Publications

This is the user manual for EMPIRE, a simulation code for electromagnetics and plasma physics.

This report documents the progress made in simulating the HERMES-III Magnetically Insulated Transmission Line (MITL) and courtyard with EMPIRE and ITS. This study focuses on the shots that were taken during the months of June and July of 2019 performed with the new MITL extension. There were a few shots where there was dose mapping of the courtyard, 11132, 11133, 11134, 11135, 11136, and 11146. This report focuses on these shots because there was full data return from the MITL electrical diagnostics and the radiation dose sensors in the courtyard. The comparison starts with improving the processing of the incoming voltage into the EMPIRE simulation from the experiment. The currents are then compared at several location along the MITL. The simulation results of the electrons impacting the anode are shown. The electron impact energy and angle is then handed off to ITS which calculates the dose on the faceplate and locations in the courtyard and they are compared to experimental measurements. ITS also calculates the photons and electrons that are injected into the courtyard, these quantities are then used by EMPIRE to calculated the photon and electron transport in the courtyard. The details for the algorithms used to perform the courtyard simulations are presented as well as qualitative comparisons of the electric field, magnetic field, and the conductivity in the courtyard. Because of the computational burden of these calculations the pressure was reduce in the courtyard to reduce the computational load. The computation performance is presented along with suggestion on how to improve both the computational performance as well as the algorithmic performance. Some of the algorithmic changed would reduce the accuracy of the models and detail comparison of these changes are left for a future study. As well as, list of code improvements there is also a list of suggested experimental improvements to improve the quality of the data return.

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.

Crossed-field diodes (CFDs) are used in multiple high-power applications and are characterized by an applied magnetic field orthogonal to the electric field, induced by the applied voltage across the anode-cathode gap. In vacuum, the Hull cutoff magnetic field (HCMF) represents the maximum applied magnetic field for which an electron from the cathode can reach the anode. This study investigates the effects of non-vacuum conditions on electron trajectories by introducing electron mobility, which represents particle collisions. We used numerical solutions of the electron force law and particle-in-cell simulations (XPDP1) to assess electron motion for various electron mobilities. For magnetic fields above the HCMF in vacuum, reducing the electron mobility increases the time for an electron emitted from the cathode to reach the anode. Reducing mobility below 22 C s/kg eliminates the HCMF for any magnetic field, meaning that an emitted electron will always cross the gap. We derived the magnetic field, mobility, and electron transit time corresponding to this condition by solving for the condition when the electron velocity in the direction across the anode-cathode gap going to zero at the anode. A parametric study of these conditions using theory and XPDP1 is performed under different gap distances, voltages, and magnetic fields.

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Simulations of several of the end-irradiated cylindrical photoelectron driven cavity experiments (also known as B-Dot cavities) that were fielded during the July 1 through 2, 2020 shot series at the National Ignition Facility are presented in this report with comparisons to experimental measurements. All cavity B-Dots fielded on the second, third, fourth, fifth and seventh shots were simulated using coupled Integrated Tiger Series (ITS) Monte Carlo transport codes and the Electromagnetic Plasmas in Realistic Environments (EMPIRE) electromagnetic particle-in-cell code.

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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.

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This report documents the outcome from the ASC ATDM Level 2 Milestone 6358: Assess Status of Next Generation Components and Physics Models in EMPIRE. This Milestone is an assessment of the EMPIRE (ElectroMagnetic Plasma In Realistic Environments) application and three software components. The assessment focuses on the electromagnetic and electrostatic particle-in-cell solu- tions for EMPIRE and its associated solver, time integration, and checkpoint-restart components. This information provides a clear understanding of the current status of the EMPIRE application and will help to guide future work in FY19 in order to ready the application for the ASC ATDM L 1 Milestone in FY20. It is clear from this assessment that performance of the linear solver will have to be a focus in FY19.

This report compares ATLOG modeling results for the response of a finite-length dissipative buried conductor interacting with a conducting ground to a measurement taken November 2016 at the High-Energy Radiation Megavolt Electron Source (HERMES) facility. We use the ATLOG frequency-domain method based on transmission line theory. Estimates of the impedance per unit length and admittance per unit length for a cable laying in a PVC pipe embedded in a concrete block are reported. Current wave shapes from both a single conductor and composite differential mode and antenna mode arrangements are close to those observed in the experiments. Intentionally Left Blank

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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.

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This LDRD investigated plasma formation, field strength, and current loss in pulsed power diodes. In particular the Self-Magnetic Pinch (SMP) e-beam diode was studied on the RITS-6 accelerator. Magnetic fields of a few Tesla and electric fields of several MV/cm were measured using visible spectroscopy techniques. The magnetic field measurements were then used to determine the current distribution in the diode. This distribution showed that significant beam current extends radially beyond the few millimeter x-ray focal spot diameter. Additionally, shielding of the magnetic field due to dense electrode surface plasmas was observed, quantified, and found to be consistent with the calculated Spitzer resistivity. In addition to the work on RITS, measurements were also made on the Z-machine looking to quantify plasmas within the power flow regions. Measurements were taken in the post-hole convolute and final feed gap regions on Z. Dopants were applied to power flow surfaces and measured spectroscopically. These measurements gave species and density/temperature estimates. Preliminary B-field measurements in the load region were attempted as well. Finally, simulation work using the EMPHASIS, electromagnetic particle in cell code, was conducted using the Z MITL conditions. The purpose of these simulations was to investigate several surface plasma generations models under Z conditions for comparison with experimental data.

We report a frequency-domain method based on transmission line theory that we name ATLOG-Analytic Transmission Line Over Ground-to model finite or infinite wires interacting with a conducting ground excited by an electromagnetic pulse. This method allows for the treatment of finite or infinite lossy, coated wires above a lossy ground, as well as resting on or buried beneath the ground. Comparisons with full-wave simulations strengthen the validity of the proposed method.

This report details the comparison of ATLOG modeling results for the response of a finite-length dissipative aerial conductor interacting with a conducting ground to a measurement taken November 2016 at the High-Energy Radiation Megavolt Electron Source (HERMES) facility. We use the ATLOG time-domain method based on transmission line theory. Good agreement is observed between simulations and experiments. Intentionally Left Blank

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This paper details a model for the response of a finite- or an infinite-length wire interacting with a conducting ground to an electromagnetic pulse excitation. We develop a frequency–domain method based on transmission line theory that we name ATLOG–Analytic Transmission Line Over Ground. This method is developed as an alternative to full-wave methods, as it delivers a fast and reliable solution. It allows for the treatment of finite or infinite lossy, coated wires, and lossy grounds. The cases of wire above ground, as well as resting on the ground and buried beneath the ground are treated. The reported method is general and the time response of the induced current is obtained using an inverse Fourier transform of the current in the frequency domain. The focus is on the characteristics and propagation of the transmission line mode. Comparisons with full-wave simulations strengthen the validity of the proposed method.

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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 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.

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