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NASA NTRS2001

Geomagnetic Cutoff Rigidity Computer Program: Theory, Software Description and Example

The access of charged particles to the earth from space through the geomagnetic field has been of interest since the discovery of the cosmic radiation. The early cosmic ray measurements found that cosmic ray intensity was ordered by the magnetic latitude and the concept of cutoff rigidity was developed. The pioneering work of Stoermer resulted in the theory of particle motion in the geomagnetic field, but the fundamental mathematical equations developed have 'no solution in closed form'. This difficulty has forced researchers to use the 'brute force' technique of numerical integration of individual trajectories to ascertain the behavior of trajectory families or groups. This requires that many of the trajectories must be traced in order to determine what energy (or rigidity) a charged particle must have to penetrate the magnetic field and arrive at a specified position. It turned out the cutoff rigidity was not a simple quantity but had many unanticipated complexities that required many hundreds if not thousands of individual trajectory calculations to solve. The accurate calculation of particle trajectories in the earth's magnetic field is a fundamental problem that limited the efficient utilization of cosmic ray measurements during the early years of cosmic ray research. As the power of computers has improved over the decades, the numerical integration procedure has grown more tractable, and magnetic field models of increasing accuracy and complexity have been utilized. This report is documentation of a general FORTRAN computer program to trace the trajectory of a charged particle of a specified rigidity from a specified position and direction through a model of the geomagnetic field.

Smart, D. F.↗

NASA NTRS1978

Energetic secondary electrons and the nonthermal galactic radio background - A probe of the magnetic field in interstellar clouds

A previous analysis of the manifestations of charged-pion-decay secondary electrons in interstellar cloud material is extended to include those contributions to the Galactic radio and soft gamma-ray backgrounds that are directly attributable to energetic secondaries. The equilibrium distribution of secondary electrons in dense interstellar clouds is calculated, synchrotron emissivity from isolated interstellar clouds is examined, and it is shown how the value of the magnetic field in these clouds may be determined by observing the radio emission in their directions. The contribution that such clouds make to the integrated radio background is evaluated, and the Galactic distribution of bremsstrahlung gamma rays that arise from interactions of secondary electrons with thermal material in dense clouds is computed. The results indicate that a magnetic field of no more than 80 microgauss is characteristic of dense clouds and that the integrated synchrotron radiation from secondary electrons in interstellar clouds will contribute a significant fraction of the nonthermal brightness along the Galactic equator even if the mean cloud field is as low as 35 microgauss.

Marscher, A. P.↗

NASA NTRS1989

A high efficiency motor/generator for magnetically suspended flywheel energy storage system

The authors discuss the theory and design of a brushless direct current motor for use in a flywheel energy storage system. The motor design is optimized for a nominal 4.5-in outside diameter operating within a speed range of 33,000-66,000 revolutions per minute with a 140-V maximum supply voltage. The equations which govern the motor's operation are used to compute a series of acceptable design parameter combinations for ideal operation. Engineering tradeoffs are then performed to minimize the irrecoverable energy loss while remaining within the design constraint boundaries. A final integrated structural design whose features allow it to be incorporated with the 500-Wh magnetically suspended flywheel is presented.

Niemeyer, W. L.↗

NASA NTRS1978

The WX-32193, a new 70 mm SEC image tube for astronomical application

The new SEC image camera tube is designed for astronomical application. Its large target allows a wide viewing angle with excellent resolution and little distortion, as the tube is magnetically focussed. The target is able to store information over several days and with proper cooling integration of weak light signals is possible over several hours. A sequential writing - reading slow scan mode is suggested for most effective application. The window is transmissive far into the vacuum UV-spectrum. Zooming with a fourfold magnification has been successfully demonstrated employing a magnetic lens in front of the image section. The tube construction is ruggedized to withstand the shock and vibration requirements of rocket launch.

Pietrzyk, J. P.↗

NASA NTRS1988

The nonlinear breakup of a magnetic layer - Instability to interchange modes

Motivated by considerations of the solar toroidal magnetic field, the behavior of a layer of uniform magnetic field embedded in a convectively stable atmosphere is studied. Since the field can support extra mass, such a configuration is top-heavy and thus instabilities of the Rayleigh-Taylor type can occur. For both static and rotating basic states, the evolution of the interchange modes (no bending of the field lines) is followed by integrating numerically the nonlinear compressible MHD equations. The initial Rayleigh-Taylor instability of the magnetic field gives rise to strong shearing motions, thereby exciting secondary Kelvin-Helmholtz instabilities which wrap the gas into regions of intense vorticity. The subsequent motions are determined primarily by the strong interactions between vortices which are responsible for the rapid disruption of the magnetic layer.

Cattaneo, F.↗

NASA NTRS1999

Melt Stabilization of PbSnTe in a Magnetic Field

Both the experimental observation and numerical simulation indicate that the Bridgman growth of PbSnTe under the microgravity environment in space is still greatly influenced by buoyancy-induced convection. The application of a magnetic field during the semiconductor growth can dampen the convective flow in the metal-like melt. However, for Bridgman growth of PbSnTe on earth (with either vertical or horizontal configuration), both experimental observation and numerical modeling suggest that even with a strong magnetic furnace (5-Tesla constant axial magnetic field), the convective flow in the melt still cannot be sufficiently suppressed to reach the diffusion-controlled level. In order to completely dampen the buoyancy-induced convection on earth, estimates based on scaling analysis indicate that for common experimental conditions, an extremely high magnetic field is required, far beyond the capacity of the experimental apparatus currently available. Therefore, it is proposed that only the combination of microgravity environment and magnetic damping will produce the desired diffusion-controlled growth state for this particular material. The primary objectives of this study are to provide a quantitative understanding of the complex transport phenomena during solidification of non-dilute binarys, to furnish a numerical tool for furnace design and growth condition optimization, to provide estimates of the required magnetic field strength for low gravity growth, and to assess the role of magnetic damping for space and earth control of the double-diffusive convection. As an integral part of a NASA research program, our numerical simulation supports both the flight and ground-based experiments in an effort to bring together a complete picture of the complex physical phenomena involved in the crystal growth process. For Bridgman growth of PbSnTe under microgravity (with both vertical and horizontal configurations), the simulations suggest that a moderate axial magnetic field of only a few kilo-Gauss in strength could effectively eliminate buoyancy-induced convection in the melt and control solute segregation. Therefore, this work confirms the idea that the combination of microgravity environment and the magnetic damping will indeed be sufficient to produce the desired diffusion-controlled growth state for PbSnTe.

Fripp, Archibald L.↗

NASA NTRS1974

Ion heating in a plasma focus

Ion acceleration and heating in a plasma focus were investigated by the numerical integration of the three-dimensional equations of motion. The electric and magnetic fields given were derived from experimental data. The results obtained show that during the collapse phase of focus formation, ions are efficiently heated to temperatures of several keV. During the phase of rapid current reduction, ions are accelerated to large velocities in the axial direction. The results obtained with the model are in general agreement with experimental results.

Hohl, F.↗

NASA NTRS1982

Initial results on the correlation between the magnetic and electric fields observed from the DE-2 satellite in the field-aligned current regions

Initial results of the electric and magnetic field observations from the DE-2 satellite show a remarkably good correlation between the north-south component of the electric field and the east-west component of the magnetic field in many passes of the field-aligned current regions. For a dayside cusp pass on August 15, 1981 the coefficient of correlation between these components was 0.996. A preliminary inspection of the available data from the first 6 months of the DE operation indicates that the similarity between the electric and magnetic field signatures of the field-aligned currents is a commonly observed feature at all local times. This high correlation is interpreted to be an indication that the closure of the field-aligned current is essentially meridional. When the correlation between these components is not good, the closure current is likely to be flowing along the auroral belt. When the correlation between the electric and magnetic fields is high, it is possible to estimate the height-integrated Pedersen conductivity from the observed field components.

Sugiura, M.↗

NASA NTRS1982

A lightweight electronically commutated dc motor for electric passenger vehicles

A functional model breadboard converter and a rare-earth-cobalt, permanent magnet motor; as well as an engineering model converter and PM motor suitable for vehicle installations were developed and tested. The converter and motor achieved an 88% peak efficiency, a maximum output of 26 kW at 26,000 rpm, and a continuous rating of 15 kW. The system also generated power to the source during braking, with a demonstrated peak power available at the converter terminals of approximately 26 kW at 88% efficiency. Major conclusions include: (1) the SAE J227a(D) driving cycle efficiency for the converter/motor is 86% to 88% when energy available for recovery at the converter terminals is included; (2) the converter initial cost is approximately five times that of the permanent magnet motor, but can be reduced by means of LSI logic and integrated liquid cooled semiconductor packages; and (3) an electronically commutated motor with a liquid cooled converter will operate reliably without service or maintenance for the life of a passenger vehicle.

Echolds, E. F.↗

NASA NTRS1983

Adaptive control system for line-commutated inverters

A control system for a permanent magnet motor driven by a multiphase line commutated inverter is provided with integration for integrating the back EMF of each phase of the motor. This is used in generating system control signals for an inverter gate logic using a sync and firing angle (alpha) control generator connected to the outputs of the integrators. A precision full wave rectifier provides a speed control feedback signal to a phase delay rectifier via a gain and loop compensation circuit and to the integrators for adaptive control of the attenuation of low frequencies by the integrators as a function of motor speed. As the motor speed increases, the attenuation of low frequency components by the integrators is increased to offset the gain of the integrators to spurious low frequencies.

Dolland, C. R.↗

NASA NTRS1987

Whistler mode emissions in the Uranian radiation belts

Voyager 2 detected intense whistler mode emissions and fluxes of energetic electrons during the outbound pass through the region of auroral L shells. The observed energetic (E greater than 22 keV) electron distribution, a model warm (E less than 27.5 keV) electron distribution, and the cold plasma density profile deduced by Kurth et al. (1987) are used to calculate the ray path-integrated spatial amplification of whistlers which arrive at Voyager 2 from the magnetic equator. By matching the calculated amplification and the relative gains at different frequencies deduced from the observed whistler power spectrum, the pitch angle anisotropy parameters of the electron distributions are determined to within a fairly narrow range of values. The estimated bounce average pitch angle diffusion coefficient indicates that electrons are on strong diffusion over a wide range in energies. The electron precipitation energy flux is sufficient to produce the observed auroral light emissions.

Coroniti, F. V.↗

NASA NTRS1989

Rotational dating of middle-aged stars

By the age of about 100 million years, the rotational velocity of solar mass stars becomes independent of the initial rotation rate on the main sequence, due to the strong dependence of the angular momentum loss rate on the rotation rate; once this common value is reached, the rotation velocity depends only on time and the mass of the star. Thus, the measured rotation rate of a low-mass star provides an estimate of its age when its mass is known. The observed rotation periods of low-mass stars in the Hyades are used to test this conclusion and to check the validity of the theoretical angular momentum loss rates. Adapting the magnetic braking model of Kawaler (1988), the angular momentum loss rate is integrated to derive a relation between rotation period and age, and this relation is converted to a period-age-color relation using simple stellar models. Using this method, a mean rotational age for the Hyades is obtained which is in close agreement with the age determined by isochrone fitting.

Kawaler, Steven D.↗

NASA NTRS1990

Particle acceleration at shocks with surface ripples

The present treatment of superthermal-ion acceleration on the surface of a fast-mode hydromagnetic shock gives attention to (1) small-amplitude surface ripples characterized by width L and amplitude A that are large relative to the energetic-ion gyroradius, and (2) shocks which are on average quasi-perpendicular. An investigation is made of the effects of the confinement, evolving geometry, and finite shock curvature associated with the ripple, by integrating along the orbits of the proton test particles. As an upstream magnetic field line convects through the surface ripple, it intersects the shock at two points, thereby forming a temporary magnetic trap. Flux-line profiles and angular distributions in a given ripple differ substantially, depending on the path it takes through the ripple and its distance from the shock.

Decker, R. B.↗

NASA NTRS1990

Follow-on cable coupling lightning test, volume 1

A redesigned solid rocket motor test article was subjected to simulated lightning strikes. This test was performed to evaluate the effects of lightning strike to the redesigned motor and Space Transportation System. The purpose of the test was to evaluate the performance of systems tunnel design changes when subjected to the lightning discharges. The goal of the design changes was to reduce lightning induced coupling to cables within the systems tunnel. The test article was subjected to several different amounts and kinds of discharges. Changes in coupling levels detected during the tests are recorded. The dominant mode of coupling appears to be caused by the diffusion of the magnetic fields through the system tunnel covers. The results from bond strap integrity testing showed that 16 of 18 bond straps survived. Design change evaluations showed that coupling reduction ranged from 0 to 36 decibels for each type of cable. The type of cable has less effect on coupling than does strike location and strike levels. Recommendations for design changes are made.

Danforth, Richard↗

NASA NTRS1992

The effects of pressure anisotropy on Birkeland currents in dipole and stretched magnetospheres

Attention is given to two effects which modify the rate of generation of Birkeland currents from the values given by the Vasyliunas (1970) formula in a dipole, namely, nonisotropic plasma pressure and the radial distention of magnetic field lines. The parallel current at any given point is the integrated effect of the diversion of perpendicular currents along the length of the flux tube from the equator. The result for j-parallel in I is fully nonlinear. In a dipole field the effect of anisotropy is modest: j-parallel at the ionosphere is, irrespective of the r0 value, about factor of 2.4 larger for a large P-parallel anisotropy (r = 0.1) than for the isotropic case and factor of 0.2 smaller for r = 10. In the stretched field the comparable values are factor of 10 and factor of 0.06 for a field line intersecting the ionosphere at a dipole colatitude of 16.4 deg and crossing the equator at r0 of 20. The results exhibit differences in plasma density and plasma pressure along field lines between the stretched and dipole models.

Birmingham, Thomas J.↗

NASA NTRS1992

Transient scattering from two-dimensional dielectric cylinders of arbitrary shape

In this work, the problem of transient scattering by arbitrary shaped two-dimensional dielectric cylinders is solved using the marching-on-in-time (MOT) technique. The dielectric problem is approached via the surface equivalence principle. A pair of coupled integral equations are derived by enforcing the continuity of the electric and magnetic fields which are solved by using the method of moments. Numerical results are presented for two cross sections, viz. a circle and a square, and compared with inverse discrete Fourier transform (IDFT) techniques. In each case, good agreement is obtained with the IDFT solution.

Vechinski, Douglas A.↗

NASA NTRS1994

The art of mapping the magnetosphere

A comprehensive review is presented of the mathematical models used to represent magnetic fields in the Earth's magnetosphere, of the way existing data-based models use these methods and of the associated problems and concepts. The magnetic field has five main components: the internal field, the magnetopause, the ring current, the tail and Birkeland currents. Methods of representing separately each of these are discussed, as is the deformation of magnetic fields; Appendix B traces the connection between deformations and the Cauchy integral. A summary section lists the uses of data-based models and their likely future evolution, and Appendix A supplements the text with a set of problems.

Stern, David P.↗

NASA NTRS2000

Inertial orientation tracker having automatic drift compensation for tracking human head and other similarly sized body

A self contained sensor apparatus generates a signal that corresponds to at least two of the three orientational aspects of yaw, pitch and roll of a human-scale body, relative to an external reference frame. A sensor generates first sensor signals that correspond to rotational accelerations or rates of the body about certain body axes. The sensor may be mounted to the body. Coupled to the sensor is a signal processor for generating orientation signals relative to the external reference frame that correspond to the angular rate or acceleration signals. The first sensor signals are impervious to interference from electromagnetic, acoustic, optical and mechanical sources. The sensors may be rate sensors. An integrator may integrate the rate signal over time. A drift compensator is coupled to the rate sensors and the integrator. The drift compensator may include a gravitational tilt sensor or a magnetic field sensor or both. A verifier periodically measures the orientation of the body by a means different from the drift sensitive rate sensors. The verifier may take into account characteristic features of human motion, such as stillness periods. The drift compensator may be, in part, a Kalman filter, which may utilize statistical data about human head motion.

Foxlin, Eric M.↗