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, , 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.
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 Magnetized Liner Inertial Fusion (MagLIF) 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 (>1013 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.
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.
Hare, Jack H.; Myers, Clayton E.; Ampleford, David A.; Chittenden, Jeremy P.; Crilly, Aidan C.; Datta, Rishabh D.; Fox, William F.; Halliday, Jack H.; Jennings, Christopher A.; Ji, Hantao J.; Kuranz, Carolyn K.; Lebedev, Sergey L.; Melean, Raul M.; Uzdensky, Dmitri U.
Datta, Rishabh D.; Hare, Jack H.; Myers, Clayton E.; Ampleford, David A.; Chittenden, Jeremy P.; Clayson, Thomas C.; Crilly, Aidan C.; Fox, Will F.; Halliday, Jack H.; Jennings, Christopher A.; Ji, Hantao J.; Kuranz, Carolyn K.; Lebedev, Sergey L.; Melean, Raul M.; Russel, Daniel R.; Suttle, Lee S.; Tang, I T.; Uzdensky, Dmitri U.
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.