Significant variety is observed in spherical crystal x-ray imager (SCXI) data for the stagnated fuel–liner system created in Magnetized Liner Inertial Fusion (MagLIF) experiments conducted at the Sandia National Laboratories Z-facility. As a result, image analysis tasks involving, e.g., region-of-interest selection (i.e. segmentation), background subtraction and image registration have generally required tedious manual treatment leading to increased risk of irreproducibility, lack of uncertainty quantification and smaller-scale studies using only a fraction of available data. We present a convolutional neural network (CNN)-based pipeline to automate much of the image processing workflow. This tool enabled batch preprocessing of an ensemble of Nscans = 139 SCXI images across Nexp = 67 different experiments for subsequent study. The pipeline begins by segmenting images into the stagnated fuel and background using a CNN trained on synthetic images generated from a geometric model of a physical three-dimensional plasma. The resulting segmentation allows for a rules-based registration. Our approach flexibly handles rarely occurring artifacts through minimal user input and avoids the need for extensive hand labelling and augmentation of our experimental dataset that would be needed to train an end-to-end pipeline. Here we also fit background pixels using low-degree polynomials, and perform a statistical assessment of the background and noise properties over the entire image database. Our results provide a guide for choices made in statistical inference models using stagnation image data and can be applied in the generation of synthetic datasets with realistic choices of noise statistics and background models used for machine learning tasks in MagLIF data analysis. We anticipate that the method may be readily extended to automate other MagLIF stagnation imaging applications.
An approach to numerically modeling relativistic magnetrons, in which the electrons are represented with a relativistic fluid, is described. A principal effect in the operation of a magnetron is space-charge-limited (SCL) emission of electrons from the cathode. We have developed an approximate SCL emission boundary condition for the fluid electron model. This boundary condition prescribes the flux of electrons as a function of the normal component of the electric field on the boundary. We show the results of a benchmarking activity that applies the fluid SCL boundary condition to the one-dimensional Child–Langmuir diode problem and a canonical two-dimensional diode problem. Simulation results for a two-dimensional A6 magnetron are then presented. Computed bunching of the electron cloud occurs and coincides with significant microwave power generation. Numerical convergence of the solution is considered. Sharp gradients in the solution quantities at the diocotron resonance, spanning an interval of three to four grid cells in the most well-resolved case, are present and likely affect convergence.
A semi-analytic fluid model has been developed for characterizing relativistic electron emission across a warm diode gap. Here we demonstrate the use of this model in (i) verifying multi-fluid codes in modeling compressible relativistic electron flows (the EMPIRE-Fluid code is used as an example; see also Ref. 1), (ii) elucidating key physics mechanisms characterizing the influence of compressibility and relativistic injection speed of the electron flow, and (iii) characterizing the regimes over which a fluid model recovers physically reasonable solutions.
The magneto-Rayleigh-Taylor instability (MRTI) plays an essential role in astrophysical systems and in magneto-inertial fusion, where it is known to be an important degradation mechanism of confinement and target performance. In this Letter, we show for the first time experimental evidence of mode mixing and the onset of an inverse-cascade process resulting from the nonlinear coupling of two discrete preseeded axial modes (400- and 550-μm wavelengths) on an Al liner that is magnetically imploded using the 20-MA, 100-ns rise-time Z Machine at Sandia National Laboratories. Four radiographs captured the temporal evolution of the MRTI. We introduce a novel unfold technique to analyze the experimental radiographs and compare the results to simulations and to a weakly nonlinear model. We find good quantitative agreement with simulations using the radiation magnetohydrodynamics code hydra. Spectral analysis of the MRTI time evolution obtained from the simulations shows evidence of harmonic generation, mode coupling, and the onset of an inverse-cascade process. The experiments provide a benchmark for future work on the MRTI and motivate the development of new analytical theories to better understand this instability.
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.
Relativistic weakly collisional plasmas describe a variety of astrophysical and terrestrial plasmas, ranging from relativistic outflows from active galactic nuclei to high power microwave and magnetically insulated transmission lines. In many such systems, high fidelity kinetic models are computationally infeasible due large dynamical scales and long dynamical times. Conversely, most fluid based models such as magnetohydrodynamics (MHD) miss many relevant aspects of plasma behavior. Between these two models, two fluid methods - where the electrons and ions are evolved as separate, coupled fluids - capture many of the plasma physics of a kinetic code while remaining computational tractable for large systems.
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.
While magnetized turbulence is ubiquitous in many astrophysical and terrestrial systems, our understanding of even the simplest physical description of this phenomena, ideal magnetohydrodynamic (MHD) turbulence, remains substantially incomplete. In this work, we highlight the shortcomings of existing theoretical and phenomenological descriptions of MHD turbulence that focus on the joint (kinetic and magnetic) energy fluxes and spectra by demonstrating that treating these quantities separately enables fundamental insights into the dynamics of MHD turbulence. This is accomplished through the analysis of the scale-wise energy transfer over time within an implicit large eddy simulation of subsonic, super-Alfvénic MHD turbulence. Our key finding is that the kinetic energy spectrum develops a scaling of approximately k -4/3 in the stationary regime as magnetic tension mediates large-scale kinetic to magnetic energy conversion and significantly suppresses the kinetic energy cascade. This motivates a reevaluation of existing MHD turbulence theories with respect to a more differentiated modeling of the energy fluxes.
Macroscopic simulations of dense plasmas rely on detailed microscopic information that can be computationally expensive and is difficult to verify experimentally. In this work, we delineate the accuracy boundary between microscale simulation methods by comparing Kohn-Sham density functional theory molecular dynamics (KS-MD) and radial pair potential molecular dynamics (RPP-MD) for a range of elements, temperature, and density. By extracting the optimal RPP from KS-MD data using force matching, we constrain its functional form and dismiss classes of potentials that assume a constant power law for small interparticle distances. Our results show excellent agreement between RPP-MD and KS-MD for multiple metrics of accuracy at temperatures of only a few electron volts. The use of RPPs offers orders of magnitude decrease in computational cost and indicates that three-body potentials are not required beyond temperatures of a few eV. Due to its efficiency, the validated RPP-MD provides an avenue for reducing errors due to finite-size effects that can be on the order of ∼ 20 %.
This report describes the high-level accomplishments from the Plasma Science and Engineering Grand Challenge LDRD at Sandia National Laboratories. The Laboratory has a need to demonstrate predictive capabilities to model plasma phenomena in order to rapidly accelerate engineering development in several mission areas. The purpose of this Grand Challenge LDRD was to advance the fundamental models, methods, and algorithms along with supporting electrode science foundation to enable a revolutionary shift towards predictive plasma engineering design principles. This project integrated the SNL knowledge base in computer science, plasma physics, materials science, applied mathematics, and relevant application engineering to establish new cross-laboratory collaborations on these topics. As an initial exemplar, this project focused efforts on improving multi-scale modeling capabilities that are utilized to predict the electrical power delivery on large-scale pulsed power accelerators. Specifically, this LDRD was structured into three primary research thrusts that, when integrated, enable complex simulations of these devices: (1) the exploration of multi-scale models describing the desorption of contaminants from pulsed power electrodes, (2) the development of improved algorithms and code technologies to treat the multi-physics phenomena required to predict device performance, and (3) the creation of a rigorous verification and validation infrastructure to evaluate the codes and models across a range of challenge problems. These components were integrated into initial demonstrations of the largest simulations of multi-level vacuum power flow completed to-date, executed on the leading HPC computing machines available in the NNSA complex today. These preliminary studies indicate relevant pulsed power engineering design simulations can now be completed in (of order) several days, a significant improvement over pre-LDRD levels of performance.
This article considers two algorithms of a finite-volume solver for the MHD equations with a real-gas equation of state (EOS). Both algorithms use a multistate form of the Harten-Lax-Van Leer approximate Riemann solver as formulated for MHD discontinuities. This solver is modified to use the generalized sound speed from the real-gas EOS. Two methods are tested: EOS evaluation at cell centers and flux interfaces where the former is more computationally efficient. A battery of 1-D and 2-D tests is employed: convergence of 1-D and 2-D linearized waves, shock tube Riemann problems, a 2-D nonlinear circularly polarized Alfvén wave, and a 2-D magneto-Rayleigh-Taylor instability test. The cell-centered-EOS-evaluation algorithm produces unresolvable thermodynamic inconsistencies in the intermediate states leading to spurious solutions while the flux-interface EOS evaluation algorithm robustly produces the correct solution. The linearized wave tests show that this inconsistency is associated with the magnetosonic waves and the magneto-Rayleigh-Taylor instability test demonstrates simulation results, where the spurious solution leads to an unphysical simulation.
Mixing of cold, higher-Z elements into the fuel region of an inertial confinement fusion target spoils the fusion burn efficiency. This mixing process is driven by both "turbulent" and "atomic" mixing processes, the latter being modeled through transport corrections to the basic hydrodynamic models. Recently, there has been a surge in the development of dense plasma transport modeling and the associated transport coefficients; however, experimental validation remains in its infancy. To address this gap in our knowledge of interfacial mixing, Sandia National Laboratories is developing a new experimental platform at the Z-facility to investigate plasma transport in dense plasmas that span the entire warm dense matter regime. Specifically, this platform is being developed to measure species transport across a V/CH interface, using an x-ray driven hohlraum to drive the sample to [?] 190eV over 5ns. The heated sample is diagnosed using radiography optimized to measure the distribution of Vanadium perpendicular the interface. In order to interpret measurements made using this experimental platform, modeling tools that incorporate transport effects in strongly coupled plasmas are required. To this end, we utilize new advances in multi-species kinetic theory, collision models applicable to strongly coupled plasmas and modeling of degenerate electron plasmas to develop such a capability. The resulting kinetic transport code has been applied, along with state-of-the-art radiation hydrodynamic codes, to model the experiments. Results from this modeling effort highlight the importance of strong electric fields, which are present in the kinetic transport code, but absent in the radiation hydrodynamics code, in driving interfacial mixing. Synthetic radiography generated from all of these models reveals the ability of experimental diagnostics to distinguish interfacial mixing driven by a range of transport effects. We demonstrate that the spatial and temporal resolution of radiography diagnostics currently available at the Z-facility can distinguish between these different transport effects when multiple (3 [?] 4) radiographs, separated in time ( [?] 2 ns ) with accurate timing are captured per experiment.
Many terrestrial and astrophysical plasmas encompass very large dynamical ranges in space and time, which are not accessible by direct numerical simulations. Thus, idealized subvolumes are often used to study small-scale effects including the dynamics of magnetized turbulence. A significant aspect of magnetized turbulence is the transfer of energy from large to small scales, in part through the operation of a turbulent cascade. In this paper, we present a new shell-to-shell energy transfer analysis framework for understanding energy transfer within magnetized turbulence and in particular, through the cascade. We demonstrate the viability of this framework through application to a series of isothermal subsonic and supersonic simulations of compressible magnetized turbulence and utilize results from this analysis to establish a nonlinear benchmark for compressible magnetized turbulence in the subsonic regime. We further study how the autocorrelation time of the driving and its normalization systematically change properties of compressible magnetized turbulence. For example, we find that δ -in-time forcing with a constant energy injection leads to a steeper slope in kinetic energy spectrum and less efficient small-scale dynamo action. We examine how these results can impact a range of diagnostics relevant for a range of terrestrial and astrophysical applications.
Miller, Nicholas C.; Grupen, Matt; Beckwith, Kristian B.; Smithe, David; Albrecht, John D.
A detailed description and analysis of the Fermi kinetics transport (FKT) equations for simulating charge transport in semiconductor devices is presented. The fully coupled nonlinear discrete FKT equations are elaborated, as well as solution methods and work-flow for the simulation of RF electronic devices under large-signal conditions. The importance of full-wave electromagnetics is discussed in the context of high-speed device simulation, and the meshing requirements to integrate the full-wave solver with the transport equations are given in detail. The method includes full semiconductor band structure effects to capture the scattering details for the Boltzmann transport equation. The method is applied to high-speed gallium nitride devices. Finally, numerical convergence and stability examples provide insight into the mesh convergence behavior of the deterministic solver.
This is the progress report for the grant "Beyond the Fluid Approximation: Improved Modeling of the Intracluster Plasma." We have made progress along several fronts, including code development and science. One paper has been published, and a second has been submitted and is about to be accepted. These are described below.