases the scale of the implosion to increase hotspot areal density and confinement time. Indirect-drive (Hohlraum driven) implosions carried out at two target sizes, 12.5% apart, have validated hydroscaling expectations. Moreover, extending comparisons to the best-performing implosions at five different capsule sizes shows that their performance also agrees well with hydroscaling expectations even though not direct hydroscales of one another. In the future, by switching to a reduced loss Hohlraum geometry, simulations indicate that we can drive 20% larger-scale implosions within the current power and energy limitations on the NIF. At the demonstrated compression and velocity of these smaller-scale implosions, these 1.2× hydroscaled implosions should put us well past the ignition threshold.

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."

Inertial confinement fusion implosions must achieve high in-flight shell velocity, sufficient energy coupling between the hot spot and imploding shell, and high areal density (ρR=∫ρdr) at stagnation. Asymmetries in ρR degrade the coupling of shell kinetic energy to the hot spot and reduce the confinement of that energy. We present the first evidence that nonuniformity in the ablator shell thickness (∼0.5% of the total thickness) in high-density carbon experiments is a significant cause for observed 3D ρR asymmetries at the National Ignition Facility. These shell-thickness nonuniformities have significantly impacted some recent experiments leading to ρR asymmetries on the order of ∼25% of the average ρR and hot spot velocities of ∼100  km/s. This work reveals the origin of a significant implosion performance degradation in ignition experiments and places stringent new requirements on capsule thickness metrology and symmetry.

In 2017–2018, record fusion yields on NIF were produced with designs that utilized high-density-carbon capsules and low-gas-fill hohlraums. Subsequently, a strategy was pursued to increase the capsule size and thus the energy absorbed by the capsule, with the latter occasionally used as a metric for these campaigns presuming that subsequent energy transfer would lead to a concomitant increase in hot-spot energy. Here we show that improved performance in recent experiments was not solely enabled by the capsule absorbed energy, which is a poor metric as it is weakly correlated with implosion performance (r ∼ 0.3). Metrics that incorporate additional information about the implosion physics or degradation mechanisms are significantly better for understanding the performance of these shots. These metrics, such as the hot-spot energy multiplied by pressure squared or the experimental ignition threshold factor (ITFX), should be used for guiding the experimental program on NIF for further improvements as they exhibit much stronger correlations with performance (r ∼ 0.8–0.9).

Experiments and simulations have been conducted to investigate the efficacy of Ta2O5-lined Hohlraum walls at reducing stimulated Brillouin backscattering (SBS) as well as any subsequent effects on the Hohlraum dynamics and capsule implosions in indirect drive experiments at the National Ignition Facility. Using a 1.1 MJ 400 TW, 351 nm, shaped laser pulse, we measure a 5× reduction in SBS power in the peak of the pulse from the wall on the outer 50° cone beams. The SBS spectrum indicates a reduction in the high-Z spectral signature when using multispecies wall materials. Detailed hydrodynamic simulations were performed using different heat conduction models with flux limiters. Additional simulations were performed on the plasma maps using the 3D parallel paraxial code pF3D to compare backscatter powers between the pure Au and Ta2O5-lined Hohlraums. Further analysis, using hydrodynamically equivalent plasmas, shows that the SBS reduction is clearly a result of the added ion Landau damping caused by the oxygen ions and not from differences in plasma conditions. The experimental and simulation results also show an increase in the wall plasma expansion when using the Ta2O5 liner leading to a 70% more oblate implosion.

Self-induced plasma gratings are now routinely used in inertial confinement fusion experiments at the National Ignition Facility (NIF) to achieve precise spatio-temporal control of the laser energy deposition directly inside the fusion targets. This novel capability is enabled by applying a few Å wavelength shifts between different groups of beams, in order to control the direction and level of light scattering off these plasma gratings. A new wavelength tuning capability was added on the NIF in January 2020 to extend the range of applications of plasma gratings; such applications include the control of several asymmetry modes during the implosion, and mitigation of backscatter from stimulated Raman or Brillouin scattering.

The mode-1 x-ray drive asymmetry of indirect-drive Inertial Confinement Fusion(ICF) implosions at the National Ignition Facility(NIF) has been estimated using a simple static ViewFactor model. The model takes as input measured laser performance data in the foot and peak, the hohlraum configuration, and laser to hohlraum pointing. These estimates are compared with neutron time-of-flight measurements of directionality and magnitude of the resultant hotspot bulk velocity (~20–100 μm/ns) for 39 NIF shots using High Density Carbon (HDC) ablators and show strong correlation on a statistically significant number of shots. The most important factors identified so far are random quad-to-quad peak power laser imbalances, the presence of lossy diagnostic windows and gaps on the hohlraum waist, capsule sag and capsule thickness mode 1. Typical mode-1 asymmetry in drive is currently ~0.5% for many of these sources on their own and, when summed, can lead to a neutron hotspot velocity of up to 100 μm /ns and a reduction in yield of 35% for current NIF DT layered implosions. Our goal is to identify, quantify and mitigate all potential sources of mode-1 asymmetry (which also include target and laser alignment imperfections, foot power and Cross Beam Energy Transfer imbalances) to enable higher quality implosions on NIF.