Modifying x-ray streak cameras for operation on igniting fusion experiments.

The National Ignition Facility produced the first nuclear fusion experiment demonstrating net positive energy gain on December 5, 2022. The x-ray streak camera that measures the bang time and burn-width from this landmark experiment had an electronic failure and did not record data. The CCD sensor was replaced with a radiation hardened CMOS sensor that has since demonstrated successful operation on repeat ignition shots. Concurrently, an instrument artifact was identified that occurs when the signal consists primarily of energetic x rays >15 keV (common on burning plasma experiments). This artifact, which appears as a background pedestal, arises from the x-ray back-fluorescence generated by the solid metal accelerating mesh behind the photocathode in the streak tube. We have mitigated this background signal by limiting the sensitive area of the photocathode. Herein, the details of the modifications and the results are presented.

Statistical data analysis of x-ray spectroscopy data enabled by neural network accelerated Bayesian inference.

Bayesian inference applied to x-ray spectroscopy data analysis enables uncertainty quantification necessary to rigorously test theoretical models. However, when comparing to data, detailed atomic physics and radiation transfer calculations of x-ray emission from non-uniform plasma conditions are typically too slow to be performed in line with statistical sampling methods, such as Markov Chain Monte Carlo sampling. Furthermore, differences in transition energies and x-ray opacities often make direct comparisons between simulated and measured spectra unreliable. We present a spectral decomposition method that allows for corrections to line positions and bound-bound opacities to best fit experimental data, with the goal of providing quantitative feedback to improve the underlying theoretical models and guide future experiments. In this work, we use a neural network (NN) surrogate model to replace spectral calculations of isobaric hot-spots created in Kr-doped implosions at the National Ignition Facility. The NN was trained on calculations of x-ray spectra using an isobaric hot-spot model post-processed with Cretin, a multi-species atomic kinetics and radiation code. The speedup provided by the NN model to generate x-ray emission spectra enables statistical analysis of parameterized models with sufficient detail to accurately represent the physical system and extract the plasma parameters of interest.

Variable-sagittal-radii elliptical x-ray crystal spectrometers for high-neutron-yield plasma diagnostics.

Sagittally focusing x-ray crystal spectrometers with elliptical profiles in the meridional (x-ray dispersion) plane are proposed for plasma diagnostics in experiments accompanied by high neutron yields. The spectrometers feature a variable sagittal radius of curvature to ensure the sagittal focusing of rays for each photon energy in a chosen detection plane. The detector is placed after the ray crossing point at the second ellipse focus, and the source-to-detector distance is maximized to reduce the neutron-induced background. The elliptical shape imposes a limitation on the spectrometer geometry such that the influence of the source size on the spectral resolution can be avoided only for a demagnifying spectrometer (the source-to-crystal distance is larger than that of crystal-to-detector). Hence, two designs are proposed. The first design, featuring high magnification and limited spectral resolution can be suitable for x-ray continuum spectroscopy. The second design of high demagnification is optimized for spectral resolution, and can be used for time-resolved spectroscopy of plasma's characteristic emission lines using streak cameras. The key performance characteristics of the two designs are verified using ray tracing.

X-ray continuum spectroscopy of inertial confinement fusion implosions at the National Ignition Facility.

A methodology for measuring x-ray continuum spectra of inertial confinement fusion (ICF) implosions is described. The method relies on the use of ConSpec, a high-throughput spectrometer using a highly annealed pyrolytic graphite crystal [MacDonald et al., J. Instrum. 14, P12009 (2019)], which measures the spectra in the ≃20-30 keV range. Due to its conical shape, the crystal is sagittally focusing a Bragg-reflected x-ray spectrum into a line, which enhances the recorded x-ray emission signal above the high neutron-induced background accompanying ICF implosions at the National Ignition Facility. To improve the overall measurement accuracy, the sensitivity of the spectrometer measured in an off-line x-ray laboratory setting was revised. The error analysis was expanded to include the accuracy of the off-line measurements, the effect of the neutron-induced background, as well as the influence of possible errors in alignment of the instrument to the ICF target. We demonstrate how the improved methodology is applied in the analysis of ConSpec data with examples of a relatively low-neutron-yield implosion using a tritium-hydrogen-deuterium mix as a fuel and a high-yield deuterium-tritium (DT) implosion producing high level of the background. In both cases, the shape of the measured spectrum agrees with the exponentially decaying spectral shape of bremsstrahlung emission to within ±10%. In the case of the high-yield DT experiment, non-monotonic deviations slightly exceeding the measurement uncertainties are observed and discussed.

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.

A Monte Carlo technique to model performance of streak camera-based time-resolving x-ray spectrometers.

A Monte Carlo technique has been developed to simulate the expected signal and the statistical noise of x-ray spectrometers that use streak cameras to achieve the time resolution required for ultrafast diagnostics of laser-generated plasmas. The technique accounts for statistics from both the photons incident on the streak camera's photocathode and the electrons emitted by the photocathode travelling through the camera's electron optics to the sensor. We use the technique to optimize the design of a spectrometer, which deduces the temporal history of electron temperature of the hotspot in an inertial confinement fusion implosion from its hard x-ray continuum emission spectra. The technique is general enough to be applied to any instrument using an x-ray streak camera.

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.

Hot Spot Evolution Measured by High-Resolution X-Ray Spectroscopy at the National Ignition Facility.

Evolution of the hot spot plasma conditions was measured using high-resolution x-ray spectroscopy at the National Ignition Facility. The capsules were filled with DD gas with trace levels of Kr and had either a high-density-carbon (HDC) ablator or a tungsten (W)-doped HDC ablator. Time-resolved measurement of the Kr Heß spectra, absolutely calibrated by a simultaneous time-integrated measurement, allows inference of the electron density and temperature through observing Stark broadening and the relative intensities of dielectronic satellites. By matching the calculated hot spot emission using a collisional-radiative code to experimental observations, the hot spot size and areal density are determined. These advanced spectroscopy techniques further reveal the effect of W dopant in the ablator on the hot spot parameters for their improved implosion performance.

A new class of focusing crystal shapes for Bragg spectroscopy of small, point-like, x-ray sources in laser produced plasmas.

This paper describes a new class of focusing crystal forms for the x-ray Bragg crystal spectroscopy of small, point-like, x-ray sources. These new crystal forms are designed with the aid of sinusoidal spirals, a family of curves, whose shapes are defined by only one parameter, which can assume any real value. The potential of the sinusoidal spirals for the design x-ray crystal spectrometers is demonstrated with the design of a toroidally bent crystal of varying major and minor radii for measurements of the extended x-ray absorption fine structure near the Ta-L3 absorption edge at the National Ignition Facility.

Enhancements in laser-generated hot-electron production via focusing cone targets at short pulse and high contrast.

We report on the increase in the accelerated electron number and energy using compound parabolic concentrator (CPC) targets from a short-pulse (∼150 fs), high-intensity (>10^{18} W/cm^{2}), and high-contrast (∼10^{8}) laser-solid interaction. We report on experimental measurements using CPC targets where the hot-electron temperature is enhanced up to ∼9 times when compared to planar targets. The temperature measured from the CPC target is 〈T_{e}〉=4.4±1.3 MeV. Using hydrodynamic and particle in cell simulations, we identify the primary source of this temperature enhancement is the intensity increase caused by the CPC geometry that focuses the laser, reducing the focal spot and therefore increasing the intensity of the laser-solid interaction, which is also consistent with analytic expectations for the geometrical focusing.

Order-of-magnitude increase in laser-target coupling at near-relativistic intensities using compound parabolic concentrators.

Achieving a high conversion efficiency into relativistic electrons is central to short-pulse laser application and fundamentally relies on creating interaction regions with intensities ≫10^{18}W/cm^{2}. Small focal length optics are typically employed to achieve this goal; however, this solution is impractical for large kJ-class systems that are constrained by facility geometry, debris concerns, and component costs. We fielded target-mounted compound parabolic concentrators to overcome these limitations and achieved nearly an order-of-magnitude increase to the conversion efficiency and more than tripled electron temperature compared to flat targets. Particle-in-cell simulations demonstrate that plasma confinement within the cone and formation of turbulent laser fields that develop from cone wall reflections are responsible for the improved laser-to-target coupling. These passive target components can be used to improve the coupling efficiency for all high-intensity short-pulse laser applications, particularly at large facilities with long focal length optics.

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.

A new toroidal x-ray crystal spectrometer for the diagnosis of high energy density plasmas at the National Ignition Facility.

The here-described spectrometer was developed for the extended x-ray absorption fine structure spectroscopy of high-density plasmas at the National Ignition Facility. It employs as the Bragg reflecting element a new type of toroidally bent crystal with a constant and very large major radius R and a much smaller, locally varying, minor radius r. The focusing properties of this crystal and the experimental arrangement of the source and detector make it possible to (a) fulfill the conditions for a perfect imaging of an ideal point source for each wavelength, (b) obtain a high photon throughput, (c) obtain a high spectral resolution by eliminating the effects of source-size broadening, and (d) obtain a one-dimensional spatial resolution with a high magnification perpendicular to the main dispersion plane.

Implementing time resolved electron temperature capability at the NIF using a streak camera.

A new capability at the National Ignition Facility (NIF) has been implemented to measure the temperature of x-ray emitting sources. Although it is designed primarily for Inertial Confinement Fusion (ICF), it can be used for any hot emitting source that is well modeled. The electron temperature (Te) of the hot spot within the core of imploded ICF capsules is an effective indicator of implosion performance. Currently, there are spatially and temporally integrated Te inferences using image plates. A temporally resolved measurement of Te will help elucidate the mechanisms for hot spot heating and cooling such as conduction to fuel, alpha-heating, mix, and radiative losses. To determine the temporally resolved Te of hot spots, specific filters are added to an existing x-ray streak camera "streaked polar instrumentation for diagnosing energetic radiation" to probe the emission spectrum during the x-ray burn history of implosions at the NIF. One of the difficulties in inferring the hot spot temperature is the attenuation of the emission due to opacity from the shell and fuel. Therefore, a series of increasingly thick titanium filters were implemented to isolate the emission in specific energy regions that are sensitive to temperatures above 3 keV while not significantly influenced by the shell/fuel attenuation. Additionally, a relatively thin zinc filter was used to measure the contribution of colder emission sources. Since the signal levels of the emission through the thicker filters are relatively poor, a dual slit (aperture) was designed to increase the detected signal at the higher end of the spectrum. Herein, the design of the filters and slit is described, an overview of the solving technique is provided, and the initial electron temperature results are reported.

Absolute calibration of a time-resolved high resolution x-ray spectrometer for the National Ignition Facility (invited).

A high resolution, Diagnostic Instrument Manipulator (DIM)-based x-ray Bragg crystal spectrometer has been calibrated for and deployed at the National Ignition Facility (NIF) to diagnose plasma conditions in ignition capsules near stagnation times. The spectrometer has two conical crystals in the Hall geometry focusing rays from the Kr Heα, Lyα, and Heß complexes onto a streak camera, with the physics objectives of measuring time-resolved electron density and temperature through observing Stark broadening and the relative intensities of dielectronic satellites. A third von Hámos crystal that time-integrates the Kr Heα, Heß and intervening energy range provides in situ calibration for the streak camera signals. The spectrometer has been absolutely calibrated using a microfocus x-ray source, an array of CCD and single-photon-counting detectors, and multiple K- and L-absorption edge filters at the Princeton Plasma Physics Laboratory (PPPL) x-ray laboratory. Measurements of the integrated reflectivity, energy range, and energy resolution for each crystal are discussed. These calibration data provide absolute x-ray signal levels for NIF measurements, enabling precise filter selection and comparisons to simulations.

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.

Publisher's Note: X-ray shadow imprint of hydrodynamic instabilities on the surface of inertial confinement fusion capsules by the fuel fill tube [Phys. Rev. E 95, 031204(R) (2017)].

This corrects the article DOI: 10.1103/PhysRevE.95.031204.

X-ray shadow imprint of hydrodynamic instabilities on the surface of inertial confinement fusion capsules by the fuel fill tube.

Measurements of hydrodynamic instability growth for a high-density carbon ablator for indirectly driven inertial confinement fusion implosions on the National Ignition Facility are reported. We observe significant unexpected features on the capsule surface created by shadows of the capsule fill tube, as illuminated by laser-irradiated x-ray spots on the hohlraum wall. These shadows increase the spatial size and shape of the fill tube perturbation in a way that can significantly degrade performance in layered implosions compared to previous expectations. The measurements were performed at a convergence ratio of ∼2 using in-flight x-ray radiography. The initial seed due to shadow imprint is estimated to be equivalent to ∼50-100 nm of solid ablator material. This discovery has prompted the need for a mitigation strategy for future inertial confinement fusion designs as proposed here.

Development of a high resolution x-ray spectrometer for the National Ignition Facility (NIF).

A high resolution (E/ΔE = 1200-1800) Bragg crystal x-ray spectrometer is being developed to measure plasma parameters in National Ignition Facility experiments. The instrument will be a diagnostic instrument manipulator positioned cassette designed mainly to infer electron density in compressed capsules from Stark broadening of the helium-ß (1s2-1s3p) lines of krypton and electron temperature from the relative intensities of dielectronic satellites. Two conically shaped crystals will diffract and focus (1) the Kr Heß complex and (2) the Heα (1s2-1s2p) and Lyα (1s-2p) complexes onto a streak camera photocathode for time resolved measurement, and a third cylindrical or conical crystal will focus the full Heα to Heß spectral range onto an image plate to provide a time integrated calibration spectrum. Calculations of source x-ray intensity, spectrometer throughput, and spectral resolution are presented. Details of the conical-crystal focusing properties as well as the status of the instrumental design are also presented.