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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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NASA NTRS2008

Using the HHT to Search for Gravitational Waves

Gravitational waves are a consequence of Einstein's theory of general relativity applied to the motion of very dense and massive objects such as black holes and neutron stars. Their detection will reveal a wealth of information about these mysterious objects that cannot be obtained with electromagnetic probes. Two projects are underway to attempt the detection of gravitational waves: NASA's Laser Interferometer Space Antenna (LISA), a space based mission being designed to search for waves from supermassive black holes at the centers of galaxies, and the NSF's Laser Interferometer Gravitational Wave Observatory (LIGO), a ground based facility that is now searching for waves from supernovae. pulsars, and the coalescence of black hole and neutron star systems. Because general relativity is an inherently non-linear theory, many of the predicted source waveforms show strong frequency modulation. In addition, the LIGO and LISA detectors are highly sensitive devices that produce a variety of non-linear transient noise features. Thus the unique capabilities of the HHT. the extraction of intrawave modulation and the characterization of non-linear and non-stationary signals, have a natural application to both signal detection and experimental characterization of the detectors. In this talk I will give an overview of the status of the field. including some of the expected sources of gravitational waves, and I will also describe the LISA and LIGO detectors. Then I will describe some applications of the HHT to waveform detection and detector noise characterization.

Camp, Jordan↗
NASA NTRS2012

Radiation from Accelerated Particles in Shocks and Reconnections

Plasma instabilities are responsible not only for the onset and mediation of collisionless shocks but also for the associated acceleration of particles. We have investigated particle acceleration and shock structure associated with an unmagnetized relativistic electron-positron jet propagating into an unmagnetized electron-positron plasma. Cold jet electrons are thermalized and slowed while the ambient electrons are swept up to create a partially developed hydrodynamic-like shock structure. In the leading shock, electron density increases by a factor of about 3.5 in the simulation frame. Strong electromagnetic fields are generated in the trailing shock and provide an emission site. These magnetic fields contribute to the electrons transverse deflection and, more generally, relativistic acceleration behind the shock. We have calculated, self-consistently, the radiation from electrons accelerated in the turbulent magnetic fields. We found that the synthetic spectra depend on the Lorentz factor of the jet, its thermal temperature and strength of the generated magnetic fields. Our initial results of a jet-ambient interaction with anti-parallelmagnetic fields show pile-up of magnetic fields at the colliding shock, which may lead to reconnection and associated particle acceleration. We will investigate the radiation in a transient stage as a possible generation mechanism of precursors of prompt emission. In our simulations we calculate the radiation from electrons in the shock region. The detailed properties of this radiation are important for understanding the complex time evolution and spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.

Nishikawa, K. I.↗
NASA NTRS1980

Analysis of electrical transients created by lightning

A series of flight tests was conducted using a specially-instrumented NASA Learjet to study the electrical transients created on an aircraft by nearby lightning. The instrumentation included provisions for the time-domain and frequency-domain recording of the electrical signals induced in sensors located both on the exterior and on the interior of the aircraft. The design and calibration of the sensors and associated measuring systems is described together with the results of the flight test measurements. The results indicate that the concept of providing instrumentation to follow the lightning signal from propagation field, to aircraft skin current, to current on interior wiring is basically sound. The results of the measurement indicate that the high frequency signals associated with lightning stroke precursor activity are important in generating electromagnetic noise on the interior of the aircraft. Indeed, the signals produced by the precursors are often of higher amplitude and of longer duration that the pulse produced by the main return stroke.

Nanevicz, J. E.↗
NASA NTRS2000

Charge Generation and Propagation in Igneous Rocks

Resistivity changes, ground potentials, electromagnetic (EM) and luminous signals prior to or during earthquakes have been reported, in addition to ground uplift and tilt, and to changes in the seismic wave propagation parameters. However, no physical model exists that ties these diverse phenomena together. Through time-resolved impacts experiments it has been observed that, when igneous rocks (gabbro, diorite, granite) are impacted at low velocities (approx. 100 m/sec), highly mobile electronic charge carriers are generated, spreading from a small volume near the impact point, causing electric potentials, EM and light emission. The rock becomes momentarily conductive. When impacted at higher velocities (approx. 1.5 km/sec), the propagation of the P and S waves is registered through the transient piezoelectric response of quartz. At the same time, the rock volume is filled with mobile charge carriers, and a positive surface potential is registered. During the next 1-2 msec the surface potential oscillates, due to electron injection from ground. These observations are consistent with positive holes, e.g. defect electrons in the O(2-) sublattice, that can travel via the O 2p-dominated valence band of the silicate minerals at the speed of a phonon-mediated charge transfer. Before activation, the positive hole charge carriers lay dormant in form of positive hole pairs, PHP, electrically inactive, chemically equivalent to peroxy links in the structures of constituent minerals. PHPs are introduced by way of hydroxyl (O3Si-OH) incorporated into nominally anhydrous minerals when they crystallize in water-laden environments. Given that sound waves of even relatively low intensity appear to cause PHPs dissociation, thus generating mobile positive holes, it is proposed that microfracturing during rock deformation cause PHP dissociation. Depending on where and how much the rock volume is stressed, the positive holes are expected to form fluctuating charge clouds in the earthquake source region that may account for earthquake-related electrical phenomena and the reported low frequency EM signals.

Freund, Friedemann↗
NASA NTRS2022

Data-driven Expectations for Electromagnetic Counterpart Searches Based on LIGO/Virgo Public Alerts

Searches for electromagnetic counterparts of gravitational-wave signals have redoubled since the first detection in2017 of a binary neutron star merger with a gamma-ray burst, optical/infrared kilonova, and panchromatic after glow. Yet, one LIGO/Virgo observing run later, there has not yet been a second, secure identification of an electromagnetic counterpart. This is not surprising given that the localization uncertainties of events in LIGO and Virgo’s third observing run, O3, were much larger than predicted. We explain this by showing that improvements in data analysis that now allow LIGO/Virgo to detect weaker and hence more poorly localized events have increased the overall number of detections, of which well-localized, gold-plated events make up a smaller proportion overall. We present simulations of the next two LIGO/Virgo/KAGRA observing runs, O4 and O5, that are grounded in the statistics ofO3 public alerts. To illustrate the significant impact that the updated predictions can have, we study the follow-up strategy for the Zwicky Transient Facility. Realistic and timely forecasting of gravitational-wave localization accuracy is paramount given the large commitments of telescope time and the need to prioritize which events are followed up. We include a data release of our simulated localizations as a public proposal planning resource for astronomers

Polina Petrov↗
NASA NTRSDate not supplied

Signal and Power Integrity Design Methodology for High-Performance Flight Computing Systems

Computing capabilities of space systems have in-creased onboard performance by orders of magnitude with the use of radiation-tolerant field-programmable gate arrays (FPGA)and processors. The incorporation of signal and power integrity analysis with printed circuit board (PCB) design in reliable computing architectures for space systems has become critical to enable future mission capabilities. Developers launch high-performance processors into a breadth of orbits and missions, running varying applications that create challenges for designing reliable computing hardware. Specifically, for these designs, academic and industry research has focused on component radiation performance, fault mitigation, and reliable architectures. How-ever, other design parameters including electromagnetic interference (EMI), PCB stackup, signal integrity (SI), voltage regulator module (VRM) design, and power distribution network (PDN)are often deprioritized or disregarded as the design matures. Since these characteristics are becoming more significant in high-performance processor designs, this research presents a hardware design and analysis methodology for high-performance, space-computing systems that focuses on a holistic design approach and PDN reliability. While these challenges exist across all space hardware, the reduced PCB dimensions imposed by SmallSats and CubeSats introduce additional hurdles, specifically to VRM and decoupling design. By examining the relationship between the PDN and radiation performance, an analytical relationship is developed that incorporates Total Ionizing Dose and Single-Event Transients to ensure reliability throughout the mission duration. The presented design methodology is applied to the SpaceCube v3.0 Mini, an FPGA-based on-board science data processing system developed at NASA Goddard Space Flight Center.

Advanced avionics↗
NASA NTRS2012

The Sun and Earth

Thus the Sun forms the basis for life on Earth via the black body radiation it emits. The Sun also emits mass in the form of the solar wind and the coronal mass ejections (CMEs). Mass emission also occurs in the form of solar energetic particles (SEPs), which happens during CMEs and solar flares. Both the mass and electromagnetic energy output of the Sun vary over a wide range of time scales, thus introducing disturbances on the space environment that extends from the Sun through the entire heliosphere including the magnetospheres and ionospheres of planets and moons of the solar system. Although our habitat is located in the neutral atmosphere of Earth, we are intimately connected to the non-neutral space environment starting from the ionosphere to the magnetosphere and to the vast interplanetary space. The variability of the solar mass emissions results in the interaction between the solar wind plasma and the magnetospheric plasma leading to huge disturbances in the geospace. The Sun ionizes our atmosphere and creates the ionosphere. The ionosphere can be severely disturbed by the transient energy input from solar flares and the solar wind during geomagnetic storms. The complex interplay between Earth's magnetic field and the solar magnetic field carried by the solar wind presents varying conditions that are both beneficial and hazardous to life on earth. This seminar presents some of the key aspects of this Sun-Earth connection that we have learned since the birth of space science as a scientific discipline some half a century ago.

Gopalswamy, Natchimuthuk↗
NASA NTRS1987

Nonlinear dynamics of attractive magnetic bearings

The nonlinear dynamics of a ferromagnetic shaft suspended by the force of attraction of 1, 2, or 4 independent electromagnets is presented. Each model includes a state variable feedback controller which has been designed using the pole placement method. The constitutive relationships for the magnets are derived analytically from magnetic circuit theory, and the effects of induced eddy currents due to the rotation of the journal are included using Maxwell's field relations. A rotor suspended by four electro-magnets with closed loop feedback is shown to have nine equilibrium points within the bearing clearance space. As the rotor spin speed increases, the system is shown to pass through a Hopf bifurcation (a flutter instability). Using center manifold theory, this bifurcation can be shown to be of the subcritical type, indicating an unstable limit cycle below the critical speed. The bearing is very sensitive to initial conditions, and the equilibrium position is easily upset by transient excitation. The results are confirmed by numerical simulation.

Hebbale, K. V.↗
NASA NTRS2002

Charge Generation and Propagation in Igneous Rocks

Various electrical phenomena have been reported prior to or concurrent with earthquakes such as resistivity changes, ground potentials, electromagnetic (EM), and luminous signals. Doubts have been raised as to whether some of these phenomena are real and indeed precursory. One of the reasons for uncertainty is that, despite decades of intense work, there is still no physically coherent model. Using low- to medium-velocity impacts to measure electrical signals with microsecond time resolution, it has now been observed that when dry gabbro and diorite cores are impacted at relatively low velocities, approximately 100 m/s, highly mobile charge carriers are generated in a small volume near the impact point. They spread through the rocks, causing electric potentials exceeding +400 mV, EM, and light emission. As the charge cloud spreads, the rock becomes momentarily conductive. When a dry granite block is impacted at higher velocity, approximately 1.5 km/s, the propagation of the P and S waves is registered through the transient piezoelectric response of quartz. After the sound waves have passed, the surface of the granite block becomes positively charged, suggesting the same charge carriers as observed during the low-velocity impact experiments, expanding from within the bulk. During the next 2-3 ms the surface potential oscillates, indicating pulses of electrons injected from ground and contact electrodes. The observations are consistent with positive holes, e.g., defect electrons in the O(2-) sublattice, traveling via the O 2p-dominated valence band of the silicate minerals. Before activation, the positive holes lay dormant in the form of electrically inactive positive hole pairs (PHP), chemically equivalent to peroxy links, O3X/OO\XO3, with X=Si(4+), Al(3+), etc. PHPs are introduced into the minerals by way of hydroxyl,O3X-OH, which all nominally anhydrous minerals incorporate when crystallizing in H2O-laden environments. The fact that positive holes can be activated by low-energy impacts, and their attendant sound waves, suggests that they can also be activated by microfracturing. Depending on where in the stressed rock volume the charge carriers are activated, they will form rapidly moving or fluctuating charge clouds that may account for earthquake-related electrical signals and EM emission. Wherever such charge clouds intersect the surface, high fields are expected, causing electric discharges and earthquake lights.

Freund, Friedemann↗
NASA NTRSDate not supplied

Lightning Instrumentation System

A new comprehensive lightning instrumentation system has been designed for the Mobile Launcher 1 (ML-1) at the Kennedy Space Center, Florida. This new instrumentation system includes the synchronized recording of three B-dot, 3-axis measurement stations, one D-dot sensor and eighteen vehicle measurement channels. Each vehicle measurement channel is comprised of two currents and one voltage measurements. The instrumentation system is composed of centralized transient recorders and digitizers, connected to the transient recorders via fiber optic cables. The transient recorders are triggered by the B-dot or D-dot sensors. When the Space Launch System (SLS) vehicle is present at the ML-1, the transient recorders record data on a dual sampling rate mode, continuous slow 5 kilo-samples per second (per channel) and event driven fast 100 mega-samples per second (per channel). Without the presence of the vehicle at the ML-1, the instrumentation system operates only as an event driven fast 100 mega-samples per second (per channel). In the absence of the vehicle, the only measurements recorded are the B-dot and D-dot stations. Additionally, a portable Lightning Monitoring System (LMS) is temporarily installed inside the Orion Crew Capsule module monitoring one portable B-dot, 3-axis measurement station, and 2 Crew Capsule BUS voltages. The portable LMS has a transient recorder independent of the ML-1 transient recorders, that is triggered by the portable B-dot sensor or transients on the vehicle BUS voltages. This portable instrumentation is removed while performing close out operations before the vehicle launch. For the ML-1 lightning instrumentation system, new custom B-dot and D-dot sensors were designed and prototypes were tested at the International Center for Lightning Research and Testing (ICLRT) at Camp Blanding, Florida. The Ground Special Power (GSP) vehicle measurement channels monitoring on the ML-1 is done via 1) Commercial off-the-shelf (COTS) current shunts and 2) custom Voltage Dividers. The new ML-1 lightning instrumentation system was designed, fabricated, deployed, and tested prior to the summer of 2019, in preparation for the first NASA's SLS mission to be launched from the Launch Complex 39B (LC-39B). The ML-1 lightning instrumentation was designed to complement the LC-39B lightning instrumentation system providing electromagnetic measurements closer to the vehicle, at different heights and inside the Crew capsule module.

Angel G Mata↗
NASA NTRS1989

Countermeasures to microgravity

Biological systems ranging from the most simple to the most complex generally survive exposure to microgravity. Changes in many characteristics of biological systems are well documented as a consequence of space flight. Attempts to devise countermeasures to microgravity may have direct pragmatic consequences for crew protection and may provide additional insights into the nature of microgravity influences on biological systems. Some of the most well documented changes occur in humans who have experienced space flight. Changes appear to be transient. Space adaption syndrome occurs relatively briefly whereas bone deterioration may require months of postflight time for restoration. It seems critical to recognize that these changes and others may derive from rather passive, active or even reactive changes in the biological systems that are hosts to them. For example, hydrostatic fluid redistributions may be quite passive occurrences that are realized through extensive fluid channels. Changes occur in cell metabolism because of fluid, nutrient and gas redistributions. Equally important are the misconstrued messages likely to be carried by fluid redistributions. These reactive events can trigger, for example, loss of fluids and electrolytes through altered kidney function. Each of these considerations must be evaluated in regard to the biological site affected. Countermeasures to the vast range of biological changes and sites are difficult to envision. The most obvious countermeasure is the restoration of gravity-like influences. Some options are discussed. Recent work has focussed on the use of magnetic fields. Pulsed electromagnetic fields (PEMF) are shown to alleviate bone deterioration produced in rodents exposed to tail suspension. Methods of PEMF exposure are consistent with human use in space. Related methods may provide muscular and neural benefits.

Luttges, Marvin W.↗
NASA NTRS2021

Direct Multipoint Observations Capturing the Reformation of a Supercritical Fast Magnetosonic Shock

Using multipoint Magnetospheric Multiscale (MMS) observations in an unusual string-of-pearls configuration, we examine in detail observations of the reformation of a fast magnetosonic shock observed on the upstream edge of a foreshock transient structure upstream of Earth’s bow shock. The four MMS spacecraft were separated by several hundred km, comparable to suprathermal ion gyro-radius scales or several ion inertial lengths. At least half of the shock reformation cycle was observed, with a new shock ramp rising up out of the “foot” region of the original shock ramp. Using the multipoint observations, we convert the observed time-series data into distance along the shock normal in the shock’s rest frame. That conversion allows for a unique study of the relative spatial scales of the shock’s various features, including the shock’s growth rate, and how they evolve during the reformation cycle. Analysis indicates that: the growth rate increases during reformation, electron-scale physics play an important role in the shock reformation, and energy conversion processes also undergo the same cyclical periodicity as reformation. Strong, thin electron-kinetic-scale current sheets and large-amplitude electrostatic and electromagnetic waves are reported. Evidence is also presented of nonlinear wave decay from electromagnetic whistler-mode “lion roars” to electrostatic solitary waves in the downstream plasma regime. Results highlight the critical cross-scale coupling between electron-kinetic-and ion-kinetic-scale processes and details of the nature of nonstationarity, shock-front reformation at collisionless, fast magnetosonic shocks.

D L Turner↗
NASA NTRS2010

JWST Planetary Observations Within the Solar System

JWST provides capabilities unmatched by other telescopic facilities in the near to mid infrared part of the electromagnetic spectrum. Its combination of broad wavelength range, high sensitivity and near diffraction-limited imaging around two microns wavelength make it a high value facility for a variety of Solar System targets. Beyond Neptune, a class of cold, large bodies that include Pluto, Triton and Eris exhibits surface deposits of nitrogen, methane, and other molecules that are poorly observed from the ground, but for which JWST might provide spectral mapping at high sensitivity and spatial resolution difficult to match with the current generation of ground-based observatories. The observatory will also provide unique sensitivity in a variety of near and mid infrared windows for observing relatively deep into the atmospheres of Uranus and Neptune, searching there for minor species. It will examine the Jovian aurora in a wavelength regime where the background atmosphere is dark. Special provision of a subarray observing strategy may allow observation of Jupiter and Saturn over a larger wavelength range despite their large surface brightnesses, allowing for detailed observation of transient phenomena including large scale storms and impact-generation disturbances. JWST's observations of Saturn's moon Titan will overlap with and go beyond the 2017 end-of-mission for Cassini, providing an important extension to the time-series of meteorological studies for much of northern hemisphere summer. It will overlap with a number of other planetary missions to targets for which JWST can make unique types of observations. JWST provides a platform for linking solar system and extrasolar planet studies through its unique observational capabilities in both arenas.

Lunine, Jonathan↗
NASA NTRS2016

Properties of the Binary Black Hole Merger GW150914

On September 14, 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected a gravitational-wave transient (GW150914); we characterize the properties of the source and its parameters. The data around the time of the event were analyzed coherently across the LIGO network using a suite of accurate waveform models that describe gravitational waves from a compact binary system in general relativity. GW150914 was produced by a nearly equal mass binary black hole of masses 36(+5/-4) solar mass and 29(+4/-4) solar mass; for each parameter we report the median value and the range of the 90% credible interval. The dimensionless spin magnitude of the more massive black hole is bound to be less than 0.7 (at 90% probability). The luminosity distance to the source is 410(+160/-180) Mpc, corresponding to a redshift 0.09(+0.03/−0.04) assuming standard cosmology. The source location is constrained to an annulus section of 610 sq deg, primarily in the southern hemisphere. The binary merges into a black hole of mass 62(+4/−4) solar mass and spin 0.67(+0.05/−0.07). This black hole is significantly more massive than any other inferred from electromagnetic observations in the stellar-mass regime.

Abbott, B. P.↗
NASA NTRS2020

The Zwicky Transient Facility Bright Transient Survey. I. Spectroscopic Classification and the Redshift Completeness of Local Galaxy Catalogs

The Zwicky Transient Facility (ZTF) is performing a three-day cadence survey of the visible northern sky (∼3π) with newly found transient candidates announced via public alerts. The ZTF Bright Transient Survey (BTS) is a large spectroscopic campaign to complement the photometric survey. BTS endeavors to spectroscopically classify all extragalactic transients with m(peak) ≤ 18.5 mag in either the g(ZTF) or r(ZTF) filters, and publicly announce said classifications. BTS discoveries are predominantly supernovae (SNe), making this the largest flux-limited SN survey to date. Here we present a catalog of 761 SNe, classified during the first nine months of ZTF (2018 April 1–2018 December 31). We report BTS SN redshifts from SN template matching and spectroscopic host-galaxy redshifts when available. We analyze the redshift completeness of local galaxy catalogs, the redshift completeness fraction (RCF; the ratio of SN host galaxies with known spectroscopic redshift prior to SN discovery to the total number of SN hosts). Of the 512 host galaxies with SNe Ia, 227 had previously known spectroscopic redshifts, yielding an RCF estimate of 44% ± 4%. The RCF decreases with increasing distance and decreasing galaxy luminosity (for z < 0.05, or ∼200 Mpc, RCF ≈ 0.6). Prospects for dramatically increasing the RCF are limited to new multifiber spectroscopic instruments or wide-field narrowband surveys. Existing galaxy redshift catalogs are only ∼50% complete at r ≈ 16.9 mag. Pushing this limit several magnitudes deeper will pay huge dividends when searching for electromagnetic counterparts to gravitational wave events or sources of ultra-high-energy cosmic rays or neutrinos.

C. Fremling↗
NASA NTRS2021

Gravitational-Wave Physics and Astronomy in the 2020s and 2030s

The 100 years since the publication of Albert Einstein’s theory of General Relativity saw significant development of the understanding of the theory, the identification of potential astrophysical sources of sufficiently strong gravitational waves, and development of key technologies for gravitational-wave detectors. In 2015, the first gravitational wave signals were detected by the two US Advanced LIGO instruments. In 2017, Advanced LIGO and the European Advanced Virgo detectors pinpointed a binary neutron star coalescence that was also seen across the electromagnetic spectrum. The field of gravitational wave astronomy is just starting, and this Roadmap of future developments surveys the potential for growth in bandwidth and sensitivity of future gravitational-wave detectors and discusses the science results anticipated to come from upcoming instruments.

Compact astrophysical objects↗
NASA NTRS2016

Prospects for Observing and Localizing Gravitational-Wave Transients with Advanced LIGO and Advanced Virgo

We present a possible observing scenario for the Advanced LIGO and Advanced Virgo gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We determine the expected sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron-star systems, which are considered the most promising for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5 sq. deg to 20 sq. deg will require at least three detectors of sensitivity within a factor of approximately 2 of each other and with a broad frequency bandwidth. Should the third LIGO detector be relocated to India as expected, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.

counterparts↗
NASA NTRS2003

Development of Numerical Codes for Modeling Electromagnetic Behavior at High Frequencies Near Large Objects

A study into the problem of determining electromagnetic solutions at high frequencies for problems involving complex geometries, large sizes and multiple sources (e.g. antennas) has been initiated. Typical applications include the behavior of antennas (and radiators) installed on complex conducting structures (e.g. ships, aircrafts, etc..) with strong interactions between antennas, the radiation patterns, and electromagnetic signals is of great interest for electromagnetic compatibility control. This includes the overall performance evaluation and control of all on-board radiating systems, electromagnetic interference, and personnel radiation hazards. Electromagnetic computational capability exists at NASA LaRC, and many of the codes developed are based on the Moment Method (MM). However, the MM is computationally intensive, and this places a limit on the size of objects and structures that can be modeled. Here, two approaches are proposed: (i) a current-based hybrid scheme that combines the MM with Physical optics, and (ii) an Alternating Direction Implicit-Finite Difference Time Domain (ADI-FDTD) method. The essence of a hybrid technique is to split the overall scattering surface(s) into two regions: (a) a MM zone (MMZ) which can be used over any part of the given geometry, but is most essential over irregular and "non-smooth" geometries, and (b) a PO sub-region (POSR). Currents induced on the scattering and reflecting surfaces can then be computed in two ways depending on whether the region belonged to the MMZ or was part of the POSR. For the MMZ, the current calculations proceed in terms of basis functions with undetermined coefficients (as in the usual MM method), and the answer obtained by solving a system of linear equations. Over the POSR, conduction is obtained as a superposition of two contributions: (i) currents due to the incident magnetic field, and (ii) currents produced by the mutual induction from conduction within the MMZ. This effectively leads to a reduction in the size of linear equations from N to N - Npo with N being the total number of segments for the entire surface and Npo the number of segments over the POSR. The scheme would be appropriate for relatively large, flat surfaces, and at high frequencies. The ADI-FDTD scheme provides for both transient and steady state analyses. The restrictive Courant-Friedrich-Levy (CFL) condition on the time-step is removed, and so large time steps can be chosen even though the spatial grids are small. This report includes the problem definition, a detailed discussion of both the numerical techniques, and numerical implementations for simple surface geometries. Numerical solutions have been derived for a few simple situations.

Joshi, R. P.↗