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.

The Z machine is a current driver producing up to 30 MA in 100 ns that utilizes a wide range of diagnostics to assess accelerator performance and target behavior conduct experiments that use the Z target as a source of radiation or high pressures. We review the existing suite of diagnostic systems, including their locations and primary configurations. The diagnostics are grouped in the following categories: pulsed power diagnostics, x-ray power and energy, x-ray spectroscopy, x-ray imaging (including backlighting, power flow, and velocimetry), and nuclear detectors (including neutron activation). We will also briefly summarize the primary imaging detectors we use at Z: image plates, x-ray and visible film, microchannel plates, and the ultrafast x-ray imager. The Z shot produces a harsh environment that interferes with diagnostic operation and data retrieval. We term these detrimental processes "threats " of which only partial quantifications and precise sources are known. We summarize the threats and describe techniques utilized in many of the systems to reduce noise and backgrounds.

Accurate understanding of x-ray diagnostics is crucial for both interpreting high-energy-density experiments and testing simulations through quantitative comparisons. X-ray diagnostic models are complex. Past treatments of individual x-ray diagnostics on a case-by-case basis have hindered universal diagnostic understanding. Here, we derive a general formula for modeling the absolute response of non-focusing x-ray diagnostics, such as x-ray imagers, one-dimensional space-resolved spectrometers, and x-ray power diagnostics. The present model is useful for both data modeling and data processing. It naturally accounts for the x-ray crystal broadening. The new model verifies that standard approaches for a crystal response can be good approximations, but they can underestimate the total reflectivity and overestimate spectral resolving power by more than a factor of 2 in some cases near reflectivity edge features. We also find that a frequently used, simplified-crystal-response approximation for processing spectral data can introduce an absolute error of more than an order of magnitude and the relative spectral radiance error of a factor of 3. The present model is derived with straightforward geometric arguments. It is more general and is recommended for developing a unified picture and providing consistent treatment over multiple x-ray diagnostics. Such consistency is crucial for reliable multi-objective data analyses.

The single-crystal spectropolarimeter envisioned by Baronova and Stepanenko splits an incident x-ray beam into two beams with mutually orthogonal linear polarizations by using simultaneous reflections at the perfectly polarizing 45° Bragg angle on certain pairs of internal planes in hexagonal or cubic crystals. These planes intersect along a threefold symmetry axis, making a 120° angle with each other, and are typically symmetric with respect to the crystal surface. In practice, the wavelength of the diagnostic x-ray lines does not exactly satisfy Bragg’s law for the crystal in the ideal polarizing orientation, so the extinction of reflections is incomplete. Accepting this limitation, this paper shows that for cubic crystals, other pairs of internal planes exist that satisfy the polarization requirements approximately. Typically, they are accessible from the perfect polarization-splitting geometry by small rotations of the crystal. This paper includes examples of such planes for cubic crystals with {110} and {211} surface cuts.

Hexagonal and cubic crystals contain paired sets of internal planes that reflect the linearly polarized components of certain x rays into two separate, perpendicular directions. For the cubic crystals, two distinct crystal orientations provide the same polarization-splitting geometry. One of the orientations may have advantages for plasma spectroscopy by suppressing unwanted reflections. This paper demonstrates the two orientations with a germanium crystal and K characteristic lines from copper and zirconium.

Pulsed power accelerators compress electrical energy in space and time to provide versatile experimental platforms for high energy density and inertial confinement fusion science. The 80-TW "Z" pulsed power facility at Sandia National Laboratories is the largest pulsed power device in the world today. Z discharges up to 22MJ of energy stored in its capacitor banks into a current pulse that rises in 100ns and peaks at a current as high as 30 MA in low-inductance cylindrical targets. Considerable progress has been made over the past 15years in the use of pulsed power as a precision scientific tool. This paper reviews developments at Sandia in inertial confinement fusion, dynamic materials science, x-ray radiation science, and pulsed power engineering, with an emphasis on progress since a previous review of research on Z in Physics of Plasmas in 2005.

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.

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.

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.

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.

Acid phthalate crystals such as KAP crystals are a method of choice to record x-ray spectra in the soft x-ray regime (E ∼ 1 keV) using the large (001) 2d = 26.63 Å spacing. Reflection from many other planes is possible, and knowledge of the 2d spacing, reflectivity, and resolution for these reflections is necessary to evaluate whether they hinder or help the measurements. Burkhalter et al. [J. Appl. Phys., 52, 4379 (1981)] showed that the (013) reflection has efficiency comparable to the 2nd order reflection (002), and it can overlap the main first order reflection when the crystal bending axis ( b -axis) is contained in the dispersion plane, thus contaminating the main (001) measurement in a convex crystal geometry. We present a novel spectrograph concept that makes these asymmetric reflections helpful by setting the crystal b -axis perpendicular to the dispersion plane. In such a case, asymmetric reflections do not overlap with the main (001) reflection and each reflection can be used as an independent spectrograph. Here we demonstrate an achieved spectral range of 0.8-13 keV with a prototype setup. The detector measurements were reproduced with a 3D ray-tracing code.

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.

We have developed a process for indirectly coating small diameter electroformed nickel replicated optics with multilayers to increase their response at high energy (i.e. >10 keV). The ability to fabricate small diameter multilayer-coated full-shell Wolter X-ray optics with narrow bandpass opens the door to several applications within astronomy and also provides a path for cross-fertilization to other fields. We report on the characterization and evaluation of the first two prototype X-ray Wolter optics to be delivered to the Z Pulsed Power Facility at Sandia National Laboratories. The intent is to develop and field several optics as part of an imaging system with targeted spectral ranges.

The Advanced Light Source beamline-9.3.1 x-rays are used to calibrate the rocking curve of bent potassium acid phthalate (KAP) crystals in the 2.3-4.5 keV photon-energy range. Crystals are bent on a cylindrically convex substrate with a radius of curvature ranging from 2 to 9 in. and also including the flat case to observe the effect of bending on the KAP spectrometric properties. As the bending radius increases, the crystal reflectivity converges to the mosaic crystal response. The X-ray Oriented Programs (xop) multi-lamellar model of bent crystals is used to model the rocking curve of these crystals and the calibration data confirm that a single model is adequate to reproduce simultaneously all measured integrated reflectivities and rocking-curve FWHM for multiple radii of curvature in both 1st and 2nd order of diffraction.