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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Towards memristor supremacy with novel machine learning algorithms

The von Neumann architecture for current computers is slowly showing signs of limitations, due to the finite bus rate between the RAM (memory) and the CPU (computing unit). In-Memory computing is an alternative to this architecture, which however is still in the early stages of development. Memristors are an analog and classical alternative, as these components can act both as a memory, or as a simple computing unit. When wired together, these can in fact be used for a variety of applications. During the course of our research, we have developed an in-depth experimental understanding of both the limitations and the real possibilities of these devices, and developed automated algorithms for their characterization; at the theoretical level, we have incorporated the experimental features to implement novel analog computing units for specific tasks. We have shown that memristors can tackle QUBO and cubic optimization problems, and exhibit tunneling phenomena.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Photo-cleaned Backgroundless Ion Chambers (Final Report for PDRD SR18010)

Ion chambers are often employed to measure the concentration of tritium within flowing gases. In real world environments the active surfaces of ion chambers become covered with tritiated surface contaminants. This tritiated surface contamination will create a large background response that can mask the signature of interest, which is the tritium concentration in the gas phase. Previous efforts to reduce the effects of surface contamination in ion chambers utilize inert coatings (e.g., gold) and low surface area electrodes (e.g., wire mesh), but this route only reduces the effect and does not necessarily alter the ratio of surface contamination to current collection area. Additionally, gold coating may add a substantial cost to the instrument. In the Tritium Facility, ion chambers are periodically cleaned using an alcohol-based process. This process is time consuming and often leads to ion chamber wear and breakage. In addition, periodic cleaning does not address tritium level ambiguities in gloveboxes. An ideal solution to this issue would be to either develop an ion chamber that does not accrue surface contamination, or one that is self-cleaning while it is in operation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Los Alamos National Laboratory Floodplain Assessment for the High Explosive Transfer Facility Blast Radius Fence Project at Technical Area 08

The National Nuclear Security Administration (NNSA), a semi-autonomous agency within the U.S. Department of Energy (DOE), is proposing to take action at Los Alamos National Laboratory (LANL) within the upper Pajarito Canyon 100-year (yr.) floodplain at Technical Area (TA) 08. This action consists of installation of a 3-strand smooth wire fence to create an operational boundary in a radius of 1250 feet (ft.) from the TA-08 High Explosive (HE) Transfer Facility (Figure 1). The proposed fence is intended to provide a barrier between the public and direct access to the HE Transfer Facility.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

AOI [1]: Passive Wireless Sensor Systems Fabricated by Direct-Writing for Temperature and Health Monitoring of Energy Systems in Harsh-Environments (Final Report)

Researchers at West Virginia University (WVU) propose to demonstrate a wireless, high-temperature sensor system for monitoring the temperature and health of energy-system components. The active sensor and electronics for wireless communication will be composed entirely of an electroceramic materials (conductive ceramics) which are capable of withstanding the harsh-environments required for fossil energy-based technologies. This work will focus primarily on the fabrication and testing of temperature (thermocouples and thermistors) and health (strain/stress and crack propagation sensors) that function at extreme temperatures (up to 700-1700ºC). The electronics will accompany the high-temperature sensor, which will include a passive wireless communication circuit that allows the transmission of the data based on the LCR resonance principle to a near-by reader antenna. This passive transmission of data will reduce the need for interconnect wires near the active, and possibly rotating, energy-system component. The research will include process development to permit the 2D/3D direct-writing of the entire sensor and communication circuit onto the energy-system component. The direct-writing will be facilitated by using silicon-based polymer-derived precursors to form the high-temperature, stable electroceramic compositions. In addition, methods for direct-writing the circuit onto a fugitive carrier substrate will be completed, which will permit a “peel-and-stick”-like transfer of the sensor circuit to the energy-system component. This feature will allow the economical and precise placement of the sensor circuit onto components of various shapes and locations, without altering the geometry and active features of the manufactured component, or the removal (or decommissioning) of the component for installation. The proposed work will be directed at the following areas: 1) Investigation of phase formation, sintering/grain growth, and electrical properties of polymer-derived electroceramic composites; 2) Definition of processes to direct-write through ink-jet and robo-casting the polymer-derived electroceramic composites onto oxide and polymer surfaces; 3) Development of methods to form monolithic "peel-and-stick" preforms that will efficiently transfer the sensor circuit to ceramic surfaces after thermal treatment; 4) Design of passive wireless LCR circuits and receiver (reader) antennas for communication and testing at high temperatures; 5) Investigation of the passive wireless sensor system developed (and method of transferring sensor system) for temperature and stress/strain measurements on a SOFC repeat unit and a singular gas turbine blade prototype as example applications.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2021

Chemical Recycling of Mixed Plastics and Valuable Metals in the Electronic Waste Using Solvent-Based Processing

Annually, 20-55 million tons of electronic waste (e-waste) is produced worldwide (5% of all municipal solid waste). Although e-waste embodies only 2% of America’s municipal waste, it accounts for a significantly larger proportion of the heavy metals and flame retardants present in the waste stream. Currently, less than 20% of all e-waste is recycled in the United States because the heterogeneity of the feedstock limits the opportunity for reuse in high value products and processing of the waste itself is often too costly to justify handling. To address this concern, the aims of this study are: 1) to identify the major plastic and metal compositions within electronic shredder residue (ESR), 2) to formulate solvents and processing conditions to separate 90% of the plastics targeted from consumer shred ESR, and 3) to develop a process design model to estimate the cost and energy efficiency of the proposed solvent-based processing. In this study, a pre-sorted heterogeneous ESR feedstock (one where aluminum, magnetic components, and hazardous battery materials removed by an e-waste recycling facility) was used, with the major compositions of the ESR characterized. It was found that 25 wt.% of the feedstock was composed of plastics, 6 wt.% rubber, 27 wt.% printed circuit boards, 23% wire, and the remainder metals and capacitors. Within the plastic portion, polystyrene (PS, 40 wt.%), acrylonitrile butadiene styrene (ABS, 25 wt.%), and styrene-acrylonitrile (SAN, 9wt.%) were identified to compose the majority of the screened plastics using Fourier transform infrared spectroscopy (FTIR). Next, selective solvents were screened using Hansen Solubility Parameter Theory (HSP) for dissolving PS and ABS. The pre-screening results show that methylene chloride (dichloromethane, DCM) and tetrahydrofuran (THF) are capable of dissolving the most PS and ABS, while methanol (MeOH) and ethylene glycol (EG) are capable of precipitating the most PS and ABS. These solvents were subsequently used to recover polymers and remove. flame retardants within the ESR feedstock. By optimizing the dissolution time and the solvents used, the highest polymer dissolution yield (99 wt.%%) was achieved using DCM for 48 hr. Both pre-screened anti-solvents (MeOH and EG) showed the highest polymer precipitation yield (71 wt.%). In terms of flame retardant removal rate, EG was found to have a high phosphorus-containing flame retardant removal rate (up to 98%). Characterization shows that the proposed solvent-based processing can preserve a high molecular weight fraction of the polymers and effectively remove flame retardants. Cost analysis indicates that the amount of the solvent/anti-solvent recovered after the reaction would play a critical role in reducing the operating costs. The energy analysis shows that the proposed solvent-based processes can save up to 60% of the embodied energy used to manufacture plastics used in electronics (PS and ABS were used for calculations). The results from this project prove the potential of solvent-based processing to produce secondary materials (plastics and metals) from e-waste for cross-industry reuse.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

X-Ray Spectroscopic Studies of X-Pinch Plasmas with 3-5 Picosecond Resolution: A Quest for Clear Experimental Evidence for Radiative Collapse in the X-ray Spectra (Final Report)

Dense Z-pinch plasmas produced from current-carrying exploding wires frequently produce very brief (less than 0.1 nanosecond), intense, bursts of soft X-rays from tiny (about 1 micrometer), very hot (10-30 million K) regions of the plasma. This project addresses the physical processes that lead to those tiny, high-energy density plasmas and develops means to measure the conditions just before and during the X-ray bursts. One possible relevant process is radiative collapse, which starts if the power radiated by a dense Z-pinch, proportional to the density-squared, exceeds the resistive heating rate from the current flow, thereby cooling the plasma and enabling the magnetic pinching force to exceed the outward plasma thermal pressure. As the resulting radius reduction further increases the radiation rate, this process produces a runaway magnetic implosion. A competing mechanism is a sausage-like instability that can develop in a Z-pinch plasma at a lower current than is needed to induce radiative collapse. This mechanism can also produce tiny hot spots in the neck regions of the sausage-shaped plasma column. It is also possible that these two mechanisms work together to produce the X-ray emitting hot spots. If radiative collapse does contribute to hot spot formation, it would be terminated when the plasma becomes so dense that the radiation cannot escape, enabling the plasma kinetic pressure to build up and stop the current-driven implosion. This project aims to study the development of the hot spots by means of high temporal and spatial resolution X-ray spectroscopy to determine if there is evidence for the presence of the radiative collapse mechanism. Progress toward this goal is presented. To summarize, during the four-year period 09/15/2017 - 9/14/2021, we have collected necessary spectroscopic data to determine the plasma conditions and continue to do so. We are also now in the process of calibrating diagnostic systems (especially the x-ray streak camera system) and analyzing data to determine plasma conditions as a function of time before, during and after the X-ray burst.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Modular Security Apparatus for Managing Distributed Cryptography for Command-and-Control Messages on Operational Technology Networks (Module-OT)

Module-OT is a bump- in- the- wire solution acting as a secure conduit for data between devices or systems across a network. Using the latest in open-source cryptographic libraries, all defined communications undergo authentication, authorization, and encryption. The core system can be easily installed through industry standard processes, and the use of popular open-source packages allows for it to be customizable customized by the developer community or deployed in unique embedded environments.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Discrete modeling of a transformer with ALEGRA

We report progress on a task to model transformers in ALEGRA using the “Transient Magnetics” option. We specifically evaluate limits of the approach resolving individual coil wires. There are practical limits to the number of turns in a coil that can be numerically modeled, but calculated inductance can be scaled to the correct number of turns in a simple way. Our testing essentially confirmed this “turns scaling” hypothesis. We developed a conceptual transformer design, representative of practical designs of interest, and that focused our analysis. That design includes three coils wrapped around a rectangular ferromagnetic core. The secondary and tertiary coils have multiple layers. The tertiary has three layers of 13 turns each; the secondary has five layers of 44 turns; the primary has one layer of 20 turns. We validated the turns scaling of inductance for simple (one-layer) coils in air (no core) by comparison to available independent calculations for simple rectangular coils. These comparisons quantified the errors versus reduced number of turns modeled. For more than 3 turns, the errors are <5%. The magnetic field solver failed to converge (within 5000 iterations) for >10 turns. Including the core introduced some complications. It was necessary to capture the core surfaces in thin grid sheaths to minimize errors in computed magnetic energy. We do not yet have quantitative benchmarks with which to compare, but calculated results are qualitatively reasonable.

42 ENGINEERING↗
DOE OSTI2021

SiC-Based Wireless Power Transformation for Data Centers & Medium Voltage Applications

Data centers have grown in physical size and their electrical power consumption has grown to levels of several 100kW and approaching 1 GW in large installations. The low voltage electrical distribution inside of Data Centers consists of several conversion stages and a lot of wiring to bring the power from medium voltage (MV) levels outside of the building to the low voltage levels that the servers and racks require. Energy losses during distribution and conversion and high incident arc flash energy levels at the point of use are significant. The electrical distribution system is complex and costly.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Processing of Ultrasonic Measurements for an Additive Manufacturing Application

Resonant ultrasonic spectroscopy is an effective methodology capable of measuring a change in modal resonant frequencies of material structures. It encompasses techniques based on ultrasonic frequencies employed to estimate elastic coefficients in solids. It is these frequencies that are uniquely characterized by the material shape, coefficients, symmetry and density that are used to improve and detect changes especially during the additive manufacturing (AM) process. In this report a variety of techniques to extract and validate material resonances are developed starting first with the background theory required to comprehend the approaches. Once the theory is established, various signal processing methodologies are applied to estimate the underlying resonances leading to the extraction of the critical elastic coefficients characterizing the specimen under test. A detailed case study based on wire arc additive manufacturing is discussed demonstrating the applicability of the various approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Securing Inverter Communication: Proactive Intrusion Detection and Mitigation System to Tap, Analyze, and Act

The electric grid has undergone rapid, revolutionary changes in recent years; from the addition of advanced smart technologies to the growing penetration of distributed energy resources (DERs) to increased interconnectivity and communications. However, these added communications, access interfaces, and third-party software to enable autonomous control schemes and interconnectivity also expand the attack surface of the grid. To address the gap of DER cybersecurity and secure the grid-edge to motivate a holistic, defense-in-depth approach, a proactive intrusion detection and mitigation system (PIDMS) device was developed to secure PV smart inverter communications. The PIDMS was developed as a distributed, flexible bump-in-the-wire (BITW) solution for protecting PV smart inverter communications. Both cyber (network traffic) and physical (power system measurements) are processed using network intrusion monitoring tools and custom machinelearning algorithms for deep packet analysis and cyber-physical event correlation. The PIDMS not only detects abnormal events but also deploys mitigations to limit or eliminate system impact; the PIDMS communicates with peer PIDMSs at different locations using the MQTT protocol for increased situational awareness and alerting. The details of the PIDMS methodology and prototype development are detailed in this report as well as the evaluation results within a cyber-physical emulation environment and subsequent industry feedback.

14 SOLAR ENERGY↗
DOE OSTI2022

Development of Surface Sampling Techniques for the Canister Deposition Field Demonstration (FY22 Update)

This report describes the proposed surface sampling techniques and plan for the multi-year Canister Deposition Field Demonstration (CDFD). The CDFD is primarily a dust deposition test that will use three commercial 32PTH2 NUHOMS welded stainless steel storage canisters in Advanced Horizontal Storage Modules, with planned exposure testing for up to 10 years at an operating ISFSI site. One canister will be left at ambient condition, unheated; the other two will have heaters to achieve canister surface temperatures that match, to the degree possible, spent nuclear fuel (SNF) loaded canisters with heat loads of 10 kW and 40 kW. Surface sampling campaigns for dust analysis will take place on a yearly or bi-yearly basis. The goal of the planned dust sampling and analysis is to determine important environmental parameters that impact the potential occurrence of stress corrosion cracking on SNF dry storage canisters. Specifically, measured dust deposition rates and deposited particle sizes will improve parameterization of dust deposition models employed to predict the potential occurrence and timing of stress corrosion cracks on the stainless steel SNF canisters. The size, morphology, and composition of the deposited dust and salt particles will be quantified, as well as the soluble salt load per unit area and the rate of deposition, as a function of canister surface temperature, location, time, and orientation. Previously, a preliminary sampling plan was developed, identifying possible sampling locations on the canister surfaces and sampling intervals; possible sampling methods were also described. Further development of the sampling plan has commenced through three different tasks. First, canister surface roughness, a potentially important parameter for air flow and dust deposition, was characterized at several locations on one of the test canisters. Second, corrosion testing to evaluate the potential lifetime and aging of thermocouple wires, spot welds, and attachments was initiated. Third, hand sampling protocols were developed, and initial testing was carried out. The results of those efforts are presented in this report. The information obtained from the CDFD will be critical for ongoing efforts to develop a detailed understanding of the potential for stress corrosion cracking of SNF dry storage canisters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Assessment of the Electrical Substation-Grid Testbed with Inside/Outside Devices and Distributed Ledger Technology

The electrical substation-grid testbed was created to integrate the GOOSE and/or DNP (Distributed Network Protocol) messages with time synchronized sources and Distributed Ledger Technology (DLT). The objective was to study the impact of faults and cyber-events at an electrical substation with inside (protective relays) and outside (power meters) substation devices. The electrical substation-grid testbed was based on the design of a 34.5/ 12.47 kV electrical substation (sectionalized bus configuration) with two power transformers, connected to radial power lines and load feeders. The electrical substation-grid testbed was installed at 252 lab space (Advanced Power System Protection), Grid Research Integration and Deployment Center (GRID-C), Oak Ridge National Laboratory. This testbed was created for Task 5, DarkNet project. The electrical substation-grid testbed was created to simulate fault and/or cyber events that could potentially result in damage to the electrical infrastructure. In addition, tests were run that are usually not allowed to be performed in an operational electrical power grid, because these test scenarios could trip breakers and/or generate fault situations that could potentially damage equipment. The number of tests performed in the electrical substation-grid testbed were executed in a better way than in a real electrical substation and/or power grid, because multiple tests could be run in a short period of time, and complex permits, and safety/ schedule restrictions like in a real electrical substation environment were not needed. The electrical substation-grid testbed was created using real measurement, communication, and protection devices that are used by electrical utilities, to have same conditions that we could observe in a real power grid or electrical substation. The electrical substation-grid testbed was based on using a real time simulator and expansion box with amplifiers that were wired to electrical substation-grid devices. This hardware-in-the-loop (HIL) was provided by protective relays, power meters, ethernet switches, remote terminal units, synchronized timing network clock, DLT devices, workstations, and servers. This report includes the design, installation, and assessment of the electrical substation-grid testbed that was similar to an operational electrical substation, integrating the power system protection, communication, and control systems. The results for the electrical substation-grid testbed were based on:• verifying the analog signals for protective relays and power meters, • observing the synchronized time source frame at devices, • authenticating the GOOSE (IEC 61850) and DNP messages from power meters and protective relays, and • verifying the trip conditions of protective relays at fault tests with the power system fault event detection, using DLT devices. For future work, the electrical substation-grid testbed with protective relays and power meters, using DLT and synchronized time source from DarkNet, will be used to study the impact of cyber-events at inside and outside substation devices. Advanced algorithms for detecting cyber-events produced by non-desired protective relay settings will be studied, to improve the detection and reliability of protection, control, and communication systems at power grids.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Electric Access System Enhancement (EASE): Assessment of a Distributed Energy Resource Management System for Enabling Dynamic Hosting Capacity

The Electric Access System Enhancement (EASE) project demonstrated a scalable, interoperable, and cost-effective means of integrating high penetration of distributed energy resources (DERs). The control architecture developed leveraged a Distributed Energy Resource Management System, Distribution System Operator for transacting energy, and 3rd Party DER Aggregator platform. The project identified ways to enhance the customer interconnection process to the grid and improve access to information from DERs and optimize the usage of DERs to provide energy services in a simulated day-ahead shadow market while maintain grid reliability. By integrating these capabilities into a scalable system of systems, the DSO can effectively balance DER generation and customer demand on the distribution network. This capability allows the grid to host more DER than traditionally possible on wires alone. Hosting more DER has the added benefit of supplying increased demand growth, sometimes beyond the capacity limits of the distribution network itself. This is known as a dynamic hosting capacity, which could help utilities manage the forecasted growth in electricity demand as California switch to electric vehicles and appliances. This could help to establish energy storage and PV generation as a “pseudo firm” generation resource mix if managed appropriately and provide sufficient resource adequacy for distribution capacity upgrade deferrals.

14 SOLAR ENERGY↗
DOE OSTI2020

Multi-Stage and Multi-Timescale Robust Co-Optimization Planning for Reliable and Sustainable Power Systems. Final Report

In this project, Clarkson University, in collaboration with Southern Methodist University and University of Pittsburgh, conducted the research to model, design, and implement a sophisticated generation and transmission co-optimization planning decision tool, called Multi-stage and Multi-timescale robust Co-Optimization Planning (MMCOP). The MMCOP decision tool intends to facilitate generation and transmission co-optimization planning of emerging power systems, while mitigating risks and uncertainties in both short-term operation dynamics and long-term policy and technology changes. Long-term power system planning aims at optimizing asset utilization by investing in a proper mix of various generation technologies and transmission lines to supply the future load growth. In particular, the Clean Power Plan (CPP), which is designed to combat climate change and reduce carbon emissions by setting a national limit on carbon pollution from power plants, may dramatically change the landscape of the power industry by further promoting clean energy and phasing out emissions-intensive generation technologies. In addition, novel non-wire alternatives (e.g., demand response (DR), distributed generation (DG), energy efficiency (EE), and smart grid technologies) and the computational complexity for large-scale systems significantly complicate the system planning procedure even further. However, existing conventional planning approaches neglect short-term variability and uncertainty of renewable energy, hourly chronological operation details, and physical nonlinear characteristics of the alternating current transmission network. As a result, existing conventional planning approaches may not work properly, and power systems reliability could be in jeopardy. In observing the limitations of existing conventional planning approaches and addressing new challenges of emerging power systems, the main scope of this project to develop co-optimization planning models within a multi-stage and multi-timescale framework. In particular, random contingencies, key uncertainty factors, and AC power flows are included to derive expansion plans while considering both long-term reliability and short-term flexibility.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

CERBERUS: CED-2 Final Design Report

The goal of the Critical Experiment Reflected By copper to bEtteR Understand Scattering [CERBERUS] is to design a critical experiment that maximizes sensitivities to copper (Cu) reactions, particularly in the intermediate energy region (0.625 eV – 100 keV) as well as the 100 – 600 keV energy region. Despite the number of experiments evaluated in the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook1 , there is still a lack of benchmarks sensitive to neutrons in the intermediate energy region. The ZEUS series was designed specifically to provide data in the intermediate energy range. The ZEUS series used Cu reflectors to allow for the construction of an intermediate energy system that could be constructed within a reasonable size. While the reflection provided by Cu reduces the size of the system, it creates a system that is very sensitive to the angular scattering in Cu. A neutron scattering off Cu at some angles reflects back into to the system, while at other angles, it is lost entirely. Of the ICSBEP benchmarks sensitive to neutrons in the intermediate energy region, very few are also sensitive to Cu in that region. Improving Cu nuclear data is important outside of the ZEUS series, because it is present in many bronze and aluminum alloys, which are used in various nuclear operations such as motors, wires, and some containers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Development of self-sensing materials for extreme environments based on metamaterial concept and additive manufacturing

Structural health monitoring of an engineered component in a harsh environment is critical for multiple DOE missions including nuclear fuel cycle, subsurface energy production/storage, and energy conversion. Supported by a seeding Laboratory Directed Research & Development (LDRD) project, we have explored a new concept for structural health monitoring by introducing a self-sensing capability into structural components. The concept is based on two recent technological advances: metamaterials and additive manufacturing. A self-sensing capability can be engineered by embedding a metastructure, for example, a sheet of electromagnetic resonators, either metallic or dielectric, into a material component. This embedment can now be realized using 3-D printing. The precise geometry of the embedded metastructure determines how the material interacts with an incident electromagnetic wave. Any change in the structure of the material (e.g., straining, degradation, etc.) would inevitably perturbate the embedded metastructures or metasurface array and therefore alter the electromagnetic response of the material, thus resulting in a frequency shift of a reflection spectrum that can be detected passively and remotely. This new sensing approach eliminates complicated environmental shielding, in-situ power supply, and wire routing that are generally required by the existing active-circuit-based sensors. The work documented in this report has preliminarily demonstrated the feasibility of the proposed concept. The work has established the needed simulation tools and experimental capabilities for future studies.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Maximum Interior Voltage and Magnetic Field Penetration Through a Ferromagnetic Layer

This report examines the problem of magnetic penetration of a conductive layer, including nonlinear ferromagnetic layers, excited by an electric current filament. The electric current filament is, for example, a nearby wire excited by a lightning strike. The internal electric field and external magnetic field are determined. Numerical results are compared to various analytical approximations to help understand the physics involved in the penetration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗