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Apollo 15 subsatellite magnetic field observations have been used to measure both the permanent and the induced lunar dipole moments. Although only an upper limit of 1.3 x 10 to the 18th gauss-cubic centimeters has been determined for the permanent dipole moment in the orbital plane, there is a significant induced dipole moment which opposes the applied field, indicating the existence of a weak lunar ionosphere.
An analysis of neutral sheet crossings detected by the NASA-Goddard Space Flight Center magnetometer on the Explorer 34 satellite has shown that the diurnal wobble of the geomagnetic dipole measurably influences the position of the neutral sheet at 30 earth radii. Viewed in the solar-ecliptic coordinate system, the dipole wobble originates from the 11 deg angle between the earth's spin axis and the dipole axis, has a period of 24 hours, and can be resolved into components of motion perpendicular and parallel to the earth-sun line. The perpendicular component exerts a torque on the magnetotail and causes the neutral sheet to pivot about an axis approximately parallel to the solar wind direction. The parallel component encourages the neutral sheet to move above and below the solar-magnetospheric equatorial plane with an amplitude of 1 earth radius. This latter motion is consistent with the neutral sheet's being hinged at a geocentric distance of 5.25 earth radii.
The mutual impedance expressions for parallel dipoles in terms of sine-integrals and cosine-integrals have been published by King (1957). The investigation reported provides analogous expressions for nonparallel dipoles. The expressions presented are most useful when the monopoles are close together. The theory of moment methods shows an approach for employing the mutual impedance of filamentary sinusoidal dipoles to calculate the impedance and scattering properties of straight and bent wires with small but finite diameter.
Power spectral density analysis using Burg's maximum entropy method (MEM) was applied to the geomagnetic dipole field and its rate of change for the years 1901-1969. Both spectra indicate relative maxima at 0.015 cycle/yr and its harmonics. These maxima correspond approximately to 66-, 33-, 22-, 17-, 13-, 11-, and 9-year spectral lines. The application of the same analysis techniques to the length of day (l.o.d.) fluctuations for the period 1865-1961 reveals similar spectral characteristics. The existence of the common spectral peaks with periods of 66 and 33 years in the l.o.d. fluctuations and the geomagnetic dipole field is clearly established. The existence of the higher harmonics is somewhat uncertain because of the line-splitting problem in the MEM spectral analysis. It is suggested that the spectral line similarity in the l.o.d. fluctuations and the dipole field variations is related to the motion within the earth's fluid core during the past 100 years.
A general technique for expanding an unknown potential field in terms of a linear summation of weighted dipole or quadrupole fields is described. Computational methods were developed for the iterative addition of dipole fields. Various solution potentials were compared inside the boundary with a more precise calculation of the potential to derive optimal schemes for locating the singularities of the dipole fields. Then, the problem of determining solutions to Laplace's equation on an unbounded domain as constrained by pertinent electron trajectory data was considered.
A model is presented for the global thermoremanent magnetization of spherical lithospheres which cool in the presence of central dipole fields. Reversals and intensity variations of the field are incorporated in this model, which is applicable to bodies whose interiors have remained above the Curie point throughout their evolution. The model demonstrates that even considering Runcorn's (1975) magnetostatics theorems for spherical shells, a nonzero magnetic permeability and a finite cooling rate in the lithosphere permit the acquisition of a sizable global remanent dipole moment, which would be detectable by external measurements after the magnetizing field has disappeared. Preliminary application of this model to Mercury, Venus, and Mars suggests that only the combination of a nonreversing ancient source field with a surface value near 1 Oe plus a sizable concentration (about 1% by volume) of ferromagnetic material in their crusts could produce remanent planetary dipole fields as large as those measured by spacecraft. On the other hand, if ancient reversing dynamos existed in these planets, it is unlikely that large planetary-scale fields like those observed at Mercury could be due to remanence in their crusts, irrespective of their composition.
A method for computing the Lorentz tensor components in single crystals via rapidly convergent sums of Bessels functions is developed using the relationship between dipole-field sums and the tensor components. The Lorentz factors for simple, body-centered, and base-centered orthorhombic lattices are computed using this method, and the derivative Lorentz factors for simple orthorhombic lattices are also determined. Both the Lorentz factors and their derivatives are shown to be very sensitive to a lattice structure. The equivalent of the Clausius-Mossotti relation for general orthorhombic lattices is derived using the Lorentz-factor formalism, and the permanent molecular dipole moment is related to crystal polarization for the case of a ferroelectric of polarizable point dipoles. It is concluded that the polarization enhancement due to self-polarization familiar from classical theory may actually be a reduction in consequences of negative Lorentz factors in one or two lattice directions for noncubic crystals.
The resonance frequency of an electric dipole placed near a conducting surface is shifted by the dipole-surface interaction. The observation and measurement of these shifts at optical frequencies is reported for an experimental system that consists of a metal-island film spaced a distance d from a continuous Ag film. The dependence of the shift in the frequency of the island resonance on d shows good agreement with that predicted by a classical theory of the dipole-surface interaction.
A 6X6 array of fan-dipoles was designed to operate in the 510 to 660 MHz frequency range for aircraft flight test and evaluation of a UHF radiometer system. A broad-band dipole design operating near the first resonance is detailed. Measured VSWR and radiation patterns for the dipole array demonstrate achievable bandwidths in the 35 percent to 40 percent range.
A calculated dipole moment of 2.39 D at R sub e = 2.79 a sub 0 is reported, obtained from complete active space SCF/configuration interaction calculations plus one natural orbital iteration. The calculation is in good agreement with the experimental value of 2.4 + or - 0.1 D measured for the lowest vibrational level. In agreement with Gray et al. (1985), it is found that the dipole moment is strongly correlated with the 3d electron population; the good agreement with experiment thus provides verification of the mixed state model of NiH. It is concluded that the electric dipole moment of NiH is a sensitive test of the quality of the NiH wave function.
Accurate theoretical dipole moments have been computed for the X2Pi ground states of Si(-)H(+) (0.118 D), Ge(+)H(-) (0.085 D), and Sn(+)H(-) (0.357 D). The trend down the periodic table is regular and follows that expected from the electronegativities of the group IV atoms. The dipole moment of 1.24 + or - 0.1 D for GeH recently derived by Brown, Evenson and Sears (1985) from the relative intensities of electric and magnetic dipole transitions in the 10-micron spectrum of the X2Pi state is seriously questioned.
Spectroscopic parameters (D sub e, r sub e, mu) are determined for the first-row transition metal hydrides using better than DZP basis sets at the modified coupled pair functional (MCPF) level. Extensive comparisons between MCPF and complete-active space self-consistent field (CASSCF)/MRCI calculations with natural orbital iterations, and studies with more extensive basis sets, show this level of treatment to supply an accurate and cost-effective treatment of these systems. For the transition metal hydrides, the bonding can arise from either the 3d(n)4s(2) or 3d(n + 1)4s(1) atomic asymptotes, or a mixture of both. Since the dipole moment arising from these two bonding mechanisms is very different, the dipole moment is found to be directly related to the 3d population. Thus, the magnitude of the dipole moments provides a sensitive test of the wave function, and gives insight into the nature of the bonding.
The vector sum of fields produced by a set of magnetic dipoles with different magnetic moments that are both tilted from the planetary spin axis and offset from the planetary center by different amounts can be used to completely represent a planetary magnetic field in the conventional form of spherical harmonic expansion. The scalar equipotential transformation analytically results in 24 equations that may subsequently be solved for the 24 adjustable parameters in dipole systems with the predetermined main dipole. Attention is given to this method's application to the Jovian magnetic field.
A three-dimensional time-dependent global magnetohydrodynamic (MHD) model of the interaction between the solar wind and the earth's magnetosphere has been used to study the effects of dipole tilt on the structure and dynamics of the magnetotail. The location of the tail neutral sheet shifts in the north-south direction following changes in the dipole tilt. When the northern edge of the geomagnetic dipole is tilted toward the sun (positive tilt), it is above the geocentric solar magnetosphere (GSM) equator, while for negative tilt, it is below. The neutral sheet forms an arc across the tail in the y-z plane for nonzero tilt. For positive tilt, the neutral sheet rises above the GSM equatorial plane near the noon-midnight meridian and returns to the equator near the magnetopause. The position and shape of the neutral sheet result from the requirement that the earthward magnetic flux equals the tailward flux and can be well explained by a simple analytical model.
A spherically symmetrical Tolman-Bondi cosmological model is presented in which the curvature of space and the entropy variety with distance from the center. The dipole and quadrupole moments in the distribution of the microwave background radiation are calculated as a function of cosmic time and position of an observer, assuming that the distance to the horizon is much smaller than any characteristic scale in the model. The quadrupole moment is found to be affected mostly by the gradient in the curvature of space while the dipole moment is dominated by the gradient of entropy. The results indicate that the observed dipole in the microwave background may be cosmological in origin. Observational tests of this argument are suggested.
It is shown that the offset tilted dipole model of Uranus and Neptune, deduced from the spherical harmonic analysis of the Voyager magnetic field observation, can be represented fairly well by the combined field of an axial and an auxiliary dipole; the latter is roughly oriented in the east-west direction and is located near the surface of the core in low latitude. The present dynamo theories of planetary magnetism consider an axial dipolar field as an essential element, since the planetary rotation plays a vital role in the dynamo process. On the other hand, the auxiliary dipoles may be a result of leakage of the toroidal field, like a pair of sunspots on the photosphere, which is also an essential part of the dynamo process.
The purpose of this note is to quantitatively study the asymptotic behavior of the dipole magnetic field in the tail region of a paraboloidal or cylindrical model of the magnetosphere, assuming the complete screening of the internal field by magnetopause currents. This screening assumption is equivalent to imposing the boundary condition that the normal component of the magnetic field is zero at the magnetopause. With this boundary condition, the screened dipole field falls off exponentially with distance down the tail, in sharp constrast to the bare dipole field. Analytic expressions for a cylindrical and paraboloidal magnetopause are given.
The Far-Infrared Absolute Spectrophotometer (FIRAS) instrument on the Cosmic Background Explorer (COBE) has determined the dipole spectrum of the cosmic microwave background radiation (CMBR) from 2 to 20/cm. For each frequency the signal is decomposed by fitting to a monopole, a dipole, and a Galactic template for approximately 60% of the sky. The overall dipole spectrum fits the derivative of a Planck function with an amplitude of 3.343 +/- 0.016 mK (95% confidence level), a temperature of 2.714 +/- 0.022 K (95% confidence level), and an rms deviation of 6 x 10(exp -9) ergs/sq cm/s/sr cm limited by a detector and cosmic-ray noise. The monopole temperature is consistent with that determined by direct measurement in the accompanying article by Mather et al.