The impact of low-mode symmetry on inertial fusion energy output in the burning plasma state.

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.

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

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

Observations and properties of the first laboratory fusion experiment to exceed a target gain of unity.

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)10.1103/PhysRevE.109.025204]. 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.

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

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

Dynamics and Power Balance of Near Unity Target Gain Inertial Confinement Fusion Implosions.

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.

Alpha heating of indirect-drive layered implosions on the National Ignition Facility.

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.

Burning plasma achieved in inertial fusion.

Obtaining a burning plasma is a critical step towards self-sustaining fusion energy1. 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 capsule2,3 through two different implosion concepts4-7. These experiments show fusion self-heating in excess of the mechanical work injected into the implosions, satisfying several burning-plasma metrics3,8. 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.

Hohlraum x-ray preheat asymmetry measurement at the ICF capsule via Mo ball fluorescence imaging.

In inertial confinement fusion, penetrating asymmetric hohlraum preheat radiation (>1.8 keV, which includes high temperature coronal M-band emission from laser spots) can lead to asymmetric ablation front and ablator-fuel interface hydrodynamic instability growth in the imploding capsule. First experiments to infer the preheat asymmetries at the capsule were performed on the National Ignition Facility for high density carbon (HDC) capsules in low density fill (0.3 mg/cc 4He) Au hohlraums by time resolved imaging of 2.3 keV fluorescence emission of a smaller Mo sphere placed inside the capsule. Measured Mo emission is pole hot (P2 > 0) since M-band is generated mainly by the outer laser beams as their irradiance at the hohlraum wall is 5× higher than for the inner beams. P2 has a large swing vs time, giving insight into the laser heated hohlraum dynamics. P4 asymmetry is small at the sphere due to efficient geometric smoothing of hohlraum P4 asymmetries at large hohlraum-to-capsule radii ratios. The asymmetry at the HDC capsule is inferred from the Mo emission asymmetry accounting for the Mo/HDC radius difference and HDC capsule opacity.

Impact of Localized Radiative Loss on Inertial Confinement Fusion Implosions.

The impact to fusion energy production due to the radiative loss from a localized mix in inertial confinement implosions using high density carbon capsule targets has been quantified. The radiative loss from the localized mix and local cooling of the reacting plasma conditions was quantified using neutron and x-ray images to reconstruct the hot spot conditions during thermonuclear burn. Such localized features arise from ablator material that is injected into the hot spot from the Rayleigh-Taylor growth of capsule surface perturbations, particularly the tube used to fill the capsule with deuterium and tritium fuel. Observations, consistent with analytic estimates, show the degradation to fusion energy production to be linearly proportional to the fraction of the total emission that is associated with injected ablator material and that this radiative loss has been the primary source of variations, of up to 1.6 times, in observed fusion energy production. Reducing the fill tube diameter has increased the ignition metric χ_{no α} from 0.49 to 0.72, 92% of that required to achieve a burning hot spot.

X-ray streaked refraction enhanced radiography for inferring inflight density gradients in ICF capsule implosions.

In the quest for reaching ignition of deuterium-tritium (DT) fuel capsule implosions, experiments on the National Ignition Facility (NIF) have shown lower final fuel areal densities than simulated. Possible explanations for reduced compression are higher preheat that can increase the ablator-DT ice density jump and induce mix at that interface or reverberating shocks. We are hence developing x-ray Refraction Enhanced Radiography (RER) to infer the inflight density profiles in layered fuel capsule implosions. We use a 5 µm slit backlit by a Ni 7.8 keV He-α NIF laser driven x-ray source positioned at 20 mm from the capsule to cast refracted images of the inflight capsule onto a streak camera in a high magnification (M ∼ 60×) setup. Our first experiments have validated our setup that recorded a streaked x-ray fringe pattern from an undriven high density carbon (HDC) capsule consistent with ray tracing calculations at the required ∼6 µm and 25 ps resolution. Streaked RER was then applied to inflight layered HDC capsule implosions using a hydrogen-tritium fuel mix rather than DT to reduce neutron yields and associated backgrounds. The first RER of an imploding capsule revealed strong features associated with the ablation front and ice-ablator interface that are not visible in standard absorption radiographs.

Absolute Equation-of-State Measurement for Polystyrene from 25 to 60 Mbar Using a Spherically Converging Shock Wave.

We have developed an experimental platform for the National Ignition Facility that uses spherically converging shock waves for absolute equation-of-state (EOS) measurements along the principal Hugoniot. In this Letter, we present one indirect-drive implosion experiment with a polystyrene sample that employs radiographic compression measurements over a range of shock pressures reaching up to 60 Mbar (6 TPa). This significantly exceeds previously published results obtained on the Nova laser [R. Cauble et al., Phys. Rev. Lett. 80, 1248 (1998)PRLTAO0031-900710.1103/PhysRevLett.80.1248] at a strongly improved precision, allowing us to discriminate between different EOS models. We find excellent agreement with Kohn-Sham density-functional-theory-based molecular dynamics simulations.

Fusion Energy Output Greater than the Kinetic Energy of an Imploding Shell at the National Ignition Facility.

A series of cryogenic, layered deuterium-tritium (DT) implosions have produced, for the first time, fusion energy output twice the peak kinetic energy of the imploding shell. These experiments at the National Ignition Facility utilized high density carbon ablators with a three-shock laser pulse (1.5 MJ in 7.5 ns) to irradiate low gas-filled (0.3 mg/cc of helium) bare depleted uranium hohlraums, resulting in a peak hohlraum radiative temperature ∼290 eV. The imploding shell, composed of the nonablated high density carbon and the DT cryogenic layer, is, thus, driven to velocity on the order of 380 km/s resulting in a peak kinetic energy of ∼21 kJ, which once stagnated produced a total DT neutron yield of 1.9×10^{16} (shot N170827) corresponding to an output fusion energy of 54 kJ. Time dependent low mode asymmetries that limited further progress of implosions have now been controlled, leading to an increased compression of the hot spot. It resulted in hot spot areal density (ρr∼0.3 g/cm^{2}) and stagnation pressure (∼360 Gbar) never before achieved in a laboratory experiment.

Generation and Beaming of Early Hot Electrons onto the Capsule in Laser-Driven Ignition Hohlraums.

In hohlraums for inertial confinement fusion (ICF) implosions on the National Ignition Facility, suprathermal hot electrons, generated by laser plasma instabilities early in the laser pulse ("picket") while blowing down the laser entrance hole (LEH) windows, can preheat the capsule fuel. Hard x-ray imaging of a Bi capsule surrogate and of the hohlraum emissions, in conjunction with the measurement of time-resolved bremsstrahlung spectra, allows us to uncover for the first time the directionality of these hot electrons and infer the capsule preheat. Data and Monte Carlo calculations indicate that for most experiments the hot electrons are emitted nearly isotropically from the LEH. However, we have found cases where a significant fraction of the generated electrons are emitted in a collimated beam directly towards the capsule poles, where their local energy deposition is up to 10× higher than the average preheat value and acceptable levels for ICF implosions. The observed "beaming" is consistent with a recently unveiled multibeam stimulated Raman scattering model [P. Michel et al., Phys. Rev. Lett. 115, 055003 (2015)], where laser beams in a cone drive a common plasma wave on axis. Finally, we demonstrate that we can control the amount of generated hot electrons by changing the laser pulse shape and hohlraum plasma.

Multibeam Stimulated Raman Scattering in Inertial Confinement Fusion Conditions.

Stimulated Raman scattering from multiple laser beams arranged in a cone sharing a common daughter wave is investigated for inertial confinement fusion (ICF) conditions in a inhomogeneous plasma. It is found that the shared electron plasma wave (EPW) process, where the lasers collectively drive the same EPW, can lead to an absolute instability when the electron density reaches a matching condition dependent on the cone angle of the laser beams. This mechanism could explain recent experimental observations of hot electrons at early times in ICF experiments, at densities well below quarter critical when two plasmon decay is not expected to occur.

Demonstration of High Performance in Layered Deuterium-Tritium Capsule Implosions in Uranium Hohlraums at the National Ignition Facility.

We report on the first layered deuterium-tritium (DT) capsule implosions indirectly driven by a "high-foot" laser pulse that were fielded in depleted uranium hohlraums at the National Ignition Facility. Recently, high-foot implosions have demonstrated improved resistance to ablation-front Rayleigh-Taylor instability induced mixing of ablator material into the DT hot spot [Hurricane et al., Nature (London) 506, 343 (2014)]. Uranium hohlraums provide a higher albedo and thus an increased drive equivalent to an additional 25 TW laser power at the peak of the drive compared to standard gold hohlraums leading to higher implosion velocity. Additionally, we observe an improved hot-spot shape closer to round which indicates enhanced drive from the waist. In contrast to findings in the National Ignition Campaign, now all of our highest performing experiments have been done in uranium hohlraums and achieved total yields approaching 10^{16} neutrons where more than 50% of the yield was due to additional heating of alpha particles stopping in the DT fuel.

Thin shell, high velocity inertial confinement fusion implosions on the national ignition facility.

Experiments have recently been conducted at the National Ignition Facility utilizing inertial confinement fusion capsule ablators that are 175 and 165 µm in thickness, 10% and 15% thinner, respectively, than the nominal thickness capsule used throughout the high foot and most of the National Ignition Campaign. These three-shock, high-adiabat, high-foot implosions have demonstrated good performance, with higher velocity and better symmetry control at lower laser powers and energies than their nominal thickness ablator counterparts. Little to no hydrodynamic mix into the DT hot spot has been observed despite the higher velocities and reduced depth for possible instability feedthrough. Early results have shown good repeatability, with up to 1/2 the neutron yield coming from α-particle self-heating.

High-density carbon capsule experiments on the national ignition facility.

Indirect-drive implosions with a high-density carbon (HDC) capsule were conducted on the National Ignition Facility (NIF) to test HDC properties as an ablator material for inertial confinement fusion. A series of five experiments were completed with 76-µm-thick HDC capsules using a four-shock laser pulse optimized for HDC. The pulse delivered a total energy of 1.3 MJ with a peak power of 360 TW. The experiment demonstrated good laser to target coupling (∼90%) and excellent nuclear performance. A deuterium and tritium gas-filled HDC capsule implosion produced a neutron yield of 1.6×10^{15}±3×10(13), a yield over simulated in one dimension of 70%.

Time-resolved measurements of the hot-electron population in ignition-scale experiments on the National Ignition Facility (invited).

In laser-driven inertial confinement fusion, hot electrons can preheat the fuel and prevent fusion-pellet compression to ignition conditions. Measuring the hot-electron population is key to designing an optimized ignition platform. The hot electrons in these high-intensity, laser-driven experiments, created via laser-plasma interactions, can be inferred from the bremsstrahlung generated by hot electrons interacting with the target. At the National Ignition Facility (NIF) [G. H. Miller, E. I. Moses, and C. R. Wuest, Opt. Eng. 43, 2841 (2004)], the filter-fluorescer x-ray (FFLEX) diagnostic-a multichannel, hard x-ray spectrometer operating in the 20-500 keV range-has been upgraded to provide fully time-resolved, absolute measurements of the bremsstrahlung spectrum with ∼300 ps resolution. Initial time-resolved data exhibited significant background and low signal-to-noise ratio, leading to a redesign of the FFLEX housing and enhanced shielding around the detector. The FFLEX x-ray sensitivity was characterized with an absolutely calibrated, energy-dispersive high-purity germanium detector using the high-energy x-ray source at NSTec Livermore Operations over a range of K-shell fluorescence energies up to 111 keV (U Kß). The detectors impulse response function was measured in situ on NIF short-pulse (∼90 ps) experiments, and in off-line tests.

Reduced instability growth with high-adiabat high-foot implosions at the National Ignition Facility.

Hydrodynamic instabilities are a major obstacle in the quest to achieve ignition as they cause preexisting capsule defects to grow and ultimately quench the fusion burn in experiments at the National Ignition Facility. Unstable growth at the ablation front has been dramatically reduced in implosions with "high-foot" drives as measured using x-ray radiography of modulations at the most dangerous wavelengths (Legendre mode numbers of 30-90). These growth reductions have helped to improve the performance of layered DT implosions reported by O. A. Hurricane et al. [Nature (London) 506, 343 (2014)], when compared to previous "low-foot" experiments, demonstrating the value of stabilizing ablation-front growth and providing directions for future ignition designs.