Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “ELECTROMAGNETIC PROPAGATION”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Diffuse ions produced by electromagnetic ion beam instabilities

The evolution of the electromagnetic ion beam instability driven by the reflected ion component backstreaming away from the earth's bow shock into the foreshock region is studied by means of computer simulation. The linear and quasi-linear stages of the instability are found to be in good agreement with known results for the resonant mode propagating parallel to the beam along the magnetic field and with theory developed in this paper for the nonresonant mode, which propagates antiparallel to the beam direction. The quasi-linear stage, which produces large amplitude delta B approximately B, sinusoidal transverse waves and 'intermediate' ion distributions, is terminated by a nonlinear phase in which strongly nonlinear, compressive waves and 'diffuse' ion distributions are produced. Additional processes by which the diffuse ions are accelerated to observed high energies are not addressed. The results are discussed in terms of the ion distributions and hydromagnetic waves observed in the foreshock of the earth's bow shock and of interplanetary shocks.

Winske, D.↗
NASA NTRS2021

Prompt Response of the Dayside Magnetosphere to Discrete Structures within the Sheath Region of a Coronal Mass Ejection

A sequence of discrete solar wind structures within the sheath region of an interplanetary coronal mass ejection (ICME) on Nov 06, 2015 caused a series of compressions and releases of the dayside magnetosphere. Each compression resulted in a brief adiabatic enhancement of ions (electrons) driving bursts of electromagnetic ion cyclotron (whistler mode chorus) wave growth across the dayside magnetosphere. Fine-structured rising tones were observed in the EMIC wave bursts, resulting in nonlinear scattering of relativistic electrons in the outer radiation belt. Multipoint observations allow us to study the spatial structure and evolution of these sheath structures as they propagate Earthward from L1 as well as the spatio-temporal characteristics of the magnetospheric response. This event highlights the importance of fine-scale solar wind structure, in particular within complex sheath regions, in driving dayside phenomena within the inner magnetosphere.

L. W. Blum↗
DOE OSTI2022

Proton deflectometry with in situ x-ray reference for absolute measurement of electromagnetic fields in high-energy-density plasmas

In this work, we report a technique of proton deflectometry that uses a grid and an in situ reference x-ray grid image for precise measurements of magnetic fields in high-energy-density plasmas. A D 3 He fusion implosion provides a bright point source of both protons and x-rays, which is split into beamlets by a grid. The protons undergo deflections as they propagate through the plasma region of interest, whereas the x-rays travel along straight lines. The x-ray image, therefore, provides a zero-deflection reference image. The line-integrated magnetic fields are inferred from the shifts of beamlets between the deflected (proton) and reference (x-ray) images. We developed a system for analysis of these data, including automatic algorithms to find beamlet locations and to calculate their deflections from the reference image. The technique is verified in an experiment performed at OMEGA to measure a nonuniform magnetic field in vacuum and then applied to observe the interaction of an expanding plasma plume with the magnetic field.

47 OTHER INSTRUMENTATION↗
DOE OSTI2017

Electromagnetic enhanced ignition

Here, we investigate how EM radiation affects the thermal decomposition pathway in HMX. The experiment used an external heat source (CO 2 laser) to rapidly heat the surface of HMX and observe the response upon application of EM energy that, on its own, is not enough power to induce heating or ignition. We hypothesize that charged intermediate decomposition species and free radicals in the gas phase interact strongly with EM energy, leading to plasma formation. These gas phase species form as a result of HMX sublimation and decomposition, and will act as “virtual antennas” and strongly couple to EM energy. The rapid absorption of EM energy during this coupling event is observed in the measured reflected power data. Ignition and plasma formation were monitored using both visible and IR photodiode probes, as well as imaged using a high-speed video camera. These observations support the hypothesis that the presence of an EM field will perturb the thermal decomposition pathway of HMX, and cause ignition to occur at a lower temperature than what is predicted under typical thermal conditions. This intense interaction results in electrically excited molecules that propagate the energy and surpass the activation barrier for ignition before the predicted ignition temperature of the bulk sample has been reached. In conclusion, understanding the decomposition of energetic materials under the influence of EM energy is important to understand and predict material response under a variety of environmental conditions.

42 ENGINEERING↗
NASA NTRS1979

Magnetohydroelectric waves in a fluid dielectric

An electromagnetic disturbance in a fluid dielectric substance placed in a uniform magnetic field in the positive z direction of a rectangular Cartesian coordinate system with an electric field that increases with time applied in the positive z direction is analyzed. A simultaneous solution to a set of four equations is obtained which indicates a propagating 'magnetohydroelectric' wave that corresponds to oscillations in magnetic, kinetic, and electrostatic energies. It is noted that this wave bears a superficial resemblance to Alfven waves in a magnetized conducting fluid.

De, B. R.↗
NASA NTRSDate not supplied

A Compact Dual-Band Bowtie Antenna for RF and ISM bands Operation

Traditionally, bowtie antennas have been known to exhibit wide impedance characteristics, omnidirectional radiation patterns, and linear polarization. There is a broad range of applications from medical imaging, archaeological survey, and Ground Penetrating Radar (GPR) to trackers and sensor networks where wideband bowtie antenna designs are required for their operations. Broadening the bandwidth of bowtie antenna requires widening the flare angle of the bowtie arms, which consequently results in a large surface area that may not be suitable for space-constrained applications. Moreover, drawback attributes of the wideband bowtie designs feature inconsistent radiation pattern across the bandwidth and low signal-to-noise (SNR) ratios. As it is known, the SNR would be improved in dual- or multi-band antennas due to their reduced bandwidth. To this end, dual-band/multi-band antennas are preferred over wideband antennas in applications where more than a single frequency of interest is present. Previously, a two-port double-dipole elements was reported, whose arms were orthogonally interleaved to facilitate operation in both the standard WLAN frequency bands (J. M. Steyn and et. al, Progress in Electromagnetic Research, Vol. – 10 pp. 151-161). Even though the antenna is not very compact it does exhibit good cross-polarization, moderate gain in both frequency bands. Another dual-band bowtie antenna which excites two bands using a single transmission line was reported (Wen Chao Zheng and et. al, IEEE Trans. Antennas propag., 2014). The design was compact and did not need multi-port feeding network. In this paper, a dual-band compact bowtie antenna operating at 900 MHz (RF band) and 2.45 GHz (ISM band) using a single excitation port is introduced. It is printed on a 1.54mm thick dielectric substrate (εr = 3.38). The antenna consists of two sets of bowtie arms, a microstrip transmission line to feed the bowtie arms, and a ground plane acting as a reflector to partially reduce the back radiation. One of the bowtie arms of each frequency is printed on the top layer and the other arm, which is mirror imaged, is printed on the bottom layer of the substrate. The length of the bowtie controls the resonance frequency of the antenna and the flare angle controls the bandwidth of the antenna. The microstrip transmission line, connected to a 50 Ω SMA probe, feeds the bowtie antenna. The compact antenna can be used for both RF and ISM band applications. The bowtie arms at the lower frequency band are miniaturized by elongating their electrical lengths. The influence of miniaturizing the bowtie arms and the supporting partial ground plane is observed in the reduced peak gain and degraded front-to-back ratio. These are partly neutralized using four quarter-wave choke-slots in the ground plane with two on each side of the feeding transmission line. The proposed antenna is numerically investigated and finalized by the finite-element based full-wave EM solver, ANSYS HFSS. The miniaturization has reduced the ground plane size by ~45% and the arms size by ~41%. In addition to the size reduction benefits, the antenna shows reasonable peak gain and front-to-back ratio in both the bands. The corresponding results will be presented and discussed at the conference.

Saininad Naik↗
DOE OSTI2021

Interaction of radio frequency waves with cylindrical density filaments: scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas , vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci. , vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

Physics↗
DOE OSTI2024

Plasmons in the Kagome metal CsV 3 Sb 5

Plasmon polaritons, or plasmons, are coupled oscillations of electrons and electromagnetic fields that can confine the latter into deeply subwavelength scales, enabling novel polaritonic devices. While plasmons have been extensively studied in normal metals or semimetals, they remain largely unexplored in correlated materials. In this paper, we report infrared (IR) nano-imaging of thin flakes of CsV3Sb5, a prototypical layered Kagome metal. We observe propagating plasmon waves in real-space with wavelengths tunable by the flake thickness. From their frequency-momentum dispersion, we infer the out-of-plane dielectric function that is generally difficult to obtain in conventional far-field optics, and elucidate signatures of electronic correlations when compared to density functional theory (DFT). We propose correlation effects might have switched the real part of ϵ c from negative to positive values over a wide range of middle-IR frequencies, transforming the surface plasmons into hyperbolic bulk plasmons, and have dramatically suppressed their dissipation.

36 MATERIALS SCIENCE↗
DOE OSTI2016

A parametric study of the linear growth of magnetospheric EMIC waves in a hot plasma

Since electromagnetic ion cyclotron (EMIC) waves in the terrestrial magnetosphere play a crucial role in the dynamic losses of relativistic electrons and energetic protons and in the ion heating, it is important to pursue a comprehensive understanding of the EMIC wave dispersion relation under realistic circumstances, which can shed significant light on the generation, amplification, and propagation of magnetospheric EMIC waves. The full kinetic linear dispersion relation is implemented in the present study to evaluate the linear growth of EMIC waves in a multi-ion (H{sup +}, He{sup +}, and O{sup +}) magnetospheric plasma that also consists of hot ring current protons. Introduction of anisotropic hot protons strongly modifies the EMIC wave dispersion surface and can result in the simultaneous growth of H{sup +}-, He{sup +}-, and O{sup +}-band EMIC emissions. Our parametric analysis demonstrates that an increase in the hot proton concentration can produce the generation of H{sup +}- and He{sup +}-band EMIC waves with higher possibility. While the excitation of H{sup +}-band emissions requires relatively larger temperature anisotropy of hot protons, He{sup +}-band emissions are more likely to be triggered in the plasmasphere or plasmaspheric plume where the background plasma is denser. In addition, the generation of He{sup +}-band waves is more sensitive to the variation of proton temperature than H{sup +}-band waves. Increase of cold heavy ion (He{sup +} and O{sup +}) density increases the H{sup +} cutoff frequency and therefore widens the frequency coverage of the stop band above the He{sup +} gyrofrequency, leading to a significant damping of H{sup +}-band EMIC waves. In contrast, O{sup +}-band EMIC waves characteristically exhibit the temporal growth much weaker than the other two bands, regardless of all considered variables, suggesting that O{sup +}-band emissions occur at a rate much lower than H{sup +}- and He{sup +}-band emissions, which is consistent with the observations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Characterizing Baselines and Change in Gas Hydrate Systems using EM Methods

The objective of this project was to advance our understanding of gas hydrate systems in nature by characterizing their electrical properties in the field and in the laboratory. In the laboratory measurements, methane hydrate was synthesized from pure water ice and flash frozen seawater, with varying amounts of sand or silt added. Electrical conductivity was determined by impedance spectroscopy, using equivalent circuit modeling to separate the effects of electrodes and to gain insight into conduction mechanisms. Silt and sand increase the conductivity of pure hydrate, inferred to be contaminant NaCl contributing to conduction in hydrate, to a peak conductivity in agreement with peak resistivities observed in well logs through massive hydrate (3,000--10,000 Ωm). The addition of silt and sand lowers the conductivity of hydrate synthesized from seawater, by an amount consistent with Archie's Law. All samples were characterized using cryogenic scanning electron microscopy and energy dispersive spectroscopy, which shows good connectivity of salt and brine phases. Electrical conductivity measurements of pure hydrate and hydrate mixed with silt during pressure-induced dissociation supports previous conclusions that sediment increases dissociation rate. In order to characterize gas hydrate systems in the field, we collected 360 line kilometers of controlled-source electromagnetic data on Walker Ridge 313, Orca Basin (WR100), Mad Dog (GC781), and Green Canyon 955 in the Gulf of Mexico, all areas with known or seismically inferred gas hydrate deposits and which have be drilled or targeted for future drilling. We deep-towed an EM transmitter that generates an alternating electric field which propagates through the seafloor geology. Data were recorded on 6 receivers towed behind the transmitter at distances between 550 and 1550 m. In the presence of conductive geology, the electric fields will be attenuated, and conversely, in resistive geology the fields will be preserved. Our data were inverted using a 2D inversion method that first optimizes the model-data misfit, then finds the smoothest model fitting the data. This ensures that resistivity structures present in the final model are likely necessary. At each of the proposed drilling sites we found increased resistivity, interpreted as increased hydrate concentrations. However, not only were the primary drilling sites not always more resistive than the alternate sites, at WR313 the strongest resistors were not at the locations targeted for drilling.

03 NATURAL GAS↗
DOE OSTI2022

Interaction of radio frequency waves with cylindrical density filaments -- scattering and radiation pressure

The propagation of radio-frequency (RF) waves in tokamaks can be affected by filamentary structures, or blobs, that are present in the edge plasma and the scrape-off layer. The difference in the permittivity between the surrounding plasma and interior of a filament leads to reflection, refraction and diffraction of the waves. This, in turn, can affect the power flow into the core of the plasma and reduce the efficiency of heating and/or current generation. The scattering of RF waves, lower hybrid, helicon and ion cyclotron waves, by a single cylindrical filament, embedded in a background plasma, is studied using a full-wave analytical theory developed previously (Ram & Hizanidis, Phys. Plasmas, vol. 23, 2016, 022504). The theory assumes that the plasma in and around a filament is homogeneous and cold. A detailed scattering analysis reveals a variety of common features that exist among the three distinctly different RF waves. These common attributes can be inferred intuitively based on an examination of the cold plasma dispersion relation. The physical intuition is a useful step to understanding experimental observations on scattering, as well as results from simulations that include general forms of edge plasma turbulence. While a filament can affect the propagation of RF waves, the radiation force exerted by the waves can influence the filament. The force on a filament is determined using the Maxwell stress tensor. In 1905, Poynting was the first to evaluate and measure the radiation force on an interface separating two different dielectric media (Poynting, London Edinburgh Dublin Philos. Mag. J. Sci., vol. 9, 1905, pp. 393–406). For ordinary light propagating in vacuum and incident on a glass surface, Poynting noted that the surface is ‘pulled’ towards the vacuum. In a magnetized cold plasma, there are two independent wave modes. Even if only one of these modes is excited by an RF antenna, a filament will couple power to the other mode: a consequence of electromagnetic boundary conditions. This facet of scattering has consequences on the radiation force that go beyond Poynting's seminal contribution. The direction of the force depends on the polarization of the incident wave and on the mode structure of the waves inside and in the vicinity of a filament. It can either pull the filament toward the RF source or push it away. For slow lower hybrid waves, filaments with densities greater than the ambient density are pulled in, while filaments with lower densities are pushed out, thereby enhancing the density in front of the antenna. In the case of fast helicon and ion cyclotron waves, the direction of the force depends on the plasma and wave parameters; in particular, on the ambient density. The radiation force, in all three frequency ranges, is large enough to affect the motion of a filament and could be measured experimentally. This also suggests the possibility of modifying the edge turbulence using RF waves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1975

Propagation of cosmic rays in the Galaxy

The galactic model of cosmic ray confinement is assumed in an in-depth theoretical investigation of cosmic ray propagation in the Galaxy, with consideration also given to the interpretation of observed data. The necessary data concerning the interstellar medium are summarized in order to form a basis for the theoretical formulation of the propagation of cosmic rays, which are assumed to be in a state of equilibrium and homogeneously distributed in the residence volume. The interaction of cosmic rays with the attenuated gases, weak magnetic fields, and radiation fields of the interstellar medium is examined. Many of these interactions lead to the production of radiations ranging the entire electromagnetic spectrum. The possible roles played by cosmic rays in some aspects of galactic dynamics such as the hydrostatic equilibrium of interstellar gas, gravitational instability and formation of clouds, and heating of interstellar gas, are also studied.

Daniel, R. R.↗
NASA NTRS1989

Calculating the electromagnetic field on the earth due to an electrodynamic tethered system in the ionosphere

A method is presented for calculating the electromagnetic wave field on the earth's surface associated with the operation of an electrodynamic tethered satellite system of constant or slowly varying current in the upper ionosphere. The wave field at the ionospheric boundary and on the earth's surface is obtained by numerical integration. The results suggest that the ionospheric waves do not propagate into the atmosphere and that the image of the Alfven wings from a steady-current tether should be greatly broadened on the earth's surface.

Estes, Robert D.↗
DOE OSTI2018

Hybrid iterative approach for simulation of radio-frequency fields in plasma

In this work, a novel iterative approach for solving discretized linear wave equations in a frequency domain, which combines time evolution with iterative relaxation schemes, is presented. In this hybrid approach, each iteration cycle consists of evolution of electromagnetic (EM) fields in time over a specified number of field periods followed by several iterative relaxations. Provided that there is sufficient dissipation, both the time evolution and the iterative relaxations contribute to the convergence of the EM fields to the solution of the formulated full wave boundary value problem. Time evolution rapidly distributes EM fields, propagating with group velocity, over the simulation domain, while the iterative relaxations smooth the fields, reducing the numerical errors such that iteration cycles converge to a steady state solution, approximating the solution of the formulated problem. This approach is intended for large scale simulations which are beyond the capabilities of direct solvers presently used for solving wave equations in the frequency domain. Lastly, the technique is demonstrated for solving wave equations on a regular grid using a cold plasma dielectric model with collisions for 2D modeling of EM fields in tokamak in an electron cyclotron frequency range.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Resonances of electromagnetically induced transparency and absorption in a light field of elliptically polarised waves

Electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) resonances excited by a strong two-frequency field are considered for various values of the total angular momenta of the ground (F{sub g}) and excited (F{sub e}) states at a degenerated optical closed transition F{sub g} → F{sub e}. The light field is formed by two co-propagating waves with arbitrary elliptical polarisations. The process of spontaneous transfer of anisotropy from the excited state to the ground state is shown to determine the formation of the EIA resonance at the transition F{sub g} = F → F{sub e} = F + 1. The results obtained generalise the classification of transitions into ‘bright’ (F{sub g} = F → F{sub e} = F + 1) and ‘dark’ (F{sub g} = F → F{sub e} = F and F{sub g} = F → F{sub e} = F – 1) transitions with respect to the direction of a subnatural resonance. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1981

Adaptation of the TH Epsilon Mu formalism for the analysis of the equivalence principle in the presence of the weak and electroweak interaction

The TH epsilon mu formalism, used in analyzing equivalence principle experiments of metric and nonmetric gravity theories, is adapted to the description of the electroweak interaction using the Weinberg-Salam unified SU(2) x U(1) model. The use of the TH epsilon mu formalism is thereby extended to the weak interactions, showing how the gravitational field affects W sub mu (+ or -1) and Z sub mu (0) boson propagation and the rates of interactions mediated by them. The possibility of a similar extension to the strong interactions via SU(5) grand unified theories is briefly discussed. Also, using the effects of the potentials on the baryon and lepton wave functions, the effects of gravity on transition mediated in high-A atoms which are electromagnetically forbidden. Three possible experiments to test the equivalence principle in the presence of the weak interactions, which are technologically feasible, are then briefly outline: (1) K-capture by the FE nucleus (counting the emitted X-ray); (2) forbidden absorption transitions in high-A atoms' vapor; and (3) counting the relative Beta-decay rates in a suitable alpha-beta decay chain, assuming the strong interactions obey the equivalence principle.

Fennelly, A. J.↗
DOE OSTI2016

MIXING THE SOLAR WIND PROTON AND ELECTRON SCALES: EFFECTS OF ELECTRON TEMPERATURE ANISOTROPY ON THE OBLIQUE PROTON FIREHOSE INSTABILITY

The double adiabatic expansion of the nearly collisionless solar wind plasma creates conditions for the firehose instability to develop and efficiently prevent the further increase of the plasma temperature in the direction parallel to the interplanetary magnetic field. The conditions imposed by the firehose instability have been extensively studied using idealized approaches that ignore the mutual effects of electrons and protons. Recently, more realistic approaches have been proposed that take into account the interplay between electrons and protons, unveiling new regimes of the parallel oscillatory modes. However, for oblique wave propagation the instability develops distinct branches that grow much faster and may therefore be more efficient than the parallel firehose instability in constraining the temperature anisotropy of the plasma particles. This paper reports for the first time on the effects of electron plasma properties on the oblique proton firehose (PFH) instability and provides a comprehensive vision of the entire unstable wave-vector spectrum, unifying the proton and the smaller electron scales. The plasma β and temperature anisotropy regimes considered here are specific for the solar wind and magnetospheric conditions, and enable the electrons and protons to interact via the excited electromagnetic fluctuations. For the selected parameters, simultaneous electron and PFH instabilities can be observed with a dispersion spectrum of the electron firehose (EFH) extending toward the proton scales. Growth rates of the PFH instability are markedly boosted by the anisotropic electrons, especially in the oblique direction where the EFH growth rates are orders of magnitude higher.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Decay Length Estimation of Single- Two- and Three-Wire Systems Above Ground under HEMP Excitation

Here, we analytically model single-, two-, and three-wires above ground to determine the decay lengths of common and differential modes induced by an E1 high-altitude electromagnetic pulse (HEMP) excitation. Decay length information is pivotal to determine whether any two nodes in the power grid may be treated as uncoupled. We employ a frequency-domain method based on transmission line theory named ATLOG - Analytic Transmission Line Over Ground to model infinitely long and finite single wires, as well as solve the eigenvalue problem of a single-,two-, and three-wire system. Our calculations show that a single, semi-infinite power line can be approximated by a10 km section of line and that the second electrical reflection for all line lengths longer than the decay length are below half the rated operating voltage. Moreover, our findings show that the differential mode propagates longer distances than the common mode in two- and three-wire systems, and this should be taken into account when performing damage assessment from HEMP excitation. Furthermore, this analysis is a significant step toward simplifying the modeling of practical continental grid lengths, yet maintaining accuracy, a result of enormous impact.

42 ENGINEERING↗