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A recurring pattern with a period of 26 7/8 days observed in the polar geomagnetic field during the interval from 1926 to 1941 appears to persist in the interplanetary magnetic field polarity observed with spacecraft during the interval from 1963 to 1968. This observation suggests the existence of a rotating solar magnetic ?dipole' with a period of 26 7/8 plus or minus 0.003 days.
Particle motion in the secularly varying geomagnetic field is investigated in terms of a dipolar magnetic field with decreasing magnetic moment M. For dM/dt equal to the rate of decay of the earth's dipole component, we find there is drift in B-L space, resulting in an inward drift of particles accompanied with increased energy and unidirectional intensity. Secular variation of the geomagnetic field appears to be a dominant mechanism for radial drift in the inner radiation belt.
With the use of a power integral formulation, a study is made of the vlf/elf radiation patterns of arbitrarily oriented electric and magnetic dipoles in a cold lossless multicomponent magnetoplasma. Expressions for the ray patterns are initially developed that apply for arbitrary values of driving frequency, static magnetic-field strength, plasma density, and composition. These expressions are subsequently specialized to vlf/elf radiation in a plasma modeled on the magnetosphere. A series of representative pattern plots are presented for frequencies between the proton and electron gyrofrequencies. These patterns illustrate the fact that focusing effects that arise from the geometrical properties of the refractive index surface tend to dominate the radiation distribution over the entire range from the electron gyrofrequency to 4.6 times the proton gyrofrequency. It is concluded that focusing effects should be of significant importance in the design of a vlf/elf satellite transmitting system in the magnetosphere.
The numerical capture cross section is calculated from the capture ratio, defined as the fraction of trajectories reaching a prescribed minimum separation of 3 A. The calculated capture cross sections for a rotational temperature of 77 K suggest large reaction cross sections in 80 K experiments for the large dipole-moment target, methyl cyanide.
Derivation of expressions for the excitation cross section in the dipole approximation of the semiclassical impact parameter and the Born approximations, making use of a formula given by Menzel (1968, 1969) for the asymptotic expansion of the oscillator strength of the hydrogen-like atoms. When only the leading term in the asymptotic expansion is retained, the expression for the cross section becomes identical with the expression obtained by the method of the classical collision and correspondence principle given by Percival and Richards (1970). Comparisons are made between the Bethe coefficients obtained by the author and the Bethe coefficients of the Born approximation for transitions where the Born calculation is available. Satisfactory agreement is obtained only for n yields n + 1 transitions, where n is the principal quantum number of the excited state.
The theory of basis set dependence in configuration interaction calculations is discussed, taking into account a perturbation model which is valid for small changes in the self-consistent field orbitals. It is found that basis set corrections are essentially additive through first order. It is shown that an error found in a previously published dipole moment calculation by Green (1972) for the metastable first excited state of CO was indeed due to an inadequate basis set as claimed.
Calculations were carried out using three Slater-type 1s orbitals in the orthogonalized valencebond theory of McWeeny. Each orbital exponent was optimized, the H2 internuclear distance was varied from 7.416 x 10 to the -11th power to 7.673 x 10 to the -11th power m (1.401 to 1.450 bohrs). The intermolecular distance was varied from 1 to 4 bohrs (0.5292 to 2.117 x 10 to the 10th power). Linear, scalene, and isosceles configurations were used. A weighted average of the interaction energies was taken for each intermolecular distance. Although energies are tabulated, the principal purpose was to calculate the electric dipole moment and its derivative with respect to H2 internuclear distance.
Previous accurate dipole moment calculation techniques are modified to be applicable to higher excited states of symmetry. The self-consistent fields and configuration interactions are calculated for the X(2)Sigma(+) and B(2)Sigma(+) states of CN. Spin hyperfine constants and spin density at the nucleus are considered in the context of one-electron operator properties. The values of the self-consistent field and configuration interaction for the spin density are compared with experimental values for several diatomic molecules.
The shape of the magnetosphere has been calculated self-consistently for inclinations of the earth's magnetic dipole from perpendicular to the solar wind. Inclination angles of 0-35 deg have been chosen in steps of 5 deg and various smooth trends in the surface characteristics with increasing inclination angle noted. The surface points and the complete field at the surface points have been calculated for the entire surfaces. The neutral point region has been given precise study in one degree steps and is found to be tangent to the solar wind velocity and to have a smooth continuous curvature.
Solutions to the problem of radiation of dipole antennas in the presence of a stratified anisotropic media are facilitated by decomposing a general wave field into transverse magnetic (TM) and transverse electric (TE) modes. Employing the propagation matrices, wave amplitudes in any region are related to those in any other regions. The reflection coefficients, which embed all the information about the geometrical configuration and the physical constituents of the medium, are obtained in closed form. In view of the general formulation, various special cases are discussed.
A combined quadrupole-dipole model has been developed for the noise generated by inlet flow distortion in a subsonic fan. A formula is derived for the total upstream-radiated acoustic power in each tone as a function of the design parameters of the fan and the properties of the inlet flow distortion. Numerical results are obtained for values of the parameters corresponding to various quiet fans. The analysis is compared with noise measurements taken on a 51-cm (20-in.) diameter research fan as well as with those taken on a number of full-scale fan stages. Fairly good agreement was obtained. It should therefore be possible to use this model to study the noise-reduction potential of the various fan design parameters.
The numerical representation of the average motion of a charged particle trapped in a geomagnetic field is developed. An assumption is made of the conservation of the first two adiabatic invariants where integration is along a field line between mirror points. The averaged motion also involved the parameters defining the magnetic field line to which the particle is attached. Methods involved in obtaining the motion in the equatorial plane of model magnetospheres are based on Hamiltonian functions. The restrictions imposed by the special nature of the dipole field are defined.
A magnetic dipole rotating around an axis perpendicular to the rotation axis of the sun can account for the characteristics of the surface large-scale solar magnetic fields through the solar cycle. The polarity patterns of the interplanetary magnetic field, predictable from this model, agree with the observed interplanetary magnetic sector structure.
Two numerical methods are used to evaluate the integrals that express the em fields due to dipole antennas radiating in the presence of a stratified medium. The first method is a direct integration by means of Simpson's rule. The second method is indirect and approximates the kernel of the integral by means of the fast Fourier transform. In contrast to previous analytical methods that applied only to two-layer cases the numerical methods can be used for any arbitrary number of layers with general properties.
The Coulomb approximation tables of Oertel and Shomo, together with binding-energy values obtained by a screening approximation, have been used to produce values of the dipole and quadrupole radial integrals needed in obtaining transition probabilities for ions of six, seven, and eight electrons. Some comparisons with more rigorously calculated values show that the present values are quite accurate, especially for ions of higher atomic number.
Microwave spectra from 12.4 to 40.0 GHz were recorded for five isotopic species of 1,1-difluoroallene. A-type transitions were observed and R-branch assignments were made for the ground state and two vibrationally excited states. Several structural parameters of the compounds were determined. The dipole moment value obtained from Stark splitting was 2.07 plus or minus 0.03 D. A Coriolis coupling was observed between the two-low-frequency C = C = C bending modes.
With applications to geophysical subsurface probings, electromagnetic fields due to a horizontal electric dipole laid on the surface of a two-layer medium are solved by a combination of analytic and numerical methods. Interference patterns are calculated for various layer thickness. The results are interpreted in terms of normal modes, and the accuracies of the methods are discussed.
The Hamiltonian for a dipole field is developed, and the result is expressed by an analytic approximation accurate to within about 1%. This allows extension of results derived for equatorial particles to particles with arbitrary pitch angles; in particular, it makes available even in the presence of electric fields orthogonal to the magnetic field a function K that is preserved by the bounce-averaged motion. This function provides at once the equations of drift paths in (alpha, beta) or of their projections onto the equatorial plane; the derivation of a pacing function that times the progress of particles along such drift paths is also described.