In magnetized liner inertial fusion (MagLIF), a cylindrical liner filled with fusion fuel is imploded with the goal of producing a one-dimensional plasma column at thermonuclear conditions. However, structures attributed to three-dimensional effects are observed in self-emission x-ray images. Despite this, the impact of many experimental inputs on the column morphology has not been characterized. We demonstrate the use of a linear regression analysis to explore correlations between morphology and a wide variety of experimental inputs across 57 MagLIF experiments. Results indicate the possibility of several unexplored effects. For example, we demonstrate that increasing the initial magnetic field correlates with improved stability. Although intuitively expected, this has never been quantitatively assessed in integrated MagLIF experiments. We also demonstrate that azimuthal drive asymmetries resulting from the geometry of the “current return can” appear to measurably impact the morphology. In conjunction with several counterintuitive null results, we expect the observed correlations will encourage further experimental, theoretical, and simulation-based studies. Finally, we note that the method used in this work is general and may be applied to explore not only correlations between input conditions and morphology but also with other experimentally measured quantities.
Mitrani, James M.; Ampleford, David J.; Chandler, Gordon A.; Eckart, Mark J.; Hahn, Kelly D.; Jeet, Justin; Kerr, Shaun M.; Mannion, Owen M.; Moore, Alastair M.; Schlossberg, David J.; Youmans, Amanda E.; Grim, Gary P.
On pulsed fusion experiments, the neutron time of flight (nToF) diagnostic provides critical information on the fusion neutron energy spectrum. This work presents an analysis technique that uses two collinear nToF detectors, potentially to measure nuclear bang time and directional flow velocities. Two collinear detectors may be sufficient to disambiguate the contributions of nuclear bang time and directional flow velocities to the first moment of the neutron energy spectrum, providing an independent measurement of nuclear bang time. Preliminary results from measured nToF traces on the National Ignition Facility and additional applications of this technique are presented.
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.
For the cylindrically symmetric targets that are normally fielded on the Z machine, two dimensional axisymmetric MHD simulations provide the backbone of our target design capability. These simulations capture the essential operation of the target and allow for a wide range of physics to be addressed at a substantially lower computational cost than 3D simulations. This approach, however, makes some approximations that may impact its ability to accurately provide insight into target operation. As an example, in 2D simulations, targets are able to stagnate directly to the axis in a way that is not entirely physical, leading to uncertainty in the impact of the dynamical instabilities that are an important source of degradation for ICF concepts. In this report, we have performed a series of 3D calculations in order to assess the importance of this higher fidelity treatment on MagLIF target performance.
This project applies methods in Bayesian inference and modern statistical methods to quantify the value of new experimental data, in the form of new or modified diagnostic configurations and/or experiment designs. We demonstrate experiment design methods that can be used to identify the highest priority diagnostic improvements or experimental data to obtain in order to reduce uncertainties on critical inferred experimental quantities and select the best course of action to distinguish between competing physical models. Bayesian statistics and information theory provide the foundation for developing the necessary metrics, using two high impact experimental platforms on Z as exemplars to develop and illustrate the technique. We emphasize that the general methodology is extensible to new diagnostics (provided synthetic models are available), as well as additional platforms. We also discuss initial scoping of additional applications that began development in the last year of this LDRD.
An x-ray imaging scheme using spherically bent crystals was implemented on the Z-machine to image x rays emitted by the hot, dense plasma generated by a Magnetized Liner Inertial Fusion (MagLIF) target. This diagnostic relies on a spherically bent crystal to capture x-ray emission over a narrow spectral range (<15 eV), which is established by a limiting aperture placed on the Rowland circle. The spherical crystal optic provides the necessary high-throughput and large field-of-view required to produce a bright image over the entire, one-cm length of the emitting column of a plasma. The average spatial resolution was measured and determined to be 18 µm for the highest resolution configuration. With this resolution, the radial size of the stagnation column can be accurately determined and radial structures, such as bifurcations in the column, are clearly resolved. The success of the spherical-crystal imager has motivated the implementation of a new, two-crystal configuration for identifying sources of spectral line emission using a differential imaging technique.
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.
In magneto-inertial fusion, the ratio of the characteristic fuel length perpendicular to the applied magnetic field R to the α-particle Larmor radius Q α is a critical parameter setting the scale of electron thermal-conduction loss and charged burn-product confinement. Using a previously developed deep-learning-based Bayesian inference tool, we obtain the magnetic-field fuel-radius product B R ∝ R / Q α from an ensemble of 16 magnetized liner inertial fusion (MagLIF) experiments. Observations of the trends in BR are consistent with relative trade-offs between compression and flux loss as well as the impact of mix from 1D resistive radiation magneto-hydrodynamics simulations in all but two experiments, for which 3D effects are hypothesized to play a significant role. Finally, we explain the relationship between BR and the generalized Lawson parameter χ. Our results indicate the ability to improve performance in MagLIF through careful tuning of experimental inputs, while also highlighting key risks from mix and 3D effects that must be mitigated in scaling MagLIF to higher currents with a next-generation driver.
Laser propagation experiments using four beams of the National Ignition Facility to deliver up to 35 kJ of laser energy at 351 nm laser wavelength to heat magnetized liner inertial fusion-scale (1 cm-long), hydrocarbon-filled gas pipe targets to ∼keV electron temperatures have demonstrated energy coupling >20 kJ with essentially no backscatter in 15% critical electron density gas fills with 0-19 T applied axial magnetic fields. The energy coupling is also investigated for an electron density of 11.5% critical and for applied field strengths up to 24 T at both densities. This spans a range of Hall parameters 0 < ω c e τ e i ≲2, where a Hall parameter of 0.5 is expected to reduce electron thermal conduction across the field lines by a factor of 4-5 for the conditions of these experiments. At sufficiently high applied field strength (and therefore Hall parameter), the measured laser propagation speed through the targets increases in the measurements, consistent with reduced perpendicular electron thermal transport; this reduces the coupled energy to the target once the laser burns through the gas pipe. The results compare well with a 1D analytic propagation model for inverse Bremsstrahlung absorption.
Helium or neopentane can be used as surrogate gas fill for deuterium (D2) or deuterium-tritium (DT) in laser-plasma interaction studies. Surrogates are convenient to avoid flammability hazards or the integration of cryogenics in an experiment. To test the degree of equivalency between deuterium and helium, experiments were conducted in the Pecos target chamber at Sandia National Laboratories. Observables such as laser propagation and signatures of laser-plasma instabilities (LPI) were recorded for multiple laser and target configurations. It was found that some observables can differ significantly despite the apparent similarity of the gases with respect to molecular charge and weight. While a qualitative behaviour of the interaction may very well be studied by finding a suitable compromise of laser absorption, electron density, and LPI cross sections, a quantitative investigation of expected values for deuterium fills at high laser intensities is not likely to succeed with surrogate gases.
A zero-dimensional magnetic implosion model with a coupled equivalent circuit for the description of an imploding nested wire array or gas puff is presented. Circuit model results have been compared with data from imploding stainless steel wire arrays, and good agreement has been found. The total energy coupled to the load, E j × B, has been applied to a simple semi-analytic K-shell yield model, and excellent agreement with previously reported K-shell yields across all wire array and gas puff platforms is seen. Trade space studies in implosion radius and mass have found that most platforms operate near the predicted maximum yield. In some cases, the K-shell yield may be increased by increasing the mass or radius of the imploding array or gas puff.
Here 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.
We present an overview of the magneto-inertial fusion (MIF) concept MagLIF (Magnetized Liner Inertial Fusion) pursued at Sandia National Laboratories and review some of the most prominent results since the initial experiments in 2013. In MagLIF, a centimeter-scale beryllium tube or "liner" is filled with a fusion fuel, axially pre-magnetized, laser pre-heated, and finally imploded using up to 20 MA from the Z machine. All of these elements are necessary to generate a thermonuclear plasma: laser preheating raises the initial temperature of the fuel, the electrical current implodes the liner and quasi-adiabatically compresses the fuel via the Lorentz force, and the axial magnetic field limits thermal conduction from the hot plasma to the cold liner walls during the implosion. MagLIF is the first MIF concept to demonstrate fusion relevant temperatures, significant fusion production (>10^13 primary DD neutron yield), and magnetic trapping of charged fusion particles. On a 60 MA next-generation pulsed-power machine, two-dimensional simulations suggest that MagLIF has the potential to generate multi-MJ yields with significant self-heating, a long-term goal of the US Stockpile Stewardship Program. At currents exceeding 65 MA, the high gains required for fusion energy could be achievable.
Detailed analysis of both the line-intensity ratios and line shapes of the K-lines of elements of different abundances (Fe, Cr, Ni, and Mn) emitted from the stagnation of a steel wire-array implosion on Z, were used to determine the line opacities. While the opacities at the early time of stagnation appear to be consistent with a nearly uniform hot-plasma cylinder on-axis surrounded by a colder annulus, the opacities during the peak K-emission strongly suggest that the main K-emission is due to small hot regions (spots) spread over the stagnating column. The spots are shown to be at least 4× denser than expected based on a uniform-cylinder emission (namely, ni > 3 ×1020 cm-3 ), are of diameters of about 200 μ or less (where the smaller the spots the higher are the densities), and are thousands in number. The total mass of the spots was determined to be 3-10 % of the load mass, and their total volume 3-15 % of the O 1.2-mm stagnation-column volume, both are less than the respective values for the earlier period of lower K power.
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.
We report on experimental measurements of how an externally imposed magnetic field affects plasma heating by kJ-class, nanosecond laser pulses. The experiments reported here took place in gas cells analogous to magnetized liner inertial fusion targets. We observed significant changes in laser propagation and energy deposition scale lengths when a 12T external magnetic field was imposed in the gas cell. We find evidence that the axial magnetic field reduces radial electron thermal transport, narrows the width of the heated plasma, and increases the axial plasma length. Reduced thermal conductivity increases radial thermal gradients. This enhances radial hydrodynamic expansion and subsequent thermal self-focusing. Our experiments and supporting 3D simulations in helium demonstrate that magnetization leads to higher thermal gradients, higher peak temperatures, more rapid blast wave development, and beam focusing with an applied field of 12T.