We present a new analysis methodology that allows for the self-consistent integration of multiple diagnostics including nuclear measurements, x-ray imaging, and x-ray power detectors to determine the primary stagnation parameters, such as temperature, pressure, stagnation volume, and mix fraction in magnetized liner inertial fusion (MagLIF) experiments. The analysis uses a simplified model of the stagnation plasma in conjunction with a Bayesian inference framework to determine the most probable configuration that describes the experimental observations while simultaneously revealing the principal uncertainties in the analysis. We validate the approach by using a range of tests including analytic and three-dimensional MHD models. An ensemble of MagLIF experiments is analyzed, and the generalized Lawson criterion χ is estimated for all experiments.
X-ray radiography has been used to diagnose a wide variety of experiments at the Z facility including inertial confinement fusion capsule implosions, the growth of the magneto-Rayleigh-Taylor instability in solid liners, and the development of helical structures in axially magnetized liner implosions. In these experiments, the Z Beamlet laser (1 kJ, 1 ns) was used to generate the x-ray source. An alternate x-ray source is desirable in experiments where the Z Beamlet laser is used for another purpose (e.g., preheating the fuel in magnetized liner inertial fusion experiments) or when multiple radiographic lines of sight are necessary.
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.
MagLIF experiments [M.R. Gomez et al., Phys. Plasmas 22, 056306 (2015)] on Z have demonstrated the basic principles of Magneto-Inertial Fusion (MIF) for wall confined plasmas. Other MIF schemes have been proposed based on the liner implosion of closed field magnetically confined plasmas such as Field Reversed Configurations (FRCs) [T. P. Intrator et al., Phys. Plasmas 15, 042505 (2008)]. We present a semi-analytical model of liner driven FRC implosions that predicts the fusion gain of such systems. The model predicts a fusion gain near unity for an FRC imploded by a liner driven by the Z Machine. We show that FRCs could be formed and imploded at the Z facility using the AutoMag liner concept [S. A. Slutz et al., Phys. Plasmas 24, 012704 (2017)]. An initial bias magnetic field can be supplied by the external magnets used in MagLIF experiments. The reverse field is then supplied by an AutoMag liner, which has helical conducting paths imbedded in an insulating substance. Experiments [Shipley et al., Phys. Plasmas 26, 052705 (2019)] have demonstrated that AutoMag can generate magnetic fields greater than 30 Tesla inside of the liner. We have performed 2D Radiation MHD simulations of the formation and implosion of an FRC, which are in good agreement with the analytical model. The FRC formation process could be studied on small pulsed power machines delivering about 1 MA.
We have commissioned a new time-resolved, x-ray imaging diagnostic for the Z facility. The primary intended application is for diagnosing the stagnation behavior of Magnetized Liner Inertial Fusion (MagLIF) and similar targets. We have a variety of imaging systems at Z, both time-integrated and time-resolved, that provide valuable x-ray imaging information, but no system at Z up to this time provides a combined high-resolution imaging with multi-frame time resolution; this new diagnostic, called TRICXI for Time Resolved In-Chamber X-ray Imager, is meant to provide time-resolved spatial imaging with high resolution. The multi-frame camera consists of a microchannel plate camera. A key component to achieving the design goals is to place the instrument inside the Z vacuum chamber within 2 m of the load, which necessitates a considerable amount of x-ray shielding as well as a specially designed, independent vacuum system. A demonstration of the imaging capability for a series of MagLIF shots is presented. Predictions are given for resolution and relative image irradiance to guide experimenters in choosing the desired configuration for their experiments.
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.
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 1.1×1013 (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.
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.