Publications

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This work presents a new multiscale method for coupling the 3D Maxwell's equations to the 1D telegrapher's equations. While Maxwell's equations are appropriate for modeling complex electromagnetics in arbitrary-geometry domains, simulation cost for many applications (e.g. pulsed power) can be dramatically reduced by representing less complex transmission line regions of the domain with a 1D model. By assuming a transverse electromagnetic (TEM) ansatz for the solution in a transmission line region, we reduce the Maxwell's equations to the telegrapher's equations. We propose a self-consistent finite element formulation of the fully coupled system that uses boundary integrals to couple between the 3D and 1D domains and supports arbitrary unstructured 3D meshes. Additionally, by using a Lagrange multiplier to enforce continuity at the coupling interface, we allow for an absorbing boundary condition to also be applied to non-TEM modes on this boundary. We demonstrate that this feature reduces non-physical reflection and ringing of non-TEM modes off of the coupling boundary. By employing implicit time integration, we ensure a stable coupling, and we introduce an efficient method for solving the resulting linear systems. We demonstrate the accuracy of the new method on two verification problems, a transient O-wave in a rectilinear prism and a steady-state problem in a coaxial geometry, and show the efficiency and weak scalability of our implementation on a cold test of the Z-machine MITL and post-hole convolute.

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Modeling and simulation of the legacy HERMES III Magnetically Insulated Transmission Line (MITL) has been performed using EMPHASIS, an unstructured time-domain electromagnetic (UTDEM) particle-in-cell (PIC) simulation software. This design when used lost roughly half of its current before the pulse reached the load. The cause of the current loss in the MITL was found to be the vacuum impedance changes along the MITL. The MITL was then redesigned to maintain constant impedance and simulated in EMPHASIS once again. Following predicting simulation results, the new MITL was then built, installed, and tested, showing minimal current loss and good agreement with simulation and theoretical results, all of which are reported here. Additionally, an analysis of experimental voltage calculation techniques using cathode and anode currents is performed and compared to simulation results.

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We report on the verification of elastic collisions in EMPIRE-PIC and EMPIRE-Fluid in support of the ATDM L2 V&V Milestone. The thermalization verification problem and the theory behind it is presented along with an analytic solution for the temperature of each species over time. The problem is run with both codes under multiple parameter regimes. The temperature over time is compared between the two codes and the theoretical results. A preliminary convergence analysis is performed on the results from EMPIRE-PIC and EMPIRE-Fluid showing the rate at which the codes converge to the analytic solution in time (EMPIRE-Fluid) and particles (EMPIRE-PIC).

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The Unstructured Time-Domain ElectroMagnetics (UTDEM) portion of the EMPHASIS suite solves Maxwell's equations using finite-element techniques on unstructured meshes. This document provides user-specific information to facilitate the use of the code for applications of interest.

EMPHASIS™/NEVADA is the SIERRA/NEVADA toolkit implementation of portions of the EMPHASIS TM code suite. The purpose of the toolkit implementation is to facilitate coupling to other physics drivers such as radiation transport as well as to better manage code design, implementation, complexity, and important verification and validation processes. This document describes the theory and implementation of the unstructured finite- element method solver, associated algorithms, and selected verification and validation.

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