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NASA NTRS2020

An Overview of the Null-Field Method. I. Formulation and Basic Results

In this paper we revisit the fundamentals of the null-field method with discrete sources. We prove the unique solvability of the null-field equations for the total field inside the particle and the internal field outside the particle, at all wavenumbers. For this purpose, we use the equivalence between the null-field and surface integral equations methods. Furthermore, we discuss the completeness property of different systems of discrete sources for a surface field approximation, and derive an infinite set of integral equations for the surface fields in a variety of discrete sources. Finally, we formulate the null-field scheme as an approach aiming to construct an approximate solution to the scattering problem. The way in which we introduce the matrix of a particle is different from the standard approach relying on the assumption that the system of regular vector spherical wave functions for the interior problem is a basis.

Null-field method↗

NASA NTRS1972

Two successful geomagnetic-field-line tracing experiments.

Two field-line tracing experiments were conducted on an L = 1.26 magnetic flux tube over Kauai, Hawaii. Barium vapor was created by the detonation of a highly explosive shaped charge aligned with the geomagnetic field at a 467-km altitude. Barium ions traveled along the field line to the conjugate ionosphere in a tube 3 to 5 km in diameter, producing a visible streak along the entire 6900-km path length. Electric fields perpendicular to the magnetic field caused the ions to drift away from the true conjugate during transit, but extrapolation from subsequent ion drift rates allowed the conjugate to be identified and compared with several field models. Differing ion drift rates and directions at the conjugate points indicated that the electric field is not transferred unattenuated along field lines.

Wescott, E. M.↗

NASA NTRS1972

Force-free magnetic-field structures and their role in solar activity.

Magnetic-field structures in solar active regions are expected to be substantially force-free. A method is proposed for calculating such structures by numerical methods. The method is applied to the study of the magnetic-field pattern associated with a sunspot of one polarity surrounded by a magnetic region of opposite polarity when the sunspot rotates with respect to the surrounding region. Rotation introduces a toroidal component of magnetic field, and the associated pressure leads to inflation of the magnetic field pattern. If the differential rotation exceeds about 180 deg, the force-free magnetic field has energy greater than that of an open magnetic-field configuration with the same photospheric boundary conditions. It is concluded that, beyond this point, the force-free field structure is metastable and can be converted into an open field structure by an explosive MHD instability.

Barnes, C. W.↗

NASA NTRS1973

Direct comparison between satellite electric field measurements and the visual aurora

Electric field data from two passes of the Injun 5 satellite, one corresponding to magnetically quiet conditions and one corresponding to substorm conditions, are compared with simultaneous all-sky camera data from College, Alaska. In each case, a significant deviation of the electric field from the expected V x B field (where V is the satellite velocity) was evident, and a distinct electric field reversal could be identified. In the region of substantial electric field equatorward of the electric field reversal, a diffuse auroral arc was observed during the magnetically quiet pass, and auroral patches were observed during the substorm pass. In the substorm case, the electric field reversal occurred very near a discrete auroral arc at the poleward side of the diffuse arcs and patches. Comparison of the quiet time and substorm cases suggests that the convection electric field penetrates deeper into the magnetosphere during a substorm.

Swift, D. W.↗

NASA NTRS1973

Subsatellite measurements of the lunar magnetic field

The Apollo 15 subsatellite magnetometer data have been used to map the lunar magnetic field over a narrow band of the lunar surface. Within this band the magnetic field is generally stronger and more variable over the farside highlands than the nearside maria. The correspondence between the strong variable lunar field regions and the source regions for limb compressions suggests that limb compressions arise as the result of the deflection of the solar wind just upstream of the terminator by the lunar magnetic field. Using this apparent relationship between field strength and limb compression source regions, it is deduced that the field strength in the northern farside highlands is not as strong as in the southern hemisphere at similar longitudes. Simultaneous measurements of the interplanetary magnetic field obtained by Explorer 35 and the Apollo 15 subsatellite above the dayside hemisphere are essentially identical. Thus, both instruments are measuring the undisturbed interplanetary field.

Russell, C. T.↗

NASA NTRS1975

Interplanetary field and plasma during initial phase of geomagnetic storms

Twenty-three geomagnetic storm events during 1966 to 1970 were studied by using simultaneous interplanetary magnetic field and plasma parameters. Explorer 33 and 35 field and plasma data were analyzed on large-scale (hourly) and small-scale (3 min.) during the time interval coincident with the initial phase of the geomagnetic storms. The solar-ecliptic Bz component turns southward at the end of the initial phase, thus triggering the main phase decrease in Dst geomagnetic field. The By component also shows large fluctuations along with Bz. When there are no clear changes in the Bz component, the By shows abrupt changes at the main phase onset. On the small-scale, behavior of the magnetic field and electric field were studied in detail for the three events; it is found that the field fluctuations in By, Bz and Ey and Ez are present in the initial phase. In the large-scale, the behavior field remains quiet because the small-scale variations are averaged out. It appears that large as well as small time scale fluctuations in the interplanetary field and plasma help to alter the internal electromagnetic state of the magnetosphere so that a ring current could causing a geomagnetic storm decrease.

Patel, V. L.↗

NASA NTRS1976

Constraints on the nature of the ancient lunar magnetic field

Assuming that the physical properties of solar-wind ions have remained unchanged over the past 4 billion years, the observation of solar-wind ions in lunar breccias with compaction ages greater than 3.2 billion years places constraints on the nature and origin of the ancient lunar magnetic field. Solar-wind ions would not be expected to occur in old lunar breccias if a surface magnetic field of more than 0.03 gauss was present. Several explanations of this phenomenon are consistent with the global lunar dynamo theory of the origin of the lunar dipole field, including a wandering of the lunar dipole axis, late onset of dynamo action, and reversals of the lunar dipole field, producing a long-term field close to zero. Models invoking external field magnetization as the cause of the ancient lunar magnetic field constrain the dipole axis, precluding field reversals, and do not provide an alternative explanation for the observed occurrence of solar-wind ions in lunar breccias.

Goswami, J. N.↗

NASA NTRS1975

Role of magnetic fields in physics and astrophysics; Proceedings of the Conference, Copenhagen, Denmark, June 5-7, 1974

The papers deal with the role of magnetism in astrophysics and the properties of matter in the presence of unusually large magnetic fields. Topics include a quantum-mechanical treatment of high-energy charged particles radiating in a homogeneous magnetic field, the solution and properties of the Dirac equation for magnetic fields of any strength up to 10 to the 13th power gauss, experimental difficulties encountered and overcome in generating megagauss fields, the effect of strong radiation damping for an ultrarelativistic charge in an external electromagnetic field, magnetic susceptibilities of nuclei and elementary particles, and Compton scattering in strong external electromagnetic fields. Other papers examine static uniform electric and magnetic polarizabilities of the vacuum in arbitrarily strong magnetic fields, quantum-mechanical processes in neutron stars, basic ideas of mean-field magnetohydrodynamics, helical MHD turbulence, relations between cosmic and laboratory plasma physics, and insights into the nature of magnetism provided by relativity and cosmology. Individual items are announced in this issue.

Canuto, V.↗

NASA NTRS1975

Quantum processes in strong magnetic fields

Quantum-mechanical processes that occur in a piece of matter embedded in a magnetic field with a strength of the order of 10 to the 13th power G are described which either are entirely due to the presence of the field or become modified because of it. The conversion of rotational energy into electromagnetic energy in pulsars is analyzed as a mechanism for producing such a field, and it is shown that a strong magnetic field is not sufficient for quantum effects to play a significant role; in addition, the density must be adjusted to be as low as possible. The pressure and energy density of a free electron gas in a uniform magnetic field are evaluated, neutron beta-decay in the presence of a strong field is examined, and the effect of such a field on neutrino reactions is discussed. The thermal history of a neutron star is studied, and it is concluded that a strong magnetic field helps to increase the cooling rate of the star by producing new channels through which neutrinos can carry away energy.

Canuto, V.↗

NASA NTRS1976

Superconducting critical fields of alkali and alkaline-earth intercalates of MoS2

Results are reported for measurements of the critical-field anisotropy and temperature dependence of group-VIB semiconductor MoS2 intercalated with the alkali and alkaline-earth metals Na, K, Rb, Cs, and Sr. The temperature dependences are compared with present theories on the relation between critical field and transition temperature in the clean and dirty limits over the reduced-temperature range from 1 to 0.1. The critical-field anisotropy data are compared with predictions based on coupled-layers and thin-film ('independent-layers') models. It is found that the critical-field boundaries are steep in all cases, that the fields are greater than theoretical predictions at low temperatures, and that an unusual positive curvature in the temperature dependence appears which may be related to the high anisotropy of the layer structure. The results show that materials with the largest ionic intercalate atom diameters and hexagonal structures (K, Rb, and Cs compounds) have the highest critical temperatures, critical fields, and critical-boundary slopes; the critical fields of these materials are observed to exceed the paramagnetic limiting fields.

Woollam, J. A.↗

NASA NTRS1977

Solar sources of the interplanetary magnetic field and solar wind

Open magnetic field lines, those which extend from the solar photosphere to interplanetary space, are traced in the current-free (potential field) approximation using measured photospheric fields as a boundary condition. It is found that (1) only a relatively small fraction of the photospheric area connects via open field lines to the interplanetary magnetic field; (2) those photospheric areas which do contribute open field lines lie beneath coronal holes and within the boundaries of the holes as projected onto the photosphere or else between loop systems of an active region; (3) the interplanetary magnetic field in the plane of the sun's equator, essentially the field in the ecliptic plane, may connect to photospheric regions of high latitude; and (4) the fastest solar wind streams are correlated with those magnetic flux tubes which expand least in cross-sectional area over the distance between the photosphere and the coronal height where the solar wind begins.

Levine, R. H.↗

NASA NTRS1978

Sources of magnetic fields in recurrent interplanetary streams

The paper examines sources of magnetic fields in recurrent streams observed by the Imp 8 and Heos spacecraft at 1 AU and by Mariner 10 en route to Mercury between October 31, 1973 and February 9, 1974, during Carrington rotations 1607-1610. Although most fields and plasmas at 1 AU were related to coronal holes and the magnetic field lines were open in those holes, some of the magnetic fields and plasmas at 1 AU were related to open field line regions on the sun which were not associated with known coronal holes, indicating that open field lines may be more basic than coronal holes as sources of the solar wind. Magnetic field intensities in five equatorial coronal holes, certain photospheric magnetic fields, and the coronal footprints of the sector boundaries on the source surface are characterized.

Burlaga, L. F.↗

NASA NTRS1980

The heating of a thermally conducting stratified medium. I - Self-gravitating gas threaded by magnetic fields

Two theoretical problems are presented to illustrate the equilibrium structure of a gravitating gas threaded by magnetic fields. The gas is heated everywhere at a rate proportional to the local density and cooled by thermal conduction channeled along the magnetic field. Emphasis is placed on the influence of anisotropic thermal conduction on the distribution of the gas. In the first problem, the magnetic field has straight field lines that are nearly parallel. The simple field line geometry allows us to calculate, in closed form, the equilibria configurations of a gas slab which is cooled nonuniformly by thermal conduction along field lines which leave the gas slab at varying angles. The problem involves the gas having a free boundary, which is one of the unknowns to be determined. A discussion is given of the set of all possible equilibria so constructed. In the second problem there is no electric current flowing in the gas but there is a potential magnetic field having curved field lines. Exact solutions of equilibriums are presented to illustrate the heating of stellar and galactic coronas.

Lerche, I.↗

NASA NTRS1980

Evolving force-free magnetic fields. III - States of nonequilibrium and the preflare stage

The paper considers whether a neighboring magnetostatic equilibrium exists to allow a magnetic field initially in a force-free configuration to accommodate any imposed weak pressure. The following problem is treated. The foot points of the field are fixed and the plasma is frozen into the field lines under the approximation of infinite electrical conductivity. A weak pressure is introduced. It is determined infinitesimal plasma displacements exist to adjust the field lines to a new equilibrium without changing the field line connectivity. The analysis is carried out for the bipolar force-free fields forming one of two evolutionary sequences modeling the development of the preflare stage. It was found that for the force-free field corresponding to the quasi-static stage of evolution, the neighboring magnetostatic equilibrium always exists and the imposed gas pressure can be accommodated with a slight departure of the field from being exactly force free.

Low, B. C.↗

NASA NTRS1981

Magnetic space-based field measurements

Because the near Earth magnetic field is a complex combination of fields from outside the Earth of fields from its core and of fields from its crust, measurements from space prove to be the only practical way to obtain timely, global surveys. Due to difficulty in making accurate vector measurements, early satellites such as Sputnik and Vanguard measured only the magnitude survey. The attitude accuracy was 20 arc sec. Both the Earth's core fields and the fields arising from its crust were mapped from satellite data. The standard model of the core consists of a scalar potential represented by a spherical harmonics series. Models of the crustal field are relatively new. Mathematical representation is achieved in localized areas by arrays of dipoles appropriately located in the Earth's crust. Measurements of the Earth's field are used in navigation, to map charged particles in the magnetosphere, to study fluid properties in the Earth's core, to infer conductivity of the upper mantels, and to delineate regional scale geological features.

Langel, R. A.↗

NASA NTRS1980

Observations of large scale steady magnetic fields in the dayside Venus ionosphere

Although the dayside ionosphere of Venus is often field-free except for fine-scale features, large-scale steady ionospheric magnetic fields with magnitudes sometimes exceeding 100 gammas are occasionally observed by the Pioneer Venus Orbiter magnetometer. These fields are mainly horizontal and can assume any angle in the horizontal plane. The orientation of the field may change along the spacecraft trajectory. The field magnitude in the upper ionosphere usually shows a distinct minimum near approximately 200 km altitude, but the altitude profile is otherwise arbitrary. With few exceptions, the observations of these large scale fields occur when periapsis is at solar zenith angles less than 50 deg. The occurrence of large-scale fields is often coincident with the observation of high solar wind dynamic pressures by the Pioneer Venus Orbiter plasma analyzer closely following the ionosphere encounter. However, the detection of this phenomenon even during some orbits for which the dynamic pressure is not extraordinarily high suggests that other factors, such as hysteresis effects, must also play a role in determining the occurrence frequency of large-scale magnetic fields in the dayside Venus ionosphere.

Luhmann, J. G.↗

NASA NTRS1981

Within-field variability of plant and soil parameters

The variability of ground truth data collected for vegetation experiments was investigated. Two fields of wheat and one field of corn were sampled on two different dates. The variability of crop and soil parameters within a field, between two fields of the same type, and within a field over time were compared statistically. The number of samples from each test site required in order to be able to determine with confidence the mean and standard deviations for a given variable was determined. Eight samples were found to be adequate for plant height determinations, while twenty samples were required for plant moisture and soil moisture characterization. Eighteen samples were necessary for detecting within field variability over time and for between field variability for the same crop. The necessary sample sites vary according to the physiological growth stage of the crop and recent weather events that affect the moisture and/or height characteristics of the field in question.

Ulaby, F. T.↗

NASA NTRS1982

Nonlinear force-free magnetic fields

The nonlinear properties of force-free magnetic fields are reviewed with particular reference to the mechanisms for the sudden release of stored energy in flares during the quasi-steady evolution of solar fields. It is shown that in the solar atmosphere, force-free fields with a nonconstant scalar function in the field equations are more likely to occur than those with a constant scalar function, and the nonlinear properties of these fields may give rise to many interesting physical effects. Consideration is then given to two possible mechanisms of field evolution: a model in which a force-free field in a medium of infinite electrical conductivity evolves in response to slowly changing boundary conditions brought about by photospheric motions in the solar active region, and a model in which a field in a medium of small finite electrical conductivity evolves in response to the slow Ohmic dissipation of the electric current.

Low, B. C.↗