We present a comprehensive study of transport coefficients including DC electrical conductivity and related optical properties, electrical contribution to the thermal conductivity, and the shear viscosity via ab initio molecular dynamics and density functional theory calculations on the “priority 1” cases from the “Second Charged-Particle Transport Coefficient Workshop” [Stanek et al., Phys. Plasmas (to be published 2024)]. The purpose of this work is to carefully document the entire workflow used to generate our reported transport coefficients, up to and including our definitions of finite size and statistical convergence, extrapolation techniques, and choice of thermodynamic ensembles. In pursuit of accurate optical properties, we also present a novel, simple, and highly accurate algorithm for evaluating the Kramers–Kronig relations. These heuristics are often not discussed in the literature, and it is hoped that this work will facilitate the reproducibility of our data.

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.

Pulsed power accelerators compress electrical energy in space and time to provide versatile experimental platforms for high energy density and inertial confinement fusion science. The 80-TW "Z" pulsed power facility at Sandia National Laboratories is the largest pulsed power device in the world today. Z discharges up to 22MJ of energy stored in its capacitor banks into a current pulse that rises in 100ns and peaks at a current as high as 30 MA in low-inductance cylindrical targets. Considerable progress has been made over the past 15years in the use of pulsed power as a precision scientific tool. This paper reviews developments at Sandia in inertial confinement fusion, dynamic materials science, x-ray radiation science, and pulsed power engineering, with an emphasis on progress since a previous review of research on Z in Physics of Plasmas in 2005.

Submitted for the DPP19 Meeting of The American Physical Society Hybrid fluid-kinetic models for high-energy-density plasmas1 SEAN MILLER, ERIC CYR, THOMAS GARDINER, MATTHEW BETTENCOURT, NATHANIEL HAMLIN, KRISTIAN BECKWITH, SIDNEY SHIELDS, Sandia National Lab — Plasma physics in the high-energy-density regime can be dominated by collisional interactions between particles. Particle-in-cell (PIC) based kinetic representations have classically been used to represent these systems in rarefied regimes, however as the density of the plasma increases or a neutral gas is introduced the computational costs of particle methods increase. The goal of this research is to develop hybrid representations where the addition of continuum fluid components to the particle solve reduces runtimes in dense plasma simulations while retaining physical accuracy in rarefied regimes. Two approaches will be presented: (1) a species-based coupling where each species is represented by a different discretization (e.g. PIC ions with fluid electrons/neutrals), and (2) a PIC discretization is used to close the fluid model commonly known as a delta-f method. The current state of our implementation will be presented and the benefits and challenges of these approaches will be discussed. 1Sandia National Labs is managed and operated by National Technology Engineering Solutions of Sandia, LLC, a subsidiary of Honeywell International, Inc., for the U.S Dept. of Energys National Nuclear Security Administration under contract DE-NA0003525. Sean Miller Sandia National Lab Date submitted: 02 Jul 2019 Electronic form version 1.4

This LDRD project was developed around the ambitious goal of applying PDE-constrained opti- mization approaches to design Z-machine components whose performance is governed by elec- tromagnetic and plasma models. This report documents the results of this LDRD project. Our differentiating approach was to use topology optimization methods developed for structural design and extend them for application to electromagnetic systems pertinent to the Z-machine. To achieve this objective a suite of optimization algorithms were implemented in the ROL library part of the Trilinos framework. These methods were applied to standalone demonstration problems and the Drekar multi-physics research application. Out of this exploration a new augmented Lagrangian approach to structural design problems was developed. We demonstrate that this approach has favorable mesh-independent performance. Both the final design and the algorithmic performance were independent of the size of the mesh. In addition, topology optimization formulations for the design of conducting networks were developed and demonstrated. Of note, this formulation was used to develop a design for the inner magnetically insulated transmission line on the Z-machine. The resulting electromagnetic device is compared with theoretically postulated designs.

A self-similar solution is derived for a radially imploding cylindrical plasma with an embedded, azimuthal magnetic field. The plasma stagnates through a strong, outward propagating shock wave of constant velocity. This analysis is an extension of the classic Noh gasdynamics problem to its ideal magnetohydrodynamics (MHD) counterpart. The present exact solution is especially suitable as a test for MHD codes designed to simulate linear Z pinches. To demonstrate the application of the new solution to code verification, simulation results from the cylindrical R-Z version of Mach2 and the 3D Cartesian code Athena are compared against the analytic solution. Alternative routines from the default ones in Athena lead to significant improvement of the results, thereby demonstrating the utility of the self-similar solution for verification.

A deflagration-to-detonation transition (DDT) can occur in environments ranging from experimental and industrial systems to astrophysical thermonuclear (type Ia) supernovae explosions. Substantial progress has been made in explaining the nature of DDT in confined systems with walls, internal obstacles, or preexisting shocks. It remains unclear, however, whether DDT can occur in unconfined media. Here we use direct numerical simulations (DNS) to show that for high enough turbulent intensities unconfined, subsonic, premixed, turbulent flames are inherently unstable to DDT. The associated mechanism, based on the nonsteady evolution of flames faster than the Chapman-Jouguet deflagrations, is qualitatively different from the traditionally suggested spontaneous reaction-wave model. Critical turbulent flame speeds, predicted by this mechanism for the onset of DDT, are in agreement with DNS results.

Deflagration-to-detonation transition (DDT) can occur in a wide variety of environments ranging from experimental and industrial systems on Earth to astrophysica l thermonuclear (type Ia) supernovae explosions. In recent years, substantial progress has been made both exp erimentally and theoretically in elucidating the nature of this phenomenon in confined systems with walls, obs tacles, etc. (see [1] for a detailed review). Shocks in such systems can be formed both by the overall fluid e xpansion caused by the energy release in the flame, as well as by the repeated interactions of the flame-gen rated acoustic waves with solid obstacles and with the flame itself. Once a shock of sufficient strength is fo rmed in the system, DDT can occur through a variety of different mechanisms, such as shock collision w ith an obstacle [2] or shock-flame interactions and the formation of the induction-time gradients [1]. At th e same time, it remains unclear whether a subsonic turbulent flame initially present in an unconfined, unp ressurized system without pre-existing shocks can undergo DDT and, if such transition is possible, what its mechanism would be.

In recent years there has been a resurgence of interest in exploring the properties of resistive magnetic reconnection layers. This was spurred on by the observations that at high Lundquist number these systems depart from the traditional Sweet-Parker scaling, opening the possibility of so-called fast resistive magnetic reconnection. This proceedings presents my recent efforts at simulating resistive magnetic reconnection layers in high Lundquist number systems highlighting the numerical algorithms, simulation results and convergence behavior.

We describe the implementation of the shearing box approximation for the study of the dynamics of accretion disks in the Athena magnetohydrodynamic (MHD) code. Second-order Crank-Nicholson time differencing is used for the Coriolis and tidal gravity source terms that appear in the momentum equation for accuracy and stability. We show that this approach conserves energy for epicyclic oscillations in hydrodynamic flows to round-off error. In the energy equation, the tidal gravity source terms are differenced as the gradient of an effective potential in a way that guarantees that total energy (including the gravitational potential energy) is also conserved to round-off error. We introduce an orbital advection algorithm for MHD based on constrained transport to preserve the divergence-free constraint on the magnetic field. This algorithm removes the orbital velocity from the time step constraint, and makes the truncation error more uniform in radial position. Modifications to the shearing box boundary conditions applied at the radial boundaries are necessary to conserve the total vertical magnetic flux. In principle, similar corrections are also required to conserve mass, momentum, and energy; however in practice we find that the orbital advection method conserves these quantities to better than 0.03% over hundreds of orbits. The algorithms have been applied to studies of the nonlinear regime of theMRI in very wide (up to 32 scale heights) horizontal domains.