Publications

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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.

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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.

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Neutron bang times for a series of MagLIF (Magnetic Liner Inertial Fusion) experiments with D₂-filled targets have been measured at the Z facility. The emitted neutrons were detected as current-mode pulses in a multichannel, neutron time-of-flight (nTOF) diagnostic with conventional, scintillator-photomultiplier-tube (PMT) detectors. In these experiments, the detectors were fielded at known, fixed distances L (690-2510 cm) from the target, and on three, non-coplanar (but convergent) lines-of-sight (LOS). The primary goal of this diagnostic was to estimate a fiducial time (bang time) relative to an externally generated time-base for synchronizing all the diagnostics in an experiment. Recorded arrival times (A7) of the pulses were characterized experimentally by three numerical methods: a first-moment estimate (centroid) and two nodal measures — Savitzky-Golay (SG) smoothing and a single point peak estimate of the raw data. These times were corrected for internal detector time delays (transit and impulse-response function) — an adjustment that linked the recorded ATs to the corresponding arrival of uncollided neutrons at each detector. The bang time was then estimated by linearly regressing the arrival times against the associated distances to the source; t_bang (on the system timescale) was taken as the temporal intercept of the regression equation at distance L = 0. This article reports the analysis for a representative shot #2584 for which (a) the recorded ATs — even without detector corrections — agreed by method in each channel to within 1-2 ns; (b) internal corrections were each ~3 — 5 ns; and (c) a 95% uncertainty (confidence) interval for t_bang in this shot was estimated at ±3 ns with 4 degrees of freedom. A secondary goal for this diagnostic was to check that the bang time measurements corresponded to neutrons emitted by the D(d,n)³He reaction in a thermalized DD plasma. According to the theoretical studies by Brysk, such neutrons should be emitted with an isotropic Gaussian distribution of mean kinetic energy $ \overline{E}$ of 2.449 MeV; this energy translates to a mean neutron speed $ \overline{u}$ of 2.160 cm/ns [D. H. Munro, Nuclear Fusion, 56(3) 036001 (2016)]. In the MagLIF series of shots there was no evidence of spatial asymmetry in the time-distance regressions, and it was possible to extract the mean neutron speed from the slope of these fits. In shot 2584 $ \overline{u}$ was estimated at 2.152 cm/ns ± 0.010 cm/ns [95 % confidence, 4 dof] and the mean kinetic energy $ \overline{E}$ (with relativistic corrections) was 2.431 MeV ± 0.022 MeV [95 % confidence, 4 dof] — results supporting the assumption that D-D neutrons were, in fact, measured.

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