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.

Achievement of Target Gain Larger than Unity in an Inertial Fusion Experiment

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.

Demonstration of improved laser preheat with a cryogenically cooled magnetized liner inertial fusion platform

We report on progress implementing and testing cryogenically cooled platforms for Magnetized Liner Inertial Fusion (MagLIF) experiments. Two cryogenically cooled experimental platforms were developed: an integrated platform fielded on the Z pulsed power generator that combines magnetization, laser preheat, and pulsed-power-driven fuel compression and a laser-only platform in a separate chamber that enables measurements of the laser preheat energy using shadowgraphy measurements. The laser-only experiments suggest that ∼89% ± 10% of the incident energy is coupled to the fuel in cooled targets across the energy range tested, significantly higher than previous warm experiments that achieved at most 67% coupling and in line with simulation predictions. The laser preheat configuration was applied to a cryogenically cooled integrated experiment that used a novel cryostat configuration that cooled the MagLIF liner from both ends. The integrated experiment, z3576, coupled 2.32 ± 0.25 kJ preheat energy to the fuel, the highest to-date, demonstrated excellent temperature control and nominal current delivery, and produced one of the highest pressure stagnations as determined by a Bayesian analysis of the data.

Neutron time-of-flight detectors (nTOF) used at Sandia's Z-Machine

Neutron time-of-flight (nTOF) detectors have been used on Sandia National Laboratories' Z-Machine for inertial confinement fusion and magnetized liner fusion experiments to infer physics parameters including the apparent fuel-ion temperature, neutron yield, the magnetic-radius product (BR), and the liner rho-r. Single-paddle, dual-paddle, and co-axial scintillation nTOF detectors are used in axial lines-of-sight (LOS) and LOS that are 12° from the midplane. Detector fabrication, characterization, and calibration are discussed.

Inferring neutron yields using indium activation samples for small fractions of tritium added to deuterium fuel in inertial confinement fusion (ICF) experiments

In inertial confinement fusion experiments, the neutron yield is an important metric for thermonuclear fusion performance. Neutron activation diagnostics can be used to infer neutron yields. The material used for neutron activation diagnostic undergoes a threshold reaction so that only neutrons having energies above the threshold energy are observed. For thermonuclear experiments using deuterium (D) and tritium (T) fuel constituents, neutrons arising from D + D reactions (DD-neutrons) and neutrons resulting from D + T reactions (DT-neutrons) are of primary interest. Indium has two neutron activation reactions that can be used to infer yields of DD-neutrons and DT-neutrons. One threshold is high enough that only DT-neutrons can induce activation, the second reaction can be activated by both DD-neutrons and DT-neutrons. Thus, to obtain the DD-neutron yield, the contribution made by DT-neutrons to the total induced activity must be extracted. In DD-fuel experiments, DT-neutrons arise from secondary reactions, which are significantly lower in number than primary DD-neutrons, and their contribution to the inferred DD-neutron yield can be ignored. When the DD- and DT-neutron yields become comparable, such as when low tritium fractions are added to DD-fuel, the contribution of DT-neutrons must be extracted to obtain accurate yields. A general method is described for this correction to DD-neutron yields.

Lawson Criterion for Ignition Exceeded in an Inertial Fusion Experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion.

Performance Scaling in Magnetized Liner Inertial Fusion Experiments

We present experimental results from the first systematic study of performance scaling with drive parameters for a magnetoinertial fusion concept. In magnetized liner inertial fusion experiments, the burn-averaged ion temperature doubles to 3.1 keV and the primary deuterium-deuterium neutron yield increases by more than an order of magnitude to 1.1×10^{13} (2 kJ deuterium-tritium equivalent) through a simultaneous increase in the applied magnetic field (from 10.4 to 15.9 T), laser preheat energy (from 0.46 to 1.2 kJ), and current coupling (from 16 to 20 MA). Individual parametric scans of the initial magnetic field and laser preheat energy show the expected trends, demonstrating the importance of magnetic insulation and the impact of the Nernst effect for this concept. A drive-current scan shows that present experiments operate close to the point where implosion stability is a limiting factor in performance, demonstrating the need to raise fuel pressure as drive current is increased. Simulations that capture these experimental trends indicate that another order of magnitude increase in yield on the Z facility is possible with additional increases of input parameters.

A neutron recoil-spectrometer for measuring yield and determining liner areal densities at the Z facility

A proof-of-principle CR-39 based neutron-recoil-spectrometer was built and fielded on the Z facility. Data from this experiment match indium activation yields within a factor of 2 using simplified instrument response function models. The data also demonstrate the need for neutron shielding in order to infer liner areal densities. A new shielded design has been developed. The spectrometer is expected to achieve signal-to-background greater than 2 for the down-scattered neutron signal and greater than 30 for the primary signal.

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.

Design and raytrace simulations of a multilayer-coated Wolter x-ray optic for the Z machine at Sandia National Laboratories

Recent breakthroughs in the fabrication of small-radii Wolter optics for astrophysics allow high energy density facilities to consider such optics as novel x-ray diagnostics at photon energies of 15-50 keV. Recently, the Lawrence Livermore National Laboratory, Sandia National Laboratories (SNL), the Smithsonian Astrophysical Observatory, and the NASA Marshall Space Flight Center jointly developed and fabricated the first custom Wolter microscope for implementation in SNL's Z machine with optimized sensitivity at 17.5 keV. To achieve spatial resolution of order 100-200 microns over a field of view of 5 × 5 × 5 mm³ with high throughput and narrow energy bandpass, the geometry of the optic and its multilayer required careful design and optimization. While the geometry mainly influences resolution and the field of view of the diagnostic, the mirror coating determines the spectral response and throughput. Here we outline the details of the design and fabrication process for the first multilayer-coated Wolter I optic for SNL's Z machine (Z Wolter), including its W/Si multilayer, and present results of raytrace simulations completed to predict and verify the performance of the optic.

An x-ray optic calibration facility for high energy density diagnostics

A facility to calibrate x-ray imaging optics was built at Lawrence Livermore National Laboratory to support high energy density (HED) and inertial confinement fusion (ICF) diagnostics such as those at the National Ignition Facility and the Sandia Z-Machine. Calibration of the spectral reflectivity and resolution of these x-ray diagnostics enable absolute determination of the x-ray flux and wavelengths generated in the HED and ICF experiments. Measurement of the optic point spread function is used to determine spatial resolution of the optic. This facility was constructed to measure (1) the x-ray reflectivity to ±5% over a spectral range from 5 to 60 keV; (2) point spread functions with a resolution of 50 μm (currently) and 13 μm (future) in the image plane; and (3) optic distance relative to the x-ray source and detector to within ±100 μm in each dimension. This article describes the capabilities of the calibration facility, concept of operations, and initial data from selected x-ray optics.

Characterization and calibration of a multilayer coated Wolter optic for an imager on the Z-machine at Sandia National Laboratories

The need for a time-resolved monochromatic x-ray imaging diagnostic at photon energies >15 keV has motivated the development of a Wolter optic to study x-ray sources on the Z-machine at Sandia National Laboratories. The work is performed in both the LLNL's x-ray calibration facility and SNL's micro-focus x-ray lab. Characterizations and calibrations include alignment, measurement of throughput within the field of view (FOV), the point-spread function within the FOV both in and out of focus, and bandpass in the FOV. These results are compared with ray tracing models, showing reasonable agreement.

A Wolter imager on the Z machine to diagnose warm x-ray sources

A new Wolter x-ray imager has been developed for the Z machine to study the emission of warm (>15 keV) x-ray sources. A Wolter optic has been adapted from observational astronomy and medical imaging, which uses curved x-ray mirrors to form a 2D image of a source with 5 × 5 × 5 mm³ field-of-view and measured 60-300-μm resolution on-axis. The mirrors consist of a multilayer that create a narrow bandpass around the Mo Kα lines at 17.5 keV. We provide an overview of the instrument design and measured imaging performance. In addition, we present the first data from the instrument of a Mo wire array z-pinch on the Z machine, demonstrating improvements in spatial resolution and a 350-4100× increase in the signal over previous pinhole imaging techniques.

A 7.2 keV spherical x-ray crystal backlighter for two-frame, two-color backlighting at Sandia's Z Pulsed Power Facility

Many experiments on Sandia National Laboratories' Z Pulsed Power Facility-a 30 MA, 100 ns rise-time, pulsed-power driver-use a monochromatic quartz crystal backlighter system at 1.865 keV (Si He_α) or 6.151 keV (Mn He_α) x-ray energy to radiograph an imploding liner (cylindrical tube) or wire array z-pinch. The x-ray source is generated by the Z-Beamlet laser, which provides two 527-nm, 1 kJ, 1-ns laser pulses. Radiographs of imploding, thick-walled beryllium liners at convergence ratios C_R above 15 [C_R=r_i(0)/r_i(t)] using the 6.151-keV backlighter system were too opaque to identify the inner radius r_i of the liner with high confidence, demonstrating the need for a higher-energy x-ray radiography system. Here, we present a 7.242 keV backlighter system using a Ge(335) spherical crystal with the Co He_α resonance line. This system operates at a similar Bragg angle as the existing 1.865 keV and 6.151 keV backlighters, enhancing our capabilities for two-color, two-frame radiography without modifying the system integration at Z. The first data taken at Z include 6.2-keV and 7.2-keV two-color radiographs as well as radiographs of low-convergence (C_R about 4-5), high-areal-density liner implosions.

Coarse spectral characterization of warm x-rays at the Z facility using a filtered thermoluminescent dosimeter array

A new collimated filtered thermoluminescent dosimeter (TLD) array has been developed at the Z facility to characterize warm x-rays (hν > 10 keV) produced by Z pinch radiation sources. This array includes a Kapton debris shield assembly to protect the TLDs from the source debris, a collimator array to limit the field of view of the TLDs to the source region, a filter wheel containing filters of aluminum, copper and tungsten up to 3 mm thick to independently filter each TLD, and a hermetically sealed cassette containing the TLDs as well as tungsten shielding on the sides and back of the array to minimize scattered radiation reaching the TLDs. Experimental results from a krypton gas puff and silver wire array shot are analyzed using two different functional forms of the energy spectrum to demonstrate the ability of this diagnostic to consistently extend the upper end of the x-ray spectrum characterization from ∼50 keV to >1 MeV.

A new time and space resolved transmission spectrometer for research in inertial confinement fusion and radiation source development

We describe the design and function of a new time and space resolved x-ray spectrometer for use in Z-pinch inertial confinement fusion and radiation source development experiments. The spectrometer is designed to measure x-rays in the range of 0.5-1.5 Å (8-25 keV) with a spectral resolution λ/Δλ ∼ 400. The purpose of this spectrometer is to measure the time- and one-dimensional space-dependent electron temperature and density during stagnation. These relatively high photon energies are required to escape the dense plasma created at stagnation and to obtain sensitivity to electron temperatures ≳3 keV. The spectrometer is of the Cauchois type, employing a large 30 × 36 mm², transmissive quartz optic for which a novel solid beryllium holder was designed. The performance of the crystal was verified using offline tests, and the integrated system was tested using experiments on the Z pulsed power accelerator.

X-ray power and yield measurements at the refurbished Z machine

Advancements have been made in the diagnostic techniques to measure accurately the total radiated x-ray yield and power from z-pinch implosion experiments at the Z machine with high accuracy. The Z machine is capable of outputting 2 MJ and 330 TW of x-ray yield and power, and accurately measuring these quantities is imperative. We will describe work over the past several years which include the development of new diagnostics, improvements to existing diagnostics, and implementation of automated data analysis routines. A set of experiments on the Z machine were conducted in which the load and machine configuration were held constant. During this shot series, it was observed that the total z-pinch x-ray emission power determined from the two common techniques for inferring the x-ray power, a Kimfol filtered x-ray diode diagnostic and the total power and energy diagnostic, gave 449 TW and 323 TW, respectively. Our analysis shows the latter to be the more accurate interpretation. More broadly, the comparison demonstrates the necessity to consider spectral response and field of view when inferring x-ray powers from z-pinch sources.

Architecture, implementation, and testing of a multiple-shell gas injection system for high current implosions on the Z accelerator

Tests are ongoing to conduct ~20 MA z-pinch implosions on the Z accelerator at Sandia National Laboratory using Ar, Kr, and D2 gas puffs as the imploding loads. The relatively high cost of operations on a machine of this scale imposes stringent requirements on the functionality, reliability, and safety of gas puff hardware. Here we describe the development of a prototype gas puff system including the multiple-shell nozzles, electromagnetic drivers for each nozzle's valve, a UV pre-ionizer, and an inductive isolator to isolate the ~2.4 MV machine voltage pulse present at the gas load from the necessary electrical and fluid connections made to the puff system from outside the Z vacuum chamber. This paper shows how the assembly couples to the overall Z system and presents data taken to validate the functionality of the overall system.

Investigation of high-temperature bright plasma X-ray sources produced in 5-MA X-pinch experiments

Using solid, machined X-pinch targets driven by currents rising from 0 to 5-6 MA in 60 ns, we observed bright spots of 5-9-keV continuum radiation from 5±2-μm diameter regions. The >6-keV radiation is emitted in about 0.4 ns, and the bright spots are roughly 75 times brighter than the bright spots measured at 1 MA. A total x-ray power of 10 TW peak and yields of 165±20 kJ were emitted from a 3-mm height. The 3-5-keV continuum radiation had a 50-90-GW peak power and 0.15-0.35-kJ yield. The continuum is plausibly from a 1275±75-eV blackbody or alternatively from a 3500±500-eV bremsstrahlung source.

Development and use of a two-dimensional interferometer to measure mass flow from a multi-shell Z-pinch gas puff

For gas puff Z-pinches, the K-shell x-ray yield is maximized with the use of a multi-shell nozzle. Optimization of the yield, verification of hydrodynamic models of the nozzle flows, and plausible MHD code modeling of the implosions require data on the radial and axial (R,Z) distribution of mass in the nozzle's flow field. Interferometry is a well-established technique for acquiring such data. We describe the development and use of a two-dimensional interferometer with emphasis on the required data reduction methods. We also show that the instrument can derive the flow from each individual nozzle in a multi-shell system.

Doppler measurement of implosion velocity in fast Z-pinch x-ray sources

The observation of Doppler splitting in K-shell x-ray lines emitted from optically thin dopants is used to infer implosion velocities of up to 70 cm/μs in wire-array and gas-puff Z pinches at drive currents of 15-20 MA. These data can benchmark numerical implosion models, which produce reasonable agreement with the measured velocity in the emitting region. Doppler splitting is obscured in lines with strong opacity, but red-shifted absorption produced by the cooler halo of material backlit by the hot core assembling on axis can be used to diagnose velocity in the trailing mass.

Compact, rugged in-chamber transmission spectrometers (7-28 keV) for the Sandia Z facility

We describe a pair of time-integrated transmission spectrometers that are designed to survey 7-28 keV (1.9 to 0.43 Å) x-ray photons produced by experiments on the Sandia Z pulsed power facility. Each spectrometer uses a quartz 10-11 crystal in a Cauchois geometry with a slit to provide spatial resolution along one dimension. The spectrometers are located in the harsh environment of the Z vacuum chamber, which necessitates that their design be compact and rugged. Example data from calibration tests and Z experiments are shown that illustrate the utility of the instruments.

Planar wire-array Z-pinch implosion dynamics and X-ray scaling at multiple-MA drive currents for a compact multisource hohlraum configuration

An indirect drive configuration is proposed wherein multiple compact Z-pinch x-ray sources surround a secondary hohlraum. Planar compact wire arrays allow reduced primary hohlraum surface area compared to cylindrical loads. Implosions of planar arrays are studied at up to 15 TW x-ray power on Saturn with radiated yields exceeding the calculated kinetic energy, suggesting other heating paths. X-ray power and yield scaling studied from 1-6 MA motivates viewfactor modeling of four 6-MA planar arrays producing 90 eV radiation temperature in a secondary hohlraum.

Observation of >400-eV precursor plasmas from low-wire-number copper arrays at the 1-MA zebra facility

Experiments with cylindrical copper wire arrays at the 1-MA Zebra facility show that high temperatures exist in the precursor plasmas formed when ablated wire array material accretes on the axis prior to the stagnation of a z pinch. In these experiments, the precursor radiated approximately 20% of the >1000 eV x-ray output, and time-resolved spectra show substantial emission from Cu L-shell lines. Modeling of the spectra shows an increase in temperature as the precursor forms, up to approximately 450 eV, after which the temperature decreases to approximately 220-320 eV until the main implosion.

Measurement of temperature, density, and particle transport with localized dopants in wire-array Z pinches

Axially localized NaF dopants are coated onto Al cylindrical wire arrays in order to act as spectroscopic tracers in the stagnated z-pinch plasma. Non-local-thermodynamic-equilibrium kinetic models fit to Na K-shell lines provide an independent measurement of the density and temperature that is consistent with spectroscopic analysis of K-shell emissions from Al and an alloyed Mg dopant. Axial transport of the Na dopant is observed, enabling quantitative study of instabilities in dense z-pinch plasmas.

Supersonic radiatively cooled rotating flows and jets in the laboratory

The first laboratory astrophysics experiments to produce a radiatively cooled plasma jet with dynamically significant angular momentum are discussed. A new configuration of wire array z pinch, the twisted conical wire array, is used to produce convergent plasma flows each rotating about the central axis. Collision of the flows produces a standing shock and jet that each have supersonic azimuthal velocities. By varying the twist angle of the array, the rotation velocity of the system can be controlled, with jet rotation velocities reaching approximately 18% of the propagation velocity.

Dynamics of cylindrically converging precursor plasma flow in wire-array Z -pinch experiments

This paper summarizes the present understanding of the processes leading to precursor column formation in cylindrical wire arrays on the 1 MA MAGPIE generator at Imperial College London. Direct experimental measurements of the diameter variation during the collapse and formation phase of the precursor column are presented, along with soft x-ray emission, and quantitative radiography. In addition, data from twisted cylindrical arrays are presented which give additional information on the behavior of coronal plasma generated in wire array z pinches. Three stages in precursor column formation are identifiable from the data: broad initial density profile, rapid contraction to small diameter, and slow expansion after formation. The correlation of emission to column diameter variation indicates the contraction phase is a nonlinear collapse resulting from the increasing on-axis density and radiative cooling rate. The variation in the minimum diameter is measured for several array materials, and data show good agreement with a pressure balance model. Comparison of column expansion rates to analytical models allows an estimate of column temperature variation, and estimates of the current in the column are also made. Formation data are in good agreement with both fluid and kinetic modeling, but highlight the need to include collisionless flow in the early time behavior.

Study of three-dimensional structure in wire-array z pinches by controlled seeding of axial modulations in wire radius

Three-dimensional perturbations have been seeded in wire-array z pinches by etching 15 microm diameter aluminum wires to introduce 20% modulations in radius with a controlled axial wavelength. These perturbations seed additional three-dimensional imploding structures that are studied experimentally and with magnetohydrodynamics calculations, highlighting the role of current path nonuniformity in perturbation-induced magnetic bubble formation.

Effect of radial-electric-field polarity on wire-array Z-pinch dynamics

The formation of plasma in wire-array Z-pinch experiments was found to depend upon the polarity of the radial-electric field near the wires. Reversing the radial-electric field midway along the length of an array resulted in the ablation rate of one-half of the array being reduced by 50%, significantly delaying the start of its implosion and altering its acceleration towards the axis. The observed phenomena cannot be explained by the standard magnetohydrodynamic models of array behavior, suggesting that effects such as electron emission may be important, especially during wire initiation.