Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “field”

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 253 records · Page 14

Optimized perturbation theory for charged scalar fields at finite temperature and in an external magnetic field

Symmetry restoration in a theory of a self-interacting charged scalar field at finite temperature and in the presence of an external magnetic field is examined. The effective potential is evaluated nonperturbatively in the context of the optimized perturbation theory method. It is explicitly shown that in all ranges of the magnetic field, from weak to large fields, the phase transition is second order and that the critical temperature increases with the magnetic field. In addition, we present an efficient way to deal with the sum over the Landau levels, which is of interest especially in the case of working with weak magnetic fields.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Generalized framework for likelihood-based field-level inference of growth rate from velocity and density fields

Measuring the growth rate of large-scale structures ( f ) as a function of redshift has the potential to break degeneracies between modified gravity and dark energy models, when combined with expansion-rate probes. Direct estimates of peculiar velocities of galaxies have attracted interest as a means of estimating fσ 8 . In particular, field-level methods can be used to fit the field nuisance parameter along with cosmological parameters simultaneously. This article aims to provide the community with a unified framework for the theoretical modeling of the likelihood-based field-level inference by performing fast field covariance calculations for velocity and density fields. Our purpose is to lay the foundations for a nonlinear extension of the likelihood-based method at the field level. We have developed a generalized framework, implemented in the dedicated software flip to perform a likelihood-based inference of fσ 8 . We derived a new field covariance model, which includes wide-angle corrections. We also included the models previously described in the literature inside our framework. We compared their performance against ours, and we validated our model by comparing it with the two-point statistics of a recent N-body simulation. The tests we performed have allowed us to validate our software and determine the appropriate wavenumber range to integrate our covariance model and its validity in terms of separation. Our framework allows for a wider wavenumber coverage to be used in our calculations than in previous works, which is particularly interesting for nonlinear model extensions. Finally, our generalized framework allows us to efficiently perform a survey geometry-dependent Fisher forecast of the fσ 8 parameter. We show that the Fisher forecast method we developed gives an error bar that is 30% closer to a full likelihood-based estimation than a standard volume Fisher forecast.

Ravoux, Corentin↗

Electric field dependent local structure of ( K x N a 1 - x ) 0.5 B i 0.5 Ti O 3

The in situ x-ray pair-distribution function (PDF) characterization technique has been used to study the behavior of (K x Na 1–x ) 0.5 Bi 0.5 TiO 3 , as a function of electric field. As opposed to conventional x-ray Bragg diffraction techniques, PDF is sensitive to local atomic displacements, detecting local structural changes at the angstrom to nanometer scale. Several field-dependent ordering mechanisms can be observed in x = 0.15, 0.18 and at the morphotropic phase boundary composition x = 0.20. X-ray total scattering shows suppression of diffuse scattering with increasing electric-field amplitude, indicative of an increase in structural ordering. Analysis of PDF peaks in the 3–4-Å range shows ordering of Bi-Ti distances parallel to the applied electric field, illustrated by peak amplitude redistribution parallel and perpendicular to the electric-field vector. A transition from < 110 > to < 112 >-type off-center displacements of Bi relative to the neighboring Ti atoms is observable with increasing x. Analysis of PDF peak shift with electric field shows the effects of Bi-Ti redistribution and onset of piezoelectric lattice strain. Furthermore, the combination of these field-induced ordering mechanisms is consistent with local redistribution of Bi-Ti distances associated with domain reorientation and an overall increase in order of atomic displacements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Robust non-Abelian spin liquid and a possible intermediate phase in the antiferromagnetic Kitaev model with magnetic field

In this work, we investigate the non-Abelian topological chiral spin-liquid phase in the two-dimensional Kitaev honeycomb model subject to a magnetic field. By combining density matrix renormalization group and exact diagonalization we study the energy spectra, entanglement, topological degeneracy, and expectation values of Wilson loop operators, allowing for a robust characterization. While the ferromagnetic Kitaev spin liquid is already destroyed by a weak magnetic field with Zeeman energy $H^{FM}_\ast ≈ 0.02$, the antiferromagnetic (AFM) spin liquid remains robust up to a magnetic field that is an order of magnitude larger, $H^{AFM}_\ast ≈ 0.2$. Interestingly, for larger fields $H^{AFM}_\ast < H < H^{AFM}_{\ast\ast}$, an intermediate gapless phase is observed, before a second transition to the high-field partially polarized paramagnet. We attribute this rich phase diagram, and the remarkable stability of the chiral topological phase in the AFM Kitaev model, to the interplay of strong spin-orbit coupling and frustration enhanced by the magnetic field. Our findings suggest relevance to recent experiments on RuCl 3 under magnetic fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Field Study of Nighttime Leakage Currents in Bifacial PV Modules: Correlation with Atmospheric Electric Field Data

Leakage currents measured on PV modules in the field originate from a potential difference between the modules' frame and the cells. They can be a relative indicator of Potential-Induced Degradation (PID) severity, especially when comparing the same module design in a different environment. As modules are not operating at night, no leakage current should be observed but our team has reported several events of nighttime leakage currents on bifacial PV modules. These events have been firstly observed during a thunderstorm that are characterized by strong atmospheric electrical field values. This lead us to believe that nighttime leakage currents could originate from the atmospheric electric charges. In this paper, we correlate nighttime leakage currents measured on bifacial PV modules with field mill data to identify the origin of nighttime leakage currents. Our results show that so far, no leakage currents at night occur when the atmospheric electric field is between 0 and 150–200 V/m (standard value for fair weather). As soon as the atmospheric electric field is out of this range, leakage currents are observed with or without rain involved. This suggests a transport of charged particles from the atmosphere to the modules' frame. A combination of heavy rain with strong atmospheric electric field results into high nighttime leakage currents with a magnitude up to 8 times higher than what observed during the day with -1500V applied. This is explained by an easier transport of the charged particles through the water droplets. Based on these results, leakage currents observed during the day might not be only due to the inherent potential difference between the frame and the cells depending on the atmospheric electric field activity. We believe that it should be taken into account in PID studies.

14 SOLAR ENERGY↗

SU-E-T-404: Simple Field-In-Field Technique for Total Body Irradiation in Large Patients

Purpose: A simple Field-in-Field technique for Total Body Irradiation (TBI) was developed for traditional AP/PA TBI treatments to improve dosimetric uniformity in patients with large separation. Methods: TBI at our institution currently utilizes an AP/PA technique at an extended source-to-surface distance (SSD) of 380cm with patients in left decubitus position during the AP beam and in right decubitus during the PA beam. Patients who have differences in thickness (separation) between the abdomen and head greater than 10cm undergo CT simulation in both left and right decubitus treatment positions. One plan for each CT is generated to evaluate dose to patient midline with both AP and PA fields, but only corresponding AP fields will be exported for treatment for patient left decubitus position and PA fields for patient right decubitus position. Subfields are added by collimating with the x-ray jaws according to separation changes at 5–7% steps to minimize hot regions to less than 10%. Finally, the monitor units (MUs) for the plans are verified with hand calculation and water phantom measurements. Results: Dose uniformity (+/−10%) is achieved with field-in-field using only asymmetric jaws. It is dosimetrically robust with respect to minor setup/patient variations inevitable due to patient conditions. MUs calculated with Pinnacle were verified in 3 clinical cases and only a 2% difference was found compared to homogeneous calculation. In-vivo dosimeters were also used to verify doses received by each patient with and confirmed dose variations less than 10%. Conclusion: We encountered several cases with separation differences that raised uniformity concerns — based on a 1% dose difference per cm separation difference assumption. This could Resultin an unintended hot spot, often in the head/neck, up to 25%. This method allows dose modulation without adding treatment complexity nor introducing radiobiological variations, providing a reasonable solution for this unique TBI situation.

60 APPLIED LIFE SCIENCES↗

SU-F-J-55: Feasibility of Supraclavicular Field Treatment by Investigating Variation of Junction Position Between Breast Tangential and Supraclavicular Fields for Deep Inspiration Breath Hold (DIBH) Left Breast Radiation

Purpose: To explore the feasibility of supraclavicular field treatment by investigating the variation of junction position between tangential and supraclavicular fields during left breast radiation using DIBH technique. Methods: Six patients with left breast cancer treated using DIBH technique were included in this study. AlignRT system was used to track patient’s breast surface. During daily treatment, when the patient’s DIBH reached preset AlignRT tolerance of ±3mm for all principle directions (vertical, longitudinal, and lateral), the remaining longitudinal offset was recorded. The average with standard-deviation and the range of daily longitudinal offset for the entire treatment course were calculated for all six patients (93 fractions totally). The ranges of average ± 1σ and 2σ were calculated, and they represent longitudinal field edge error with the confidence level of 68% and 95%. Based on these longitudinal errors, dose at junction between breast tangential and supraclavicular fields with variable gap/overlap sizes was calculated as a percentage of prescription (on a representative patient treatment plan). Results: The average of longitudinal offset for all patients is 0.16±1.32mm, and the range of longitudinal offset is −2.6 to 2.6mm. The range of longitudinal field edge error at 68% confidence level is −1.48 to 1.16mm, and at 95% confidence level is −2.80 to 2.48mm. With a 5mm and 1mm gap, the junction dose could be as low as 37.5% and 84.9% of prescription dose; with a 5mm and 1mm overlap, the junction dose could be as high as 169.3% and 117.6%. Conclusion: We observed longitudinal field edge error at 95% confidence level is about ±2.5mm, and the junction dose could reach 70% hot/cold between different DIBH. However, over the entire course of treatment, the average junction variation for all patients is within 0.2mm. The results from our study shows it is potentially feasible to treat supraclavicular field with breast tangents.

60 APPLIED LIFE SCIENCES↗

Magnetic Field Penetration Technique to Study High Field Shielding of Multilayered Superconductors

The SIS structure which consists of alternative thin layers of superconductors and insulators on a bulk niobium has been proposed to shield niobium cavity surface from high magnetic field and hence increase the accelerating gradient. The study of the behavior of multilayer super-conductors in an external magnetic field is essential to optimize their SRF performance. In this work we report the development of a simple and efficient technique to measure penetration of magnetic field into bulk, thin film and multilayer superconductors. Experimental setup contains a small superconducting solenoid which can produce a parallel surface magnetic field up to 0.5 T and Hall probes to detect penetrated magnetic field across the superconducting sample. This system was calibrated and used to study the effect of niobium sample thickness on the field of full magnetic flux penetration. We determined the optimum thickness of the niobium substrate to fabricate the multilayer structure for the measurements in our setup. This technique was used to measure penetration fields of Nb₃Sn thin films and Nb₃Sn/Al₂O₃ multi-layers deposited on Al₂O₃ wafers.

Senevirathne, I. H.↗

Small Scale Field Test Demonstrating CO 2 Sequestration In Arbuckle Saline Aquifer And By CO 2 -Eor At Wellington Field, Sumner County, Kansas

The objectives of this project are to understand the processes that occur when a maximum of 70,000 metric tonnes of CO 2 are injected into two different formations to evaluate the response in different lithofacies and depositional environments. The evaluation will be accomplished through the use of both in situ and indirect MVA (monitoring, verification, and accounting) technologies. The project will optimize for carbon storage accounting for 99% of the CO 2 using lab and field testing and comprehensive characterization and modeling techniques. Site characterization and CO 2 injection should demonstrate state-of-the-art MVA tools and techniques to monitor and visualize the injected CO 2 plume and to refine geomodels developed using nearly continuous core, exhaustive wireline logs, and well tests and a multi-component 3-D seismic survey. Reservoir simulation studies will map the injected CO 2 plume and estimate tonnage of CO 2 stored in solution, as residual gas, and by mineralization and integrate MVA results and reservoir models shall be used to evaluate CO 2 leakage. A rapid-response mitigation plan was developed to minimize CO 2 leakage and provide a comprehensive risk management strategy. The CO 2 was intended to be supplied from a reliable facility and have an adequate delivery and quality of CO 2 . However, several unforeseen circumstances complicated this plan: (1) the initially negotiated CO 2 supply facility went offline and contracts associated with CO 2 supply had to be renegotiated, (2) a UIC Class VI permit proved to be difficult to obtain due to the experimental nature of the project. Both subjects are detailed in separate deliverables attached to this report. The CO 2 enhanced oil recovery (EOR) and geologic storage in Mississippian carbonate reservoir was sucessully deployed. Approximately 20,000 metric tons of CO 2 was injected in the upper part of the Mississippian reservoir to verify CO 2 EOR viability in carbonate reservoirs and evaluate a potential of transitioning to geologic CO 2 storage through EOR. A total of 1,101 truckloads, 19,803 metric tons—an average of 120 tonnes per day—were delivered over the course of injection that lasted from January 9 to June 21, 2016. After cessation of CO 2 injection, the KGS 2-32 well was converted to water injector and continues to operate. CO 2 EOR progression in the field was monitored weekly with fluid level, temperature, and production recording and formation fluid composition sampling. It is important to note that normally, CO 2 EOR pilots are less efficient than commercial operations due to lack of directional and precise well control, lack of surface facilities for CO 2 recycling, and other factors. As a result of this pilot CO 2 injection, the observed incremental average oil production increase was ~68% with only ~18% of injected CO 2 produced back. Decline curve analysis forecasts of additional cumulative oil produced were 32.44M STB to the end of 2027. Wellington Mississippian pilot efficiency by the end of forecast calculations is 11 MCF per barrel of produced oil. Using 32M STB oil production and $1,964,063 cost of CO 2 , CO 2 EOR cost per barrel of oil production is ~$60. Simple but robust monitoring technologies proved to be very efficient in detecting and locating CO 2 . High CO 2 reservoir retentions with low yields within an actively producing field could help to estimate real-world risks of CO 2 geological storage for future projects. The Wellington Field CO 2 EOR was executed in a controlled environment with high efficiency. This case study proves that CO 2 EOR could be successfully applied in Kansas carbonate reservoirs if CO 2 sources and associated infrastructure are available. Recent developments in unconventional resources development in Mid-Continent USA and associated large volume disposal of backflow water and the resulting seismic activity have brought more focus and attention to the Arbuckle Group in southern Kansas. Despite the commercial interest, limited essential information about reservoir properties and structural elements has impeded the management and regulation of disposal, an issue brought to the forefront by recent seismicity in and near areas of large volumes and rates of brine disposal. The Kansas Geological Survey (KGS) collected, compiled, and analyzed available data, including well logs, core data, step rate tests, drill stem tests, 2-D and 3-D seismic data, water level measurements, and others types of data. Several exploratory wells were drilled and core was collected and modern suites of logs were analyzed. Reservoir properties were populated into several site-specific geological models. The geological models illustrate the highly heterogeneous nature of the Arbuckle Group. Vertical and horizontal variability results in several distinct hydro-stratigraphic units that are the result of both depositional and diagenetic processes. During the course of this project, it has been demonstrated that advanced seismic interpretation methods can be used successfully for characterization of the Mississippian reservoir and Arbuckle saline aquifer. Analysis of post-stack 3-D seismic data at the Mississippian reservoir showed the response of a gradational velocity transition. Pre-stack gather analysis showed that porosity zones of the Mississippian and Arbuckle reservoirs exhibit characteristic amplitude versus offset (AVO) response. Simultaneous AVO inversion estimated P- and S-impedances. The 3-D survey gather azimuthal anisotropy analysis (AVAZ) provided information about the fault and fracture network and showed good agreement to the regional stress field and well data. Mississippian reservoir porosity and fracture predictions agreed well with the observed mobility of injected CO 2 in KGS well 2-32. Fluid substitution modeling predicted acoustic impedance reduction in the Mississippian carbonate reservoir introduced by the presence of CO 2 . Seismicity in the United States midcontinent has increased by orders of magnitude over the past decade. Spatiotemporal correlations of seismicity to wastewater injection operations have suggested that injection-related pore fluid pressure increases are inducing the earthquakes. In this investigation, we examine earthquake occurrence in southern Kansas and northern Oklahoma and its relation to the change in pore pressure. The main source of data comes from the Wellington Array in the Wellington oil field, in Sumner County, Kansas, which has monitored for earthquakes in central Sumner County, Kansas, since early 2015. The seismometer array was established to monitor CO 2 injection operations at Wellington Field. Although no seismicity was detected in association with the spring 2016 Mississippian CO 2 injection, the array has recorded more than 2,500 earthquakes in the region and is providing valuable understanding to induced seismicity. A catalog of earthquakes was built from this data and was analyzed for spatial and temporal changes, stress information, and anisotropy information. The region of seismic concern has been shown to be expanding through use of the Wellington earthquake catalog, which has revealed a northward progression of earthquake activity reaching the metropolitan area of Wichita. The stress orientation was also calculated from this earthquake catalog through focal mechanism inversion. The calculated stress orientation was confirmed through comparison to other stress measurements from well data and previous earthquake studies in the region. With this knowledge of the stress orientation, the anisotropy in the basement could be understood. This allowed for the anisotropy measurements to be correlated to pore pressure increases. The increase in pore pressure was monitored through time-lapse shear-wave anisotropy analysis. Since the onset of the observation period in 2010, the orientation of the fast shear wave has rotated 90°, indicating a change associated with critical pore pressure build up. The time delay between fast and slow shear wave arrivals has increased, indicating a corresponding increase in anisotropy induced by pore pressure rise. In-situ near-basement fluid pressure measurements corroborate the continuous pore pressure increase revealed by the shear-wave anisotropy analysis over the earthquake monitoring period. This research is the first to identify a change in pore fluid pressure in the basement using seismological data and it was recently published in the AAAS journal Science Advances (Nolte et al., 2017). The shear-wave splitting analysis is a novel application of the technique, which can be used in other regions to identify an increase in pore pressure. This increasing pore fluid pressure has become more regionally extensive as earthquakes are occurring in southern Kansas, where they previously were absent. These monitoring techniques and analyses provide new insight into mitigating induced seismicity’s impact on society.

02 PETROLEUM↗

Displacement Analysis of Geothermal Field Based on PSInSAR And SOM Clustering Algorithms A Case Study of Brady Field, Nevada—USA

The availability of free and high temporal resolution satellite data and advanced SAR techniques allows us to analyze ground displacement cost-effectively. Our aim was to properly define subsidence and uplift areas to delineate a geothermal field and perform time-series analysis to identify temporal trends. A Persistent Scatterer Interferometry (PSI) algorithm was used to estimate vertical displacement in the Brady geothermal field located in Nevada by analyzing 70 Sentinel-1A Synthetic-Aperture Radar (SAR) images, between January 2017 and December 2019. To classify zones affected by displacement, an unsupervised Self-Organizing Map (SOM) algorithm was applied to classify points based on their behavior in time, and those clusters were used to determine subsidence, uplift, and stable regions automatically. Finally, time-series analysis was applied to the clustered data to understand the inflection dates. The maximum subsidence is –19 mm/yr with an average value of –6 mm/yr within the geothermal field. The maximum uplift is 14 mm/yr with an average value of 4 mm/yr within the geothermal field. The uplift occurred on the NE of the field, where the injection wells are located. On the other hand, subsidence is concentrated on the SW of the field where the production wells are located. The coupling of the PSInSAR and the SOM algorithms was shown to be effective in analyzing the direction and pattern of the displacements observed in the field.

54 ENVIRONMENTAL SCIENCES↗

Demonstrating magnetic field robustness and reducing temporal T1 noise in transmon qubits through magnetic field engineering

The coherence of superconducting transmon qubits is often disrupted by fluctuations in the energy relaxation time (T1), limiting their performance for quantum computing. While background magnetic fields can be harmful to superconducting devices, we demonstrate that both trapped magnetic flux and externally applied static magnetic fields can suppress temporal fluctuations in T1 without significantly degrading its average value or qubit frequency. Using a three-axis Helmholtz coil system, we applied calibrated magnetic fields perpendicular to the qubit plane during cooldown and operation. Remarkably, transmon qubits based on tantalum-capped niobium (Nb/Ta) capacitive pads and aluminum-based Josephson junctions (JJs) maintained T1 lifetimes near 300 μs even when cooled in fields as high as 600 mG. Both trapped flux up to 600 mG and applied fields up to 400 mG reduced T1 fluctuations by more than a factor of two, while higher field strengths caused rapid coherence degradation. We attribute this stabilization to the polarization of paramagnetic impurities, the role of trapped flux as a sink for non-equilibrium quasiparticles (QPs), and partial saturation of fluctuating two-level systems (TLSs). These findings challenge the conventional view that magnetic fields are inherently detrimental and introduce a strategy for mitigating noise in superconducting qubits, offering a practical path toward more stable and scalable quantum systems.

Abdisatarov, Bektur [Fermilab; Jefferson Lab]↗

Polar cap electric field distributions related to the interplanetary magnetic field direction

The correlations between the azimuthal direction of the interplanetary magnetic field and the most simple polar cap signatures are discussed. Only the spatial distribution of the dawn-dusk polar cap field is considered. For each OGO 6 traverse across the northern or southern polar cap, the simultaneous values of the interplanetary magnetic field in solar-equatorial coordinates were recorded by the Explorer 33 magnetometer. Histograms of these values are presented and are discussed. The high degree of correlation with the longitudinal angle indicates that the relative geometry of the interplanetary magnetic field and magnetospheric magnetic fields must be fundamental to explaining the distribution of polar cap electric fields. The sign of the solar-equatorial component perpendicular to the sun-earth line appears to be a more critical parameter than the sign of the component toward the sun. The Svalgaard-Mansurov correlation and the correspondence between fast convection and parallel magnetospheric and interplanetary magnetic fields are described.

Heppner, J. P.↗

Simultaneous particle and field observations of field-aligned currents

Simultaneous measurements of low energy precipitating electrons and magnetic fluctuations from the low altitude polar orbiting satellite OGO-4 have been compared. Analysis of the two sets of experimental data for isolated events led to the classification of high latitude field-aligned currents as purely temporal or purely spatial variations. Magnetic field disturbances calculated using these simple current models and the measured particle fluxes were in good agreement with measured field values. While fluxes of greater than 1 keV electrons are detected primarily on the nightside, magnetometer disturbances indicative of field-aligned currents were seen at all local times, both in the visual auroral regions and dayside polar cusp. Thus electrons with energies less than approximately 1 keV are the prime charge carriers in high latitude dayside field-aligned currents. The satellite measurements are in good agreement with previously measured field-aligned current values and with values predicted from several models involving magnetospheric field-aligned currents.

Berko, F. W.↗

Relation between near field and far field acoustic measurements

Several approaches to the problem of determining the far field directivity of an acoustic source located in a reverberant environment, such as a wind tunnel, are investigated analytically and experimentally. The decrease of sound pressure level with distance is illustrated; and the spatial extent of the hydrodynamic and geometric near fields, the far field, and the reverberant field are described. A previously-prosposed analytical technique for predicting the far field directivity of the acoustic source on the basis of near field data is investigated. Experiments are conducted with small acoustic sources and an analysis is performed to determine the variation with distance from the source of the directionality of the sound field. A novel experiment is conducted in which the sound pressure measured at various distances from an acoustic driver located in the NASA Ames 40 x 80 ft wind tunnel is crosscorrelated with the driver excitation voltage.

Bies, D. A.↗

Hydraulic concentration of magnetic fields in the solar photosphere. III - Fields of one or two kilogauss

Detailed analysis of weak and strong lines suggests that the magnetic fields in isolated intense flux tubes in supergranule boundaries in the solar photosphere may be as large as 2000 gauss. This paper is a concise systematic review of hydrodynamic effects that might compress a magnetic field to great intensity. The properties of force-free fields are reviewed to show that they do not contribute to concentration of magnetic fields, in spite of the popular notion to the contrary. Of the seven effects considered, it is concluded that only cooling of the gas within the field can produce the high field densities inferred from observation. It is shown that inhibition of convection appears not to possess the necessary qualitative cooling features and that overstability, generating transverse hydromagnetic waves - essentially Alfven waves - is the only way to account for the cooling and field intensification.

Parker, E. N.↗

Spatial power spectra of the crustal geomagnetic field and core geomagnetic field

Equations providing numerical values of the geomagnetic field spherical harmonic spatial power spectrum as defined by Lowes (1966, 1974) are obtained and this power spectrum is related to various other power spectra. Equations relating the spherical harmonic spatial power spectrum to average great circle power spectra for components of the vector magnetic field in the radial direction, along the great circle track and perpendicular to the first two directions are derived under the assumption that the sources of the field are internal. A statistical model for the crustal and core geomagnetic fields is proposed and used to derive equations for the expected main and crustal spherical harmonic power spectra. The model equations are then compared with observations to determine a scale factor which is then used to obtain an estimate for the core radius and a great circle power spectrum for the field component perpendicular to the great circle and radial directions which are in good agreement with observations. The predicted spherical harmonic power spectrum for the crustal field is found to be consistent with POGO satellite and aircraft data. Other possible models for the crustal and core geomagnetic fields are also briefly considered.

Mcleod, M. G.↗

The electromagnetic force field, fluid flow field and temperature profiles in levitated metal droplets

A mathematical representation was developed for the electromagnetic force field, the flow field, the temperature field (and for transport controlled kinetics), in a levitation melted metal droplet. The technique of mutual inductances was employed for the calculation of the electromagnetic force field, while the turbulent Navier - Stokes equations and the turbulent convective transport equations were used to represent the fluid flow field, the temperature field and the concentration field. The governing differential equations, written in spherical coordinates, were solved numerically. The computed results were in good agreement with measurements, regarding the lifting force, and the average temperature of the specimen and carburization rates, which were transport controlled.

El-Kaddah, N.↗