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.
During the trials during November 2016 at the HERMES III facility, a number of sensors were fielded to measure the free fields and currents coupled to aerial and buried cables. Here, we report on the work done to compensate, correct, and analyze these signals. Average results are presented for selected sets of sensors and prelimi- nary analyses are provided of the time and frequency domain signals. Electric fields were typically on the order of 10 kV/m, magnetic fields were approximately 10 AT, and currents were around 10 A. Several opportunities for improvement are identified including quantification of radiation effects on sensors, higher accuracy compensation techniques, increased sensitivity in differential sensor measurements, and exploration of the use of I-dots in conductivity calculations.
A suite of coupled computational models for simulating the radiation, plasma, and electromagnetic (EM) environment in the High-Energy Radiation Megavolt Electron Source (HERMES) courtyard has been developed. In principle, this provides a predictive forward-simulation capability based solely on measured upstream anode and cathode current waveforms in the Magnetically Insulated Transmission Line (MITL). First, 2D R-Z ElectroMagnetic Particle-in-Cell (EM-PIC) simulations model the MITL and diode to compute a history of all electrons incident on the converter. Next, radiation transport simulations use these electrons as a source to compute the time-dependent dose rate and volumetric electron production in the courtyard. Finally, the radiation transport output is used as sources for EM-PIC simulations of the courtyard to com- pute electromagnetic responses. This suite has been applied to the November 2016 trials, shots 10268-10313. Modeling and experiment differ in significant ways. This is just the first iteration of a long process to improve the agreement, as outlined in the summary.
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.
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 ap plications of interest. Acknowledgement The authors would like to thank all of those individuals who have helped to bring EMPHASIS/Nevada to the point it is today, including Bill Bohnhoff, Rich Drake, and all of the NEVADA code team.
EMPHASIS TM /NEVADA is the SIERRA/NEVADA toolkit implementation of portions of the EMP HASIS TM code suite. The purpose of the toolkit i m- plementation is to facilitate coupling to other physics drivers such as radi a- tion transport as well as to better manage code design, implementation, co m- plexity, 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 valid a- tion . Acknowledgement The author would like to recognize all of the ALEGRA team members for their gracious and willing support through this initial Nevada toolkit - implementation process. Although much of the knowledge needed was gleaned from document a- tion and code context, they were always willing to consult personally on some of the less obvious issues and enhancements necessary.
A new method for including electrode plasma effects in particle-in-cell simulation of high power devices is presented. It is not possible to resolve the plasma Debye length, {lambda}{sub D} {approx} 1 {mu}m, but using an explicit, second-order, energy-conserving particle pusher avoids numerical heating at large {delta}x/{lambda}{sub D} >> 1. Non-physical plasma oscillations are mitigated with Coulomb collisions and a damped particle pusher. A series of 1-D simulations show how plasma expansion varies with cell size. This reveals another important scale length, {lambda}{sub E} = T/(eE), where E is the normal electric field in the first vacuum cell in front of the plasma, and T is the plasma temperature. For {delta}x/{lambda}{sub E} < {approx}1, smooth, physical plasma expansion is observed. However, if {delta}x/{lambda}{sub E} >> 1, the plasma 'expands' in abrupt steps, driven by a numerical instability. For parameters of interest, {lambda}{sub E} << 100 {mu}m. It is not feasible to use cell sizes small enough to avoid this instability in large 3-D simulations.
This report summarizes the work completed during FY2007 and FY2008 for the LDRD project ''Hybrid Plasma Modeling''. The goal of this project was to develop hybrid methods to model plasmas across the non-continuum-to-continuum collisionality spectrum. The primary methodology to span these regimes was to couple a kinetic method (e.g., Particle-In-Cell) in the non-continuum regions to a continuum PDE-based method (e.g., finite differences) in continuum regions. The interface between the two would be adjusted dynamically ased on statistical sampling of the kinetic results. Although originally a three-year project, it became clear during the second year (FY2008) that there were not sufficient resources to complete the project and it was terminated mid-year.
An analytic model for electron flow in a system driving a fixed inductive load is described and evaluated with particle in cell simulations. The simple model allows determining the impedance profile for a magnetically insulated transmission line given the minimum gap desired, and the lumped inductance inside the transition to the minimum gap. The model allows specifying the relative electron flow along the power flow direction, including cases where the fractional electron flow decreases in the power flow direction. The electrons are able to return to the cathode because they gain energy from the temporally rising magnetic field. The simulations were done with small cell size to reduce numerical heating. An experiment to compare electron flow to the simulations was done. The measured electron flow is {approx}33% of the value from the simulations. The discrepancy is assumed to be due to a reversed electric field at the cathode because of the inductive load and falling electron drift velocity in the power flow direction. The simulations constrain the cathode electric field to zero, which gives the highest possible electron flow.
An important issue in designing a higher-power version of the Z machine at Sandia National Laboratories is electron current loss in the vacuum section, which consists of four radial transmission lines and a convolute (current-adder). There is evidence from experiments on Z that 1-2MA of current out of about 20MA is lost in the vacuum section before reaching the wire-array load [1]. Calculations using the LSP [2] and QUICKSILVER [3] particle-in-cell codes have shown much less current loss [4,5,6]. The current loss in the calculations is due to sheath-current loss in the region of the convolute, and is associated with the magnetic nulls which are intrinsic to the current splitting in the convolute Detailed 2-D calculations for the radial MITLs show that, in the region between the insulator stack and a radius of about 20cm (over which the radial-line vacuum impedance increases slowly from 2Ω to 3Ω), excess electron sheath current is mostly retrapped to the cathode electrode. The electron sheath current is given approximately by Mendel's force-balance expression [7] applied locally, and as a result, the sheath current decreases as Zv-2, where Zv is the vacuum impedance. Between a radius of 20cm and the convolute, where the radial-line vacuum impedance increases more sharply (to 6Ω at 10cm) there is significant "launching" of sheath current. The sheath behavior in this region is qualitatively similar to that predicted using a "constant flow impedance" model, but in the simulations the sheath is unstable and breaks up into vortices.