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Formulas are derived that express the contributions of the electric quadrupole-quadrupole and dipole-octupole forces, respectively, to the dispersion energy of two unexcited molecules possessing axial symmetry. The formulas are valid in situations where the optical dispersion curve of each molecule is adequately characterized by a pair of resonance frequencies.
One of the quadrupole terms in the main geomagnetic field is found to contribute to a north-south 'shear distortion' of the particle-drift shells, whereas one of the octupole components causes a longitude-dependent radial deformation and associated 'drift-shell splitting.' The collective action of all higher multipoles on trapped-particle motion is then used to analyze the 'true' anomalies or distortions of the internal geomagnetic field that are independent of the quadrupole-related eccentricity of the main dipole. These 'true' anomalies must originate in upper-mantle or crustal perturbations that lie relatively near the earth's surface on both sides of the mid-Atlantic ridge; they influence trapped-particle drift shells only where the latter have their closest approach to the earth (South Atlantic and South African areas). The quadrupole and octupole perturbations, on the other hand, obviously originate deep in the earth's core. In the final part of this review, we discuss the effects of external magnetospheric currents. A time-dependent symmetric ring current causes drift shells to be displaced radially, with associated particle acceleration; magnetopause currents introduce a day-night asymmetry, causing shell splitting.
The main magnetic field of Jupiter has been measured by the Goddard Space Flight Center flux gate magnetometer on Pioneer 11. Analysis of the data yields a more detailed model than that obtained from Pioneer 10 results. In a spherical harmonic octupole representation the dipole term (with opposite polarity to earth's) has a magnitude of 4.28 G times the radial distance cubed at a tilt angle of 9.6 deg and a system 111 longitude of 232 deg. The quadrupole and octupole moments are 24% and 21% of the dipole, respectively. This leads to a significant deviation of the planetary magnetic field from a simple offset dipole topology at distances of less than three times the radial distance. The north polar field strength is 14 G, and in the Northern Hemisphere the 'footprint' of the Io associated flux tube traverses the magnetic polar region. Associated L shell splitting in the radiation belts, warping of the charged particle equatorial planes, and enhanced absorption effects due to the satellites Amalthea and Io are expected as a result of the field complexity.
This paper presents a model for the magnetospheric magnetic field of Mercury in which the external field is represented by an image dipole and a tail field and the internal field includes a dipole, a quadrupole, and an octupole. The dipole moment estimated by this model is approximately 2.4 x 10 to the 22nd G cu cm, tilted 2.3 degrees from the normal to the planetary orbital plane and having the same directional sense as that of the earth. The dipole, quadrupole, and octupole moment intensities are in the approximate ratios 1:0.4:0.3, respectively. All planetary field lines of the model magnetosphere are confined to a magnetospherelike region. Results are obtained which show the geometry, field line configuration, and field isointensity contours inside the magnetosphere of Mercury.
A three-dimensional quantitative model of Mercury's magnetosphere based on Mariner 10 data is presented. The model assumes that the Mercury surface magnetic field consists of a dipole, a quadrupole, and an octupole. The dipole moment is determined, noting that the intensity of the quadrupole moment is 45% of the dipole, and that of the octupole moment is 29% of the dipole. The model meets four critical tests: (1) it produces the smallest residuals, (2) it can reproduce the crossing of a tail current sheet by Mariner 10, (3) all planetary field lines are confined inside the model magnetosphere, and (4) the size of the model agrees with the magnetopause crossings observed from Mariner 10. In addition, the plasma characteristics and regions of quiet and disturbed signatures observed from Mariner 10 are discussed.
The magnetic field geometries of Uranus and Neptune are superficially similar, and are similarly unlike those of other planets: the field strengths are similar, and they contain extraordinarily large non-dipolar components. As a corollary, the best dipolar field models of each of the two planets comprises a dipole that is considerably offset from the planetary center and tilted away from the rotational axis. However, in other respects the best field models of the two planets are quite different. Uranus has a quadrupole model in which all the terms are well determined and in which none of the higher order terms is determined. To represent the magnetometer data acquired during Voyager's Neptune encounter requires a model of order 8 (instead of Uranus' order 2), yet many of the coefficients are poorly determined. A second model, an octupole model comprising the terms up to order three of the order 8 model, has been suggested by the magnetometer team as being useful; its use, however, is limited only to the region outside of about 2R(exp N), whereas planetary radio emissions have their sources well inside this surface. Computer code has been written that permits an analysis of the detailed motion of low energy charged particles moving in general planetary magnetic fields. At Uranus, this code reveals the existence of an isolated region of the inner magnetosphere above the day side in which particles may be trapped, separate from the more general magnetospheric trapping. An examination of the so-call ordinary mode uranian radio emissions leads us to believe that these emissions are in fact extraordinary mode emissions coming from particles trapped in this isolated region. A similar attempt to discover trapping regions at Neptune has proved, unfortunately, to be impossible. This arises from three factors: (1) the computation needed to track particles in an eighth order field is more than an order of magnitude greater than that needed to perform a similar calculation in a quadrupole field, and is beyond the capacity of workstation-class computers; (2) the octupole field model is known to be in error by too large an ammount for it, or any similarly truncated version of the eighth order model, to produce trustworthy results; (3) the eighth order model can, in effect, be infinitely varied without affecting the field strength along the spacecraft trajectory.
The structure of Mercury's internal magnetic field has been determined from analysis of orbital Magnetometer measurements by the MESSENGER spacecraft. We identified the magnetic equator on 531 low-altitude and 120 high-altitude equator crossings from the zero in the radial cylindrical magnetic field component, Beta (sub rho). The low-altitude crossings are offset 479 +/- 6 km northward, indicating an offset of the planetary dipole. The tilt of the magnetic pole relative to the planetary spin axis is less than 0.8 deg.. The high-altitude crossings yield a northward offset of the magnetic equator of 486 +/- 74 km. A field with only nonzero dipole and octupole coefficients also matches the low-altitude observations but cannot yield off-equatorial Beta (sub rho) = 0 at radial distances greater than 3520 km. We compared offset dipole and other descriptions of the field with vector field observations below 600 km for 13 longitudinally distributed, magnetically quiet orbits. An offset dipole with southward directed moment of 190 nT-R-cube (sub M) yields root-mean-square (RMS) residuals below 14 nT, whereas a field with only dipole and octupole terms tuned to match the polar field and the low-altitude magnetic equator crossings yields RMS residuals up to 68 nT. Attributing the residuals from the offset-dipole field to axial degree 3 and 4 contributions we estimate that the Gauss coefficient magnitudes for the additional terms are less than 4% and 7%, respectively, relative to the dipole. The axial alignment and prominent quadrupole are consistent with a non-convecting layer above a deep dynamo in Mercury's fluid outer core.
It is known from the Apollo magnetometer experiments that significant electromagnetic induction takes place in the lunar interior. This induction is excited by fluctuations of the interplanetary magnetic field and is detected by the induced fields on the surface of the moon. These results are reviewed briefly and the formal properties of the theory are discussed. It is shown that the mathematical treatment parallels that for classical electromagnetic scattering. Further the wavelength spectrum of the fluctuations of the interplanetary magnetic field include scales consistent with the radius of the moon. The consequence is that the moon is excited in several modes. Quadrupole and possibly octupole magnetic multipoles are found in the data. The electric type radiation corresponding to transverse magnetic excitation appears suppressed and far below the detection threshold of the magnetometers.
Beams of 42-MeV alpha particles were elastically and inelastically scattered from Cu-65 in an attempt to excite states which may be described in terms of an excited core model. Angular distributions were measured for 17 excited states. Seven of the excited states had angular distributions similar to a core quadrupole excitation and eight of the excited states had angular distributions similar to a core octupole excitation. The excited state at 2.858 MeV had an angular distribution which suggests that it may have results from the particle coupling to a two-phonon core state. An extended particle-core coupling calculation was performed and the predicted energy levels and reduced transition probabilities compared to the experimental data. The low lying levels are described quite well and the wavefunctions of these states explain the large spectroscopic factors measured in stripping reactions. For Cu-65 the coupling of the particle to the core is no larger weak as in the simpler model, and configuration mixing results.
Computations on an 80-coefficient model of the earth's field illustrate the 'topography' of the magnetic equatorial surface and the geometry of the drift shells of geomagnetically trapped particles. Individual terms in the spherical harmonic expansion of the geomagnetic scalar potential V(r, theta, phi) are either even or odd in cos theta, where theta = 90 deg denotes the dipole equator. Terms that are even in cos theta tend to 'warp' the equatorial surface, but do not (in first order) distort particle drift shells radially nor split the drift shells of particles having different equatorial pitch angles. Azimuthally asymmetric terms that are odd in cos theta do cause shell splitting in first order. Shell splitting at large L values (neglecting deformation of the earth's field by the solar wind) is found to be dominated by the geomagnetic octupole. At L approximately equal to 1, shell splitting is strongly enhanced by the South American and South African anomalies. When combined with pitch angle diffusion caused by atmospheric scattering, these results may be able to account for anomalous radial diffusion of inner zone electrons.
Based on the results of the Apollo magnetometer experiments, it is shown that the wavelength spectrum of the fluctuations of the interplanetary magnetic field includes scales consistent with the radius of the moon. Quadrupole and possibly octupole magnetic multipoles are found in the data and indicate that the moon is excited in several modes.
The main magnetic field of Jupiter was measured by the Fluxgate Magnetometer on Pioneer 11 and analysis reveals it to be relatively more complex than expected. In a centered spherical harmonic representation with a maximum order of n = 3 (designated GSFC model 04), the dipole term (with opposite polarity to the Earth's) has a moment of 4.28 Gauss x (Jupiter radius cubed), tilted by 9.6 deg towards a system 111 longitude of 232. The quadrupole and octupole moments are significant, 24% and 21% of the dipole moment respectively, and this leads to deviations of the planetary magnetic field from a simple offset tilted dipole for distances smaller than three Jupiter radii. The GSFC model shows a north polar field strength of 14 Gauss and a south polar field strength of 10.4 Gauss. Enhanced absorption effects in the radiation belts may be predicted as a result of field distortion.
A high-field triaxial fluxgate magnetometer was mounted on Pioneer 11 to measure the main magnetic field of Jupiter. It is found that this planetary magnetic field is more complex than that indicated by the results of the Pioneer 10 vector helium magnetometer. At distances less than 3 Jupiter radii, the magnetic field is observed to increase more rapidly than an inverse-cubed distance law associated with any simple dipole model. Contributions from higher-order multipoles are significant, with the quadrupole and octupole being 24 and 21 percent of the dipole moment, respectively. Implications of the results for the study of trapped particles, planetary radio emission, and planetary interiors are discussed. Major conclusions are that the deviation of the main planetary magnetic field from a simple dipole leads to distortion of the L shells of the charged particles and to warping of the magnetic equator. Enhanced absorption effects associated with Amalthea and Io are predicted.
A geometrical model is presented in which the apparent source locations of the Io-independent decameter radiation are computed. The calculations assume that the radiation is produced by stably trapped electrons radiating near the electron gyrofrequency and that the emission is then beamed onto a conical surface. The maximum occurrence probability of noise storms is associated with regions in the Jovian magnetosphere where the axis of the emission cone is most inclined toward the Jovian equatorial plane. The calculations utilize and compare two of the octupole spherical harmonic expansions of the Jovian magnetic field constructed from data accumulated by the fluxgate and vector helium magnetometers on board Pioneer 11.
A theory of the Io-independent decameter radiation is developed. The radiation results from excitation of the electromagnetic loss-cone instability by keV electrons, stably trapped near L = 6. The radiation is excited in Band 3 of the extraordinary mode. When the effects of refraction are estimated, it is shown that above 10 MHz radiation is beamed into the equatorial plane in a wide, but thin, conical sheet (Psi approximately equals 80 degrees). When the instability analysis is coupled with one of the octupole models of the Jovian magnetic field, the maximum convective growth of the instability occurs in the directions of the non-Io A, B, and C sources. The shape of the peak radio flux frequency spectrum is found to be a consequence of the loss cone shape of the electron distribution function.
Some field-geometric features of relevance to particle trapping in the inner magnetosphere and polar-cap regions of Jupiter are described using an internal-field model that includes terms up to the order of n equals 3 (octupole). Adiabatic particle parameters for detectors on Pioneers 10 and 11 during their flights through Jupiter's inner magnetosphere are determined along with the configuration of the intersections of particle drift shells with the planetary ionosphere. Possible correlations between drift-shell contours and the planet-locked characteristics of Jovian decametric radio emission are investigated, and longitudinal asymmetries of the ionospheric plasma source function are analyzed. It is shown that if the ionosphere is the main source of magnetospheric plasma, the latitude dependence of the plasma source function should have a considerable effect on the longitudinal asymmetry of the corotating plasma.
Data from Mariner 10 observations of Mercury indicate that there exists an intrinsic magnetic field of the planet, sufficiently strong at present to deflect the solar wind flow around the planet and to form a detached bow shock wave in the super Alfvenic solar wind. Four methods used to analyze the magnetic field data and derive quantitative values for the description of the planetary field include (1) comparison of bow shock and magnetopause relative positions at Mercury to those at Earth; (2) direct spherical harmonic analysis of the data; (3) modeling of the magnetosphere by an image dipole and infinite 2-D current sheet in addition to the planetary field; and (4) scaling of a mathematical model for the terrestrial magnetosphere. The results obtained yield dipole moments ranging from 2.4 to 5.1x10 to the 22d power, with the lower values associated cw cm with certain models using partial quadrupole and octupole terms to improve the least squares fitting of models to observations.
The paper examines the magnetic field observations and their analyses relating to the determination of the Mercury magnetic field. Methods of analyzing data included: (1) comparison of bow shock and magnetopause relative positions at Mercury to the earth, (2) direct spherical harmonic analysis, (3) magnetosphere modeling by an image dipole, and (4) scaling of a mathematical model for the terrestrial magnetosphere. Dipole moments were determined using partial quadrupole and octupole terms to improve the least-square fit of models to observations; analyses by method (2) yield a convergent series of dipole moments values considered to best represent the intrinsic planetary field. Finally, it is suggested that the origin of the magnetic field of Mercury cannot be uniquely determined, but the sources of convective energy may be radiogenic decay and heat release, gravitational settling, and differentiation of processional torques.