Publications

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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.

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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.

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Inertial Fusion is being supported by the NNSA for weapon physics and, although net gain has not yet been attained, significant progress has been made. National Ignition Facility (NIF) capsules have attained fusion gain within the fuel. MagLIF, which is presently being studied at the Z facility, has demonstrated the basic principles of Magneto-Inertial Fusion (MIF), which may provide an alternative path to fusion. Despite these successes there is presently no effort to determine if inertial fusion can be used to generate electrical energy. It would be prudent to have a small program directed to the application of inertial fusion for energy (IFE). This program would not have the same goals as the NNSA and should thus be funded by OFES.

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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.

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Magneti zed Liner Inerti al Fusion (MagLIF ) is an inertial confinement fusion (ICF) concept that includes a strong magnetic field embedded in the fuel to mitigate thermal conduction loss during the implosion . MagLIF experiments on Sandia's 20 MA Z Machine uses an external Helmholtz - like coil pair for fuel premagnetization . By contrast, t he novel AutoMag concept employs a composite liner (cylindrical tube) with helically oriented conduction paths separated by insulating material to provide axial premagnetization of the fuel . Initially, during a current prepulse that slowly rises to %7E1 MA, current flows helically through the AutoMag liner , and so urces the fuel with an axial field . Next, a rapidly rising main current pulse breaks down the insulation and current in th e liner becomes purely axial. The liner and premagnetized fuel are then compressed by the rapidly growing azimuthal field external to t he liner. This integrated axial - field - production mechanism offers a few potential advantages when compared to the externa l premagnetization coils. AutoMag can increase drive current to MagLIF experiments by enabling a lower inductance transmission line , provide higher premagnetization field (>30 T), and greatly increase radial x - ray diagnostic access. 3D electromagnetic si mulations using ANSYS Maxwell have been completed in order to explore the current distributions within the helical conduction paths, the inter - wire dielectric strength properties, and the thermal properties of the helical conduction paths during premagneti zation (%7E1 MA in 100ns). Th ree liner designs , of varying peak field strength, and associated varying risk of dielectric breakdown, will soon be tested in experiments on the %7E 1 MA, 100ns Mykonos facility. Experiments will measure B z (t) inside of the line r and assess failure mechanisms.

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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.

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Presented is a semi-analytic model of magnetized liner inertial fusion (MagLIF). This model accounts for several key aspects of MagLIF, including: (1) preheat of the fuel (optionally via laser absorption); (2) pulsed-power-driven liner implosion; (3) liner compressibility with an analytic equation of state, artificial viscosity, internal magnetic pressure, and ohmic heating; (4) adiabatic compression and heating of the fuel; (5) radiative losses and fuel opacity; (6) magnetic flux compression with Nernst thermoelectric losses; (7) magnetized electron and ion thermal conduction losses; (8) end losses; (9) enhanced losses due to prescribed dopant concentrations and contaminant mix; (10) deuterium-deuterium and deuterium-tritium primary fusion reactions for arbitrary deuterium to tritium fuel ratios; and (11) magnetized α-particle fuel heating. We show that this simplified model, with its transparent and accessible physics, can be used to reproduce the general 1D behavior presented throughout the original MagLIF paper [S. A. Slutz et al., Phys. Plasmas 17, 056303 (2010)]. We also discuss some important physics insights gained as a result of developing this model, such as the dependence of radiative loss rates on the radial fraction of the fuel that is preheated.

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.

It is shown that charged particle beams are not promising as an approach to preheating the fuel in a MagLIF implosion.

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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 T_e ≈ T_i, 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.

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Novel experimental data are reported that reveal helical instability formation on imploding z -pinch liners that are premagnetized with an axial field. Such instabilities differ dramatically from the mostly azimuthally symmetric instabilities that form on unmagnetized liners. The helical structure persists at nearly constant pitch as the liner implodes. This is surprising since, at the liner surface, the azimuthal drive field presumably dwarfs the axial field for all but the earliest stages of the experiment. These fundamentally 3D results provide a unique and challenging test for 3D-magnetohydrodynamics simulations.

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The Meier-Moir economic model for Pulsed Power Driven Inertial Fusion Energy shows at least two approaches for fusion energy at 7 to 8 cents/kw-hr: One with large yield at 0.1 Hz and presented by M. E. Cuneo at ICENES 2011 and one with smaller yield at 3 Hz presented in this paper. Both use very efficient and low cost Linear Transformer Drivers (LTDs) for the pulsed power. Here, we report the system configuration and end-to-end simulation for the latter option, which is called the Plasma Power Station (PPS), and report the first results on the two, least mature, enabling technologies: a magnetically driven Quasi Spherical Direct Drive (QSDD) capsule for the fusion yield and an Inverse Diode for coupling the driver to the target. In addition, we describe the issues and propose to address the issues with a prototype of the PPS on the Saturn accelerator and with experiments on a short pulse modification of the Z accelerator test the validity of simulations showing megajoule thermonuclear yield with DT on a modified Z.

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Magnetic Liner Inertial Fusion (MagLIF) [S. A. Slutz, et al., Phys. Plasmas 17 056303 (2010)] is a promising new concept for achieving >100 kJ of fusion yield on Z. The greatest threat to this concept is the Magneto-Rayleigh-Taylor (MRT) instability. Thus an experimental campaign has been initiated to study MRT growth in fast-imploding (<100 ns) cylindrical liners. The first sets of experiments studied aluminum liner implosions with prescribed sinusoidal perturbations (see talk by D. Sinars). By contrast, this poster presents results from the latest sets of experiments that used unperturbed beryllium (Be) liners. The purpose for using Be is that we are able to radiograph 'through' the liner using the 6-keV photons produced by the Z-Beamlet backlighting system. This has enabled us to obtain time-resolved measurements of the imploding liner's density as a function of both axial and radial location throughout the field of view. This data is allowing us to evaluate the integrity of the inside (fuel-confining) surface of the imploding liner as it approaches stagnation.

Numerical simulations [S.A. Slutz et al Phys. Plasmas 17, 056303 (2010)] indicate that fuel magnetization and preheat could enable cylindrical liner implosions to become an efficient means to generate fusion conditions. A series of simulations has been performed to study the stability of magnetically driven liner implosions. These simulations exhibit the initial growth and saturation of an electro-thermal instability. The Rayleigh-Taylor instability further amplifies the resultant density perturbations developing a spectrum of modes initially peaked at short wavelengths. With time the spectrum of modes evolves towards longer wavelengths developing an inverse cascade. The effects of mode coupling, the radial dependence of the magnetic pressure, and the initial surface roughness will be discussed.

The magneto-Rayleigh-Taylor (MRT) instability is the most important instability for determining whether a cylindrical liner can be compressed to its axis in a relatively intact form, a requirement for achieving the high pressures needed for inertial confinement fusion (ICF) and other high energy-density physics applications. While there are many published RT studies, there are a handful of well-characterized MRT experiments at time scales >1 {micro}s and none for 100 ns z-pinch implosions. Experiments used solid Al liners with outer radii of 3.16 mm and thicknesses of 292 {micro}m, dimensions similar to magnetically-driven ICF target designs [1]. In most tests the MRT instability was seeded with sinusoidal perturbations ({lambda} = 200, 400 {micro}m, peak-to-valley amplitudes of 10, 20 {micro}m, respectively), wavelengths similar to those predicted to dominate near stagnation. Radiographs show the evolution of the MRT instability and the effects of current-induced ablation of mass from the liner surface. Additional Al liner tests used 25-200 {micro}m wavelengths and flat surfaces. Codes being used to design magnetized liner ICF loads [1] match the features seen except at the smallest scales (<50 {micro}m). Recent experiments used Be liners to enable penetrating radiography using the same 6.151 keV diagnostics and provide an in-flight measurement of the liner density profile.

Numerical simulations indicate that significant fusion yields (>100 kJ) may be obtained by pulsed-power-driven implosions of cylindrical metal liners onto magnetized and preheated deuterium-tritium fuel. The primary physics risk to this approach is the Magneto-Rayleigh-Taylor (MRT) instability, which operates during both the acceleration and deceleration phase of the liner implosion. We have designed and performed some experiments to study the MRT during the acceleration phase, where the light fluid is purely magnetic. Results from our first series of experiments and plans for future experiments will be presented. According to simulations, an initial axial magnetic field of 10 T is compressed to >100 MG within the liner during the implosion. The magnetic pressure becomes comparable to the plasma pressure during deceleration, which could significantly affect the growth of the MRT instability at the fuel/liner interface. The MRT instability is also important in some astronomical objects such as the Crab Nebula (NGC1962). In particular, the morphological structure of the observed filaments may be determined by the ratio of the magnetic to material pressure and alignment of the magnetic field with the direction of acceleration [Hester, ApJ, 456, 225 1996]. Potential experiments to study this MRT behavior using the Z facility will be presented.

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We examine the scaling to ignition of the energy deposition of laser generated electrons in compressed fast ignition cores. Relevant cores have densities of several hundred g/cm{sup 3}, with a few keV initial temperature. As the laser intensities increase approaching ignition systems, on the order of a few 10{sup 21}W/cm{sup 2}, the hot electron energies expected to approach 100MeV. Most certainly anomalous processes must play a role in the energy transfer, but the exact nature of these processes, as well as a practical way to model them, remain open issues. Traditional PIC explicit methods are limited to low densities on current and anticipated computing platforms, so the study of relevant parameter ranges has received so far little attention. We use LSP to examine a relativistic electron beam (presumed generated from a laser plasma interaction) of legislated energy and angular distribution is injected into a 3D block of compressed DT. Collective effects will determine the stopping, most likely driven by magnetic field filamentation. The scaling of the stopping as a function of block density and temperature, as well as hot electron current and laser intensity is presented. Sub-grid models may be profitably used and degenerate effects included in the solution of this problem.

The intense magnetic field generated in the 20 MA Z-machine is used to accelerate metallic flyer plates to high velocity for the purpose of generating strong shocks in equation of state experiments. We present results pertaining to experiments in which a 0.085 cm thick Al flyer plate is magnetically accelerated across a vacuum gap into a quartz target. Peak magnetic drive pressures up to 4.9 Mbar were produced, which yielded a record 34 km/s flyer velocity without destroying it by shock formation or Joule heating. Two-dimensional MHD simulation was used to optimize the magnetic drive pressure on the flyer surface, shape the current pulse to accelerate the flyer without shock formation (i.e., quasi-isentropically), and predict the flyer velocity. Shock pressures up to 11.5 Mbar were produced in quartz. Accurate measurements of the shock velocity indicate that a fraction of the flyer is at solid density when it arrives at the target. Comparison of measurements and simulation results yields a consistent picture of the flyer state at impact with the quartz target.

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The intense magnetic field produced by the 20 MA Z accelerator is used as an impulsive pressure source to accelerate metal flyer plates to high velocity for the purpose of performing plate impact, shock wave experiments. This capability has been significantly enhanced by the recently developed pulse shaping capability of Z, which enables tailoring the rise time to peak current for a specific material and drive pressure to avoid shock formation within the flyer plate during acceleration. Consequently, full advantage can be taken of the available current to achieve the maximum possible magnetic drive pressure. In this way, peak magnetic drive pressures up to 490 GPa have been produced, which shocklessly accelerated 850 {micro}m aluminum (6061-T6) flyer plates to peak velocities of 34 km/s. We discuss magnetohydrodynamic (MHD) simulations that are used to optimize the magnetic pressure for a given flyer load and to determine the shape of the current rise time that precludes shock formation within the flyer during acceleration to peak velocity. In addition, we present results pertaining to plate impact, shock wave experiments in which the aluminum flyer plates were magnetically accelerated across a vacuum gap and impacted z-cut, {alpha}-quartz targets. Accurate measurements of resulting quartz shock velocities are presented and analyzed through high-fidelity MHD simulations enhanced using optimization techniques. Results show that a fraction of the flyer remains at solid density at impact, that the fraction of material at solid density decreases with increasing magnetic pressure, and that the observed abrupt decrease in the quartz shock velocity is well correlated with the melt transition in the aluminum flyer.

A dynamic hohlraum is created when an annular z-pinch plasma implodes onto a cylindrical 0.014 g/cc 6-mm-diameter CH{sub 2} foam. The impact launches a radiating shock that propagates toward the axis at {approx}350 {micro}m/ns. The radiation trapped by the tungsten z-pinch plasma forms a {approx}200 eV hohlraum that provides X-rays for indirect drive inertial confinement fusion capsule implosion experiments. We are developing the ability to diagnose the hohlraum interior using emission and absorption spectroscopy of Si atoms added as a tracer to the central portion of the foam. Time- and space-resolved Si spectra are recorded with an elliptical crystal spectrometer viewing the cylindrical hohlraum end-on. A rectangular aperture at the end of the hohlraum restricts the field of view so that the 1D spectrometer resolution corresponds approximately to the hohlraum radial direction. This enables distinguishing between spectra from the unshocked radiation-heated foam and from the shocked foam. Typical spectral lines observed include the Si Ly{alpha} with its He-like satellites and the He-like resonance sequence including He{alpha}, He{beta}, and He{gamma}, along with some of their associated Li-like satellites. Work is in progress to infer the hohlraum conditions using collisional-radiative modeling that accounts for the radiation environment and includes both opacity effects and detailed Stark broadening calculations. These 6-mm-scale radiation-heated plasmas might eventually also prove suitable for testing Stark broadening line profile calculations or for opacity measurements.

A series of numerical simulations have been performed to determine scaling laws for fast ignition break even of a hot spot formed by energetic particles created by a short pulse laser. Hot spot break even is defined to be when the fusion yield is equal to the total energy deposited in the hot spot through both the initial compression and the subsequent heating. In these simulations, only a small portion of a previously compressed mass of deuterium-tritium fuel is heated on a short time scale, i.e., the hot spot is tamped by the cold dense fuel which surrounds it. The hot spot tamping reduces the minimum energy required to obtain break even as compared to the situation where the entire fuel mass is heated, as was assumed in a previous study [S. A. Slutz, R. A. Vesey, I. Shoemaker, T. A. Mehlhorn, and K. Cochrane, Phys. Plasmas 7, 3483 (2004)]. The minimum energy required to obtain hot spot break even is given approximately by the scaling law E{sub T} = 7.5({rho}/100){sup -1.87} kJ for tamped hot spots, as compared to the previously reported scaling of E{sub UT} = 15.3({rho}/100){sup -1.5} kJ for untamped hotspots. The size of the compressed fuel mass and the focusability of the particles generated by the short pulse laser determines which scaling law to use for an experiment designed to achieve hot spot break even.