Significant variety is observed in spherical crystal x-ray imager (SCXI) data for the stagnated fuel–liner system created in Magnetized Liner Inertial Fusion (MagLIF) experiments conducted at the Sandia National Laboratories Z-facility. As a result, image analysis tasks involving, e.g., region-of-interest selection (i.e. segmentation), background subtraction and image registration have generally required tedious manual treatment leading to increased risk of irreproducibility, lack of uncertainty quantification and smaller-scale studies using only a fraction of available data. We present a convolutional neural network (CNN)-based pipeline to automate much of the image processing workflow. This tool enabled batch preprocessing of an ensemble of Nscans = 139 SCXI images across Nexp = 67 different experiments for subsequent study. The pipeline begins by segmenting images into the stagnated fuel and background using a CNN trained on synthetic images generated from a geometric model of a physical three-dimensional plasma. The resulting segmentation allows for a rules-based registration. Our approach flexibly handles rarely occurring artifacts through minimal user input and avoids the need for extensive hand labelling and augmentation of our experimental dataset that would be needed to train an end-to-end pipeline. Here we also fit background pixels using low-degree polynomials, and perform a statistical assessment of the background and noise properties over the entire image database. Our results provide a guide for choices made in statistical inference models using stagnation image data and can be applied in the generation of synthetic datasets with realistic choices of noise statistics and background models used for machine learning tasks in MagLIF data analysis. We anticipate that the method may be readily extended to automate other MagLIF stagnation imaging applications.
Making reliable predictions in the presence of uncertainty is critical to high-consequence modeling and simulation activities, such as those encountered at Sandia National Laboratories. Surrogate or reduced-order models are often used to mitigate the expense of performing quality uncertainty analyses with high-fidelity, physics-based codes. However, phenomenological surrogate models do not always adhere to important physics and system properties. This project develops surrogate models that integrate physical theory with experimental data through a maximally-informative framework that accounts for the many uncertainties present in computational modeling problems. Correlations between relevant outputs are preserved through the use of multi-output or co-predictive surrogate models; known physical properties (specifically monotoncity) are also preserved; and unknown physics and phenomena are detected using a causal analysis. By endowing surrogate models with key properties of the physical system being studied, their predictive power is arguably enhanced, allowing for reliable simulations and analyses at a reduced computational cost.
A forward analytic model is required to rapidly simulate the neutron time-of-flight (nToF) signals that result from magnetized liner inertial fusion (MagLIF) experiments at Sandia’s Z Pulsed Power Facility. Various experimental parameters, such as the burn-weighted fuel-ion temperature and liner areal density, determine the shape of the nToF signal and are important for characterizing any given MagLIF experiment. Extracting these parameters from measured nToF signals requires an appropriate analytic model that includes the primary deuterium-deuterium neutron peak, once-scattered neutrons in the beryllium liner of the MagLIF target, and direct beamline attenuation. Mathematical expressions for this model were derived from the general-geometry time- and energy-dependent neutron transport equation with anisotropic scattering. Assumptions consistent with the time-of-flight technique were used to simplify this linear Boltzmann transport equation into a more tractable form. Models of the uncollided and once-collided neutron scalar fluxes were developed for one of the five nToF detector locations at the Z-Machine. Numerical results from these models were produced for a representative MagLIF problem and found to be in good agreement with similar neutron transport simulations. Twenty experimental MagLIF data sets were analyzed using the forward models, which were determined to only be significantly sensitive to the ion temperature. The results of this work were also found to agree with values obtained separately using a zero scatter analytic model and a high-fidelity Monte Carlo simulation. Inherent difficulties in this and similar techniques are identified, and a new approach forward is suggested.
Fuel magnetization in magneto-inertial fusion (MIF) experiments improves charged burn product confinement, reducing requirements on fuel areal density and pressure to achieve self-heating. By elongating the path length of 1.01 MeV tritons produced in a pure deuterium fusion plasma, magnetization enhances the probability for deuterium-tritium reactions producing 11.8−17.1 MeV neutrons. Nuclear diagnostics thus enable a sensitive probe of magnetization. Characterization of magnetization, including uncertainty quantification, is crucial for understanding the physics governing target performance in MIF platforms, such as magnetized liner inertial fusion (MagLIF) experiments conducted at Sandia National Laboratories, Z-facility. We demonstrate a deep-learned surrogate of a physics-based model of nuclear measurements. A single model evaluation is reduced from CPU hours on a high-performance computing cluster down to ms on a laptop. This enables a Bayesian inference of magnetization, rigorously accounting for uncertainties from surrogate modeling and noisy nuclear measurements. The approach is validated by testing on synthetic data and comparing with a previous study. We analyze a series of MagLIF experiments systematically varying preheat, resulting in the first ever systematic experimental study of magnetic confinement properties of the fuel plasma as a function of fundamental inputs on any neutron-producing MIF platform. We demonstrate that magnetization decreases from B ∼0.5 to B MG cm as laser preheat energy deposited increases from preheat ∼460 J to E preheat ∼1.4 kJ. This trend is consistent with 2D LASNEX simulations showing Nernst advection of the magnetic field out of the hot fuel and diffusion into the target liner.
The inductively driven transmission line (IDTL) is a miniature current-carrying device that passively couples to fringe magnetic fields in the final power feed on the Z Pulsed Power Facility. The IDTL redirects a small amount of Z's magnetic energy along a secondary path to ground, thereby enabling pulsed power diagnostics to be driven in parallel with the primary load for the first time. IDTL experiments and modeling presented here indicate that IDTLs operate non-perturbatively on Z and that they can draw in excess of 150 kA of secondary current, which is enough to drive an X-pinch backlighter. Additional experiments show that IDTLs are also capable of making cleaner, higher-fidelity measurements of the current flowing in the final feed.
Mixing of cold, higher-Z elements into the fuel region of an inertial confinement fusion target spoils the fusion burn efficiency. This mixing process is driven by both "turbulent" and "atomic" mixing processes, the latter being modeled through transport corrections to the basic hydrodynamic models. Recently, there has been a surge in the development of dense plasma transport modeling and the associated transport coefficients; however, experimental validation remains in its infancy. To address this gap in our knowledge of interfacial mixing, Sandia National Laboratories is developing a new experimental platform at the Z-facility to investigate plasma transport in dense plasmas that span the entire warm dense matter regime. Specifically, this platform is being developed to measure species transport across a V/CH interface, using an x-ray driven hohlraum to drive the sample to [?] 190eV over 5ns. The heated sample is diagnosed using radiography optimized to measure the distribution of Vanadium perpendicular the interface. In order to interpret measurements made using this experimental platform, modeling tools that incorporate transport effects in strongly coupled plasmas are required. To this end, we utilize new advances in multi-species kinetic theory, collision models applicable to strongly coupled plasmas and modeling of degenerate electron plasmas to develop such a capability. The resulting kinetic transport code has been applied, along with state-of-the-art radiation hydrodynamic codes, to model the experiments. Results from this modeling effort highlight the importance of strong electric fields, which are present in the kinetic transport code, but absent in the radiation hydrodynamics code, in driving interfacial mixing. Synthetic radiography generated from all of these models reveals the ability of experimental diagnostics to distinguish interfacial mixing driven by a range of transport effects. We demonstrate that the spatial and temporal resolution of radiography diagnostics currently available at the Z-facility can distinguish between these different transport effects when multiple (3 [?] 4) radiographs, separated in time ( [?] 2 ns ) with accurate timing are captured per experiment.
The morphology of the stagnated plasma resulting from Magnetized Liner Inertial Fusion (MagLIF) is measured by imaging the self-emission x-rays coming from the multi-keV plasma, and the evolution of the imploding liner is measured by radiographs. Equivalent diagnostic response can be derived from integrated rad-MHD simulations from programs such as Hydra and Gorgon. There have been only limited quantitative ways to compare the image mor- phology, that is the texture, of simulations and experiments. We have developed a metric of image morphology based on the Mallat Scattering Transformation (MST), a transformation that has proved to be effective at distinguishing textures, sounds, and written characters. This metric has demonstrated excellent performance in classifying ensembles of synthetic stagnation images. We use this metric to quantitatively compare simulations to experimen- tal images, cross experimental images, and to estimate the parameters of the images with uncertainty via a linear regression of the synthetic images to the parameter used to generate them. This coordinate space has proved very adept at doing a sophisticated relative back- ground subtraction in the MST space. This was needed to compare the experimental self emission images to the rad-MHD simulation images. We have also developed theory that connects the transformation to the causal dynamics of physical systems. This has been done from the classical kinetic perspective and from the field theory perspective, where the MST is the generalized Green's function, or S-matrix of the field theory in the scale basis. From both perspectives the first order MST is the current state of the system, and the second order MST are the transition rates from one state to another. . An efficient, GPU accelerated, Python implementation of the MST was developed. Future applications are discussed.
We recently developed a one-dimensional imager of neutrons on the Z facility. The instrument is designed for Magnetized Liner Inertial Fusion (MagLIF) experiments, which produce D-D neutrons yields of ∼3 × 1012. X-ray imaging indicates that the MagLIF stagnation region is a 10-mm long, ∼100-μm diameter column. The small radial extents and present yields precluded useful radial resolution, so a one-dimensional imager was developed. The imaging component is a 100-mm thick tungsten slit; a rolled-edge slit limits variations in the acceptance angle along the source. CR39 was chosen as a detector due to its negligible sensitivity to the bright x-ray environment in Z. A layer of high density poly-ethylene is used to enhance the sensitivity of CR39. We present data from fielding the instrument on Z, demonstrating reliable imaging and track densities consistent with diagnosed yields. For yields ∼3 × 1012, we obtain resolutions of ∼500 μm.
The size, temporal and spatial shape, and energy content of a laser pulse for the pre-heat phase of magneto-inertial fusion affect the ability to penetrate the window of the laser-entrance-hole and to heat the fuel behind it. High laser intensities and dense targets are subject to laser-plasma-instabilities (LPI), which can lead to an effective loss of pre-heat energy or to pronounced heating of areas that should stay unexposed. While this problem has been the subject of many studies over the last decades, the investigated parameters were typically geared towards traditional laser driven Inertial Confinement Fusion (ICF) with densities either at 10% and above or at 1% and below the laser's critical density, electron temperatures of 3-5 keV, and laser powers near (or in excess of) 1 × 1015 W/cm2. In contrast, Magnetized Liner Inertial Fusion (MagLIF) [Slutz et al., Phys. Plasmas 17, 056303 (2010) and Slutz and Vesey, Phys. Rev. Lett. 108, 025003 (2012)] currently operates at 5% of the laser's critical density using much thicker windows (1.5-3.5 μm) than the sub-micron thick windows of traditional ICF hohlraum targets. This article describes the Pecos target area at Sandia National Laboratories using the Z-Beamlet Laser Facility [Rambo et al., Appl. Opt. 44(12), 2421 (2005)] as a platform to study laser induced pre-heat for magneto-inertial fusion targets, and the related progress for Sandia's MagLIF program. Forward and backward scattered light were measured and minimized at larger spatial scales with lower densities, temperatures, and powers compared to LPI studies available in literature.
Photonic Doppler velocimetry tracks motion during high-speed, single-event experiments using telecommunication fiber components. The same technology can be applied in situations where there is no actual motion, but rather a change in the optical path length. Migration of plasma into vacuum alters the refractive index near a fiber probe, while intense radiation modifies the refractive index of the fiber itself. These changes can diagnose extreme environments in a flexible, time-resolved manner.
Hydrodynamic instability growth is a fundamentally limiting process in many applications. In High Energy Density Physics (HEDP) systems such as inertial confinement fusion implosions and stellar explosions, hydro instabilities can dominate the evolution of the object and largely determine the final state achievable. Of particular interest is the process by which instabilities cause perturbations at a density or material interface to grow nonlinearly, introducing vorticity and eventually causing the two species to mix across the interface. Although quantifying instabilities has been the subject of many investigations in planar geometry, few have been done in converging geometry. During FY17, the team executed six convergent geometry instability experiments. Based on earlier results, the platform was redesigned and improved with respect to load centering at installation making the installation reproducible and development of a new 7.2 keV, Co He-a backlighter system to better penetrate the liner. Together, the improvements yielded significantly improved experimental results. The results in FY17 demonstrate the viability of using experiments on Z to quantify instability growth in cylindrically convergent geometry. Going forward, we will continue the partnership with staff and management at LANL to analyze the past experiments, compare to hydrodynamics growth models, and design future experiments.
Sandia National Laboratories is pursuing a variation of Magneto-Inertial Fusion called Magnetized Liner Inertial Fusion, or MagLIF. The MagLIF approach requires magnetization of the deuterium fuel, which is accomplished by an initial external B-Field and laser-driven pre-heat. While magnetization is crucial to the concept, it is challenging to couple sufficient energy to the fuel, since laser-plasma instabilities exist, and a compromise between laser spot size, laser entrance window thickness, and fuel density must be found. Nonlinear processes in laser plasma interaction, or laser-plasma instabilities (LPI), complicate the deposition of laser energy by enhanced absorption, backscatter, filamentation and beam-spray. Key LPI processes are determined, and mitigation methods are discussed. Results with and without improvement measures are presented.
We report on the progress made to date for a Laboratory Directed Research and Development (LDRD) project aimed at diagnosing magnetic flux compression on the Z pulsed-power accelerator (0-20 MA in 100 ns). Each experiment consisted of an initially solid Be or Al liner (cylindrical tube), which was imploded using the Z accelerator's drive current (0-20 MA in 100 ns). The imploding liner compresses a 10-T axial seed field, B z ( 0 ) , supplied by an independently driven Helmholtz coil pair. Assuming perfect flux conservation, the axial field amplification should be well described by B z ( t ) = B z ( 0 ) x [ R ( 0 ) / R ( t )] 2 , where R is the liner's inner surface radius. With perfect flux conservation, B z ( t ) and dB z / dt values exceeding 10 4 T and 10 12 T/s, respectively, are expected. These large values, the diminishing liner volume, and the harsh environment on Z, make it particularly challenging to measure these fields. We report on our latest efforts to do so using three primary techniques: (1) micro B-dot probes to measure the fringe fields associated with flux compression, (2) streaked visible Zeeman absorption spectroscopy, and (3) fiber-based Faraday rotation. We also mention two new techniques that make use of the neutron diagnostics suite on Z. These techniques were not developed under this LDRD, but they could influence how we prioritize our efforts to diagnose magnetic flux compression on Z in the future. The first technique is based on the yield ratio of secondary DT to primary DD reactions. The second technique makes use of the secondary DT neutron time-of-flight energy spectra. Both of these techniques have been used successfully to infer the degree of magnetization at stagnation in fully integrated Magnetized Liner Inertial Fusion (MagLIF) experiments on Z [P. F. Schmit et al. , Phys. Rev. Lett. 113 , 155004 (2014); P. F. Knapp et al. , Phys. Plasmas, 22 , 056312 (2015)]. Finally, we present some recent developments for designing and fabricating novel micro B-dot probes to measure B z ( t ) inside of an imploding liner. In one approach, the micro B-dot loops were fabricated on a printed circuit board (PCB). The PCB was then soldered to off-the-shelf 0.020- inch-diameter semi-rigid coaxial cables, which were terminated with standard SMA connectors. These probes were recently tested using the COBRA pulsed power generator (0-1 MA in 100 ns) at Cornell University. In another approach, we are planning to use new multi-material 3D printing capabilities to fabricate novel micro B-dot packages. In the near future, we plan to 3D print these probes and then test them on the COBRA generator. With successful operation demonstrated at 1-MA, we will then make plans to use these probes on a 20-MA Z experiment.
The standard approaches to inertial confinement fusion (ICF) rely on implosion velocities greater than 300 km/s and spherical convergence to achieve the high fuel temperatures (T > 4 keV) and areal densities (ρr > 0.3 g/cm2) required for ignition1. Such high velocities are achieved by heating the outside surface of a spherical capsuleeither directly with a large number of laser beams (Direct Drive) or with x-rays generated within a hohlraum (Indirect Drive). A much more energetically efficient approach is to use the magnetic pressure generated by a pulsed power machine to directly drive an implosion. In this approach 5-10% of the stored energy can be converted to the implosion of a metal tube generally referred to as a “liner”. However, the implosion velocity is not very high 70-100 km/s and the convergence is cylindrical (rather than spherical) making it more difficult to achieve the high temperatures and areal densities needed for ignition.
This Letter presents results from the first fully integrated experiments testing the magnetized liner inertial fusion concept [S.A. Slutz et al., Phys. Plasmas 17, 056303 (2010)], in which a cylinder of deuterium gas with a preimposed axial magnetic field of 10 T is heated by Z beamlet, a 2.5 kJ, 1 TW laser, and magnetically imploded by a 19 MA current with 100 ns rise time on the Z facility. Despite a predicted peak implosion velocity of only 70 km/s, the fuel reaches a stagnation temperature of approximately 3 keV, with Te ≈ Ti, and produces up to 2e12 thermonuclear DD neutrons. In this study, X-ray emission indicates a hot fuel region with full width at half maximum ranging from 60 to 120 μm over a 6 mm height and lasting approximately 2 ns. The number of secondary deuterium-tritium neutrons observed was greater than 1010, indicating significant fuel magnetization given that the estimated radial areal density of the plasma is only 2 mg/cm2.
We present a general methodology to determine the diagnostic sensitivity that is directly applicable to neutron-activation diagnostics fielded on a wide variety of neutron-producing experiments, which include inertial-confinement fusion (ICF), dense plasma focus, and ion beam-driven concepts. This approach includes a combination of several effects: (1) non-isotropic neutron emission; (2) the 1/r2 decrease in neutron fluence in the activation material; (3) the spatially distributed neutron scattering, attenuation, and energy losses due to the fielding environment and activation material itself; and (4) temporally varying neutron emission. As an example, we describe the copper-activation diagnostic used to measure secondary deuterium-tritium fusion-neutron yields on ICF experiments conducted on the pulsed-power Z Accelerator at Sandia National Laboratories. Using this methodology along with results from absolute calibrations and Monte Carlo simulations, we find that for the diagnostic configuration on Z, the diagnostic sensitivity is 0.037% ± 17% counts/neutron per cm2 and is ~ 40% less sensitive than it would be in an ideal geometry due to neutron attenuation, scattering, and energy-loss effects.