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.

Neutron source reconstruction using a generalized expectation-maximization algorithm on one-dimensional neutron images from the Z facility.

Magnetized Liner Inertial Fusion experiments have been performed at the Z facility at Sandia National Laboratories. These experiments use deuterium fuel, which produces 2.45 MeV neutrons on reaching thermonuclear conditions. To study the spatial structure of neutron production, the one-dimensional imager of neutrons diagnostic was fielded to record axial resolved neutron images. In this diagnostic, neutrons passing through a rolled edge aperture form an image on a CR-39-based solid state nuclear track detector. Here, we present a modified generalized expectation-maximization algorithm to reconstruct an axial neutron emission profile of the stagnated fusion plasma. We validate the approach by comparing the reconstructed neutron emission profile to an x-ray emission profile provided by a time-integrated pinhole camera.

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.

A coded aperture with sub-mean free-path thickness for neutron implosion geometry imaging on inertial confinement fusion and inertial fusion energy experiments.

Inertial confinement fusion and inertial fusion energy experiments diagnose the geometry of the fusion region through imaging of the neutrons released through fusion reactions. Pinhole arrays typically used for such imaging require thick substrates to obtain high contrast along with a small pinhole diameter to obtain high resolution capability, resulting in pinholes that have large aspect ratios. This leads to expensive pinhole arrays that have small solid angles and are difficult to align. Here, we propose a coded aperture with scatter and partial attenuation (CASPA) for fusion neutron imaging that relaxes the thick substrate requirement for good image contrast. These coded apertures are expected to scale to larger solid angles and are easier to align without sacrificing imaging resolution or throughput. We use Monte Carlo simulations (Geant4) to explore a coded aperture design to measure neutron implosion asymmetries on fusion experiments at the National Ignition Facility (NIF) and discuss the viability of this technique, matching the current nominal resolution of 10 µm. The results show that a 10 mm thick tungsten CASPA can image NIF implosions with neutron yields above 1014 with quality comparable to unprocessed data from a current NIF neutron imaging aperture. This CASPA substrate is 20 times thinner than the current aperture arrays for fusion neutron imaging and less than one mean free-path of 14.1 MeV neutrons through the substrate. Since the resolution, solid angle, and throughput are decoupled in coded aperture imaging, the resolution and solid angle achievable with future designs will be limited primarily by manufacturing capability.

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.

Neutron imaging of inertial confinement fusion implosions.

We review experimental neutron imaging of inertial confinement fusion sources, including the neutron imaging systems that have been used in our measurements at the National Ignition Facility. These systems allow measurements with 10 µm resolution for fusion deuterium-deuterium and deuterium-tritium neutron sources with mean radius up to 400 µm, including measurements of neutrons scattered to lower energy in the remaining cold fuel. These measurements are critical for understanding the fusion burn volume and the three-dimensional effects that can reduce the neutron yields.

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.

Experimental achievement and signatures of ignition at the National Ignition Facility.

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.

Design of an inertial fusion experiment exceeding the Lawson criterion for ignition.

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."

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.

Measurement of Dark Ice-Ablator Mix in Inertial Confinement Fusion.

We present measurements of ice-ablator mix at stagnation of inertially confined, cryogenically layered capsule implosions. An ice layer thickness scan with layers significantly thinner than used in ignition experiments enables us to investigate mix near the inner ablator interface. Our experiments reveal for the first time that the majority of atomically mixed ablator material is "dark" mix. It is seeded by the ice-ablator interface instability and located in the relatively cooler, denser region of the fuel assembly surrounding the fusion hot spot. The amount of dark mix is an important quantity as it is thought to affect both fusion fuel compression and burn propagation when it turns into hot mix as the burn wave propagates through the initially colder fuel region surrounding an igniting hot spot. We demonstrate a significant reduction in ice-ablator mix in the hot-spot boundary region when we increase the initial ice layer thickness.

Observation of Hydrodynamic Flows in Imploding Fusion Plasmas on the National Ignition Facility.

Inertial confinement fusion implosions designed to have minimal fluid motion at peak compression often show significant linear flows in the laboratory, attributable per simulations to percent-level imbalances in the laser drive illumination symmetry. We present experimental results which intentionally varied the mode 1 drive imbalance by up to 4% to test hydrodynamic predictions of flows and the resultant imploded core asymmetries and performance, as measured by a combination of DT neutron spectroscopy and high-resolution x-ray core imaging. Neutron yields decrease by up to 50%, and anisotropic neutron Doppler broadening increases by 20%, in agreement with simulations. Furthermore, a tracer jet from the capsule fill-tube perturbation that is entrained by the hot-spot flow confirms the average flow speeds deduced from neutron spectroscopy.

Three-dimensional diagnostics and measurements of inertial confinement fusion plasmas.

Recent inertial confinement fusion measurements have highlighted the importance of 3D asymmetry effects on implosion performance. One prominent example is the bulk drift velocity of the deuterium-tritium plasma undergoing fusion ("hotspot"), vHS. Upgrades to the National Ignition Facility neutron time-of-flight diagnostics now provide vHS to better than 1 part in 104 and enable cross correlations with other measurements. This work presents the impact of vHS on the neutron yield, downscatter ratio, apparent ion temperature, electron temperature, and 2D x-ray emission. The necessary improvements to diagnostic suites to take these measurements are also detailed. The benefits of using cross-diagnostic analysis to test hotspot models and theory are discussed, and cross-shot trends are shown.

Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using a cylindrical-harmonics expansion.

Inertial confinement fusion capsule implosions produce neutron, gamma-ray, and x-ray emission, which are recorded by a variety of detectors, both time integrated and time resolved, to determine the performance of the implosion. Two-dimensional emission images from multiple directions can now be combined to infer three-dimensional structures in the implosion, such as the distribution of thermonuclear fuel density, carbon ablator, and impurities. Because of the cost and complexity of the imaging systems, however, only a few measurements can be made, so reconstructions of the source must be made from a limited number of views. Here, a cylindrical-harmonics decomposition technique to reconstruct the three-dimensional object from two views in the same symmetry plane is presented. In the limit of zero order, this method recovers the Abel inversion method. The detailed algorithms used for this characterization and the resulting reconstructed neutron source from an experiment collected at the National Ignition Facility are presented.

Time-Resolved Fuel Density Profiles of the Stagnation Phase of Indirect-Drive Inertial Confinement Implosions.

The implosion efficiency in inertial confinement fusion depends on the degree of stagnated fuel compression, density uniformity, sphericity, and minimum residual kinetic energy achieved. Compton scattering-mediated 50-200 keV x-ray radiographs of indirect-drive cryogenic implosions at the National Ignition Facility capture the dynamic evolution of the fuel as it goes through peak compression, revealing low-mode 3D nonuniformities and thicker fuel with lower peak density than simulated. By differencing two radiographs taken at different times during the same implosion, we also measure the residual kinetic energy not transferred to the hot spot and quantify its impact on the implosion performance.

Hotspot parameter scaling with velocity and yield for high-adiabat layered implosions at the National Ignition Facility.

This paper presents a study on hotspot parameters in indirect-drive, inertially confined fusion implosions as they proceed through the self-heating regime. The implosions with increasing nuclear yield reach the burning-plasma regime, hotspot ignition, and finally propagating burn and ignition. These implosions span a wide range of alpha heating from a yield amplification of 1.7-2.5. We show that the hotspot parameters are explicitly dependent on both yield and velocity and that by fitting to both of these quantities the hotspot parameters can be fit with a single power law in velocity. The yield scaling also enables the hotspot parameters extrapolation to higher yields. This is important as various degradation mechanisms can occur on a given implosion at fixed implosion velocity which can have a large impact on both yield and the hotspot parameters. The yield scaling also enables the experimental dependence of the hotspot parameters on yield amplification to be determined. The implosions reported have resulted in the highest yield (1.73×10^{16}±2.6%), yield amplification, pressure, and implosion velocity yet reported at the National Ignition Facility.

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.

Modeling the one-dimensional imager of neutrons (ODIN) for neutron response functions at the Sandia Z facility.

The one-dimensional imager of neutrons (ODIN) at the Sandia Z facility consists of a 10-cm block of tungsten with rolled edges, creating a slit imager with slit widths of either 250, 500, or 750 µm. Designed with a 1-m neutron imaging line of sight, we achieve about 4:1 magnification and 500-µm axial spatial resolution. The baseline inertial confinement fusion concept at Sandia is magnetized liner inertial fusion, which nominally creates a 1-cm line source of neutrons. ODIN was designed to determine the size, shape, and location of the neutron producing region, furthering the understanding of compression quality along the cylindrical axis of magnetized liner implosions. Challenges include discriminating neutrons from hard x-rays and gammas with adequate signal-to-noise in the 2 × 1012 deuterium-deuterium (DD) neutron yield range, as well as understanding the point spread function of the imager to various imaging detectors (namely, CR-39). Modeling efforts were conducted with MCNP6.1 to determine neutron response functions for varying configurations in a clean DD neutron environment (without x-rays or gammas). Configuration alterations that will be shown include rolled-edge slit orientation and slit width, affecting the resolution and response function. Finally, the experiment to determine CR-39 neutron sensitivity, with and without a high density polyethylene (n, p) converter, an edge spread function, and resolution will be discussed.

Aperture design for the third neutron and first gamma-ray imaging systems for the National Ignition Facility.

The current construction of a new nuclear-imaging view at the National Ignition Facility will provide a third line of sight for hotspot and cold fuel imaging and the first dedicated line of sight for 4.4-MeV γ-ray imaging of the remaining carbon ablator. To minimize the effort required to hold and align apertures inside the vacuum chamber, the apertures for the two lines of sight will be contained in the same array. In this work, we discuss the system requirements for neutron and γ-ray imaging and the resulting aperture array design.