Eccentric Dipole Research Articles

Current and potential fields generated by two dipoles.

The distribution of currents and potentials in a circular conducting medium surrounding two eccentric dipoles was studied to establish how much information on the number, location, and orientation of the dipoles could be deduced from measurements of potential in the medium at various distances from the generators. When a single, eccentric dipole was active, the curve illustrating the distribution of potentials along the boundary exhibited different kinds of asymmetry, which revealed that the dipole was eccentric and gave some information about its orientation. When both dipoles were active, two maxima and two minima, revealing the presence of two generators, appeared along the boundary when the angle between dipole moments was 150° or more. Along internal circumferences two maxima and two minima appeared at smaller angles between dipole moments and the location of the maxima was closely related to that of the dipole anodes. When the dipoles lay on the same diameter and had opposite polarity, the presence of two generators was clearly detectable from boundary measurements, whereas vector representation was zero. These data improve our understanding of electrical signals recorded from the body surface, whether in the form of electrocardiograms, vectorcardiograms, or equipotential contour maps.

Auroral proton oval

The auroral spectrum was recorded at Byrd Station, Antarctica, during the austral winter of 1967. Hydrogen Balmer line radiation was detected throughout the 24-hour day, depending on magnetic activity. The radiation defines an oval of proton precipitation that, as viewed from the particular location, appears as an equatorward movement around noon (eccentric dipole time) and as a poleward recession after midnight. The position and extent of the oval appear to depend on the degree of magnetic activity. Based on the latitude interval accessible to observation (65° to 73°S geomagnetic latitude), the proton precipitation oval is displaced with respect to the Akasofu-Feldstein (electron) oval, and thus it is equatorward in the afternoon sector and overlaps the electron oval during the forenoon period.

Eccentric dipole coefficients and magnetic centres

Eccentric dipole coefficients and magnetic centres

Prediction of Geomagnetic Secular Change confirmed

THERE is a strong (0.93) correlation1,2 between the change in the length of day and the change in westward velocity of the eccentric dipole or “magnetic centre” (as defined by Schmidt3) of the geomagnetic field, presumably because of the conservation of the angular momentum of the Earth. If the motion of the eccentric dipole is related to a motion somewhere in the core in which the magnetic field is “frozen” into the fluid, then a change in westward motion and angular momentum in the core must be compensated for by a change in angular momentum of the mantle. This appears as a change in the length of day, as determined astronomically.

Geomagnetic Secular Variation and its Changes, 1942.5 to 1962.5

A uniform set of geomagnetic data from observatories has been analysed to determine secular variation of the geomagnetic field for the interval 1942.5 to 1962.5 and to reveal any changes in secular variation during this time. The epoch to epoch changes are much smoother than have been previously found, and permit an examination of the movements of the centred and eccentric dipoles and changes in westward drift. The secular variation has also been used to determine surface motions of the Earth's core. Changes in secular variation are presented in the form of charts of secular acceleration.

Transformation of Spherical Harmonics Under Change of Reference Frame

Summary The problem of transforming spherical harmonics under a linear change of reference frame is solved analytically and numerically. In contrast to other methods both translation and rotation are treated with the same background theory which is comparatively straightforward and is formulated in geophysical terms; the directions of translation and rotation are arbitrary; and generally, combinations of harmonics of the same order can be dealt with equally as readily as individual harmonics. It is found that the expansion coefficients of a translated spherical harmonic are themselves spherical harmonics in the co-ordinates of the translation vector. As a special case, the potential of an eccentric dipole is briefly discussed. Very useful byproducts of this paper are the ways in which the given numerical algorithms can be used to evaluate any linear combination of harmonics.

Changes in geomagnetic multipole parameters 1942.5?1962.5

From a smooth series of spherical harmonic coefficients for the geomagnetic potential, the corresponding multipole parameters have been calculated for five epochs from 1942.5 until 1962.5, at five year intervals. Changes in multipole parameters are discussed in relation to the secular variation field and to theSchmidt eccentric dipole.

The Role of the Main Geomagnetic Field in Locating Conjugate Points

A sample distribution of conjugate points is calculated from various models of the main geomagnetic field, evaluated at different epochs. A summary of the conclusions is: (1) For L < 4 the errors are of the order of a few tens of kilometers; (2) older models of the field such as the Finch‐Leaton give results within a few degrees of the latest more accurate models; (3) use of the eccentric dipole approximation gives errors that range from a few tens of kilometers at high latitude to several hundred kilometers near the equator; and (4) the secular change of conjugate‐point locations is very small, averaging 1 to 10 km/yr. Inclusion of Mead's boundary field for a trace from Macquarie Island to Alaska (L = S) shifts the conjugate only about 100 km. It is concluded that for L ⩾ 5 the field line passes through regions where the field intensity is weak enough to require that realistic estimates of the distortions due to plasma interactions be included in conjugate‐point determinations. (These estimates are not now available.)

The eccentric dipole

An up to date (1965) collection of the geometric parameters of the eccentric dipole is given and a new approach to the theory is introduced visualising the eccentric dipole as a superposition of multipoles. Formulae are also given for the determination of the theoretical north and south dip-poles.

Auroral Poles

The centred dipole geomagnetic poles and the eccentric dipole geomagnetic poles are established mathematical entities (Chapman and Bartels 1940). Here the related concept of the "auroral" poles is outlined. The relationship of the auroral pole to the maximum iso-aurore of the auroral zone as well as to the instantaneous auroral belt is indicated.

Surface Potential Errors Introduced by the Truncation of the Infinite Series that Represents an Eccentric Dipole

Surface Potential Errors Introduced by the Truncation of the Infinite Series that Represents an Eccentric Dipole

Geomagnetic multipoles, 1965.0

Following the recent appearance of spherical harmonic coefficients for the potential of the geomagnetic field for epoch 1965.0, the strengths and axes for a dipole, quadrupole and octupole have been computed from first, second and third order spherical harmonic coefficients respectively. An interesting relation existing between the parameters of the dipole, quadrupole and geomagnetic eccentric dipole is also indicated.

A Ready Method for finding Eccentric Dipole Time

ECCENTRIC geomagnetic dipole1 time at an observatory (O) is defined for present purposes as the difference in eccentric dipole longitude (ɛ′) of the Sun (as distinct from the sub-polar point) and the observatory being measured eastwards from the Sun to the observatory, that is: Elsewhere2,3 it has been shown by different approaches that tecc. runs parallel to ordinary geomagnetic time (a centric system) differing by a constant C0, which is a characteristic of the observatory for the particular epoch of the Earth's magnetic field. Thus, also : where ɛ represents geomagnetic longitude. where3: X=−0.0577, Y=0.0320, Z=0.0184 for epoch 1955.0 and (θ0, ɛ0) are geographic co-ordinates of the observatory.

“Body surface” potentials produced by the eccentric dipole in the heart wall of the nonhomogeneous volume conductor

“Body surface” potentials produced by the eccentric dipole in the heart wall of the nonhomogeneous volume conductor

Eccentric Dipole Coordinates

Recently, Bond and Jacka (1962) sought to order the average frequency of occurrence of visible auroras in eccentric dipole latitude. It is considered that eccentric dipole co-latitudes (q''), longitudes (f'), and times for places on the surface of the Earth (here assumed spherical) may be of interest to workers in various fields. Mapped grids of q'' and f' are reproduced here.

Distribution of Auroras in the Southern Hemisphere. II. Nightly Probability of Overhead Aurora

The probability P of overhead occurrence of aurora during a night is estimated for 22 southern hemisphere stations during the I.G.Y. The distribution of probability of occurrence is represented in terms of three measures of colatitude: 81 is defined in terms of the eccentric dipole representation of the geomagnetic field; 82 is defined in terms of projections from circles in the equatorial plane, along the geomagnetic lines of force, onto the Earth; 83 is defined in terms of the integral invariant f; (I-F IF m)!dl of charged particle motion in the geomagnetic field.

Geomagnetic Secular Variation during the Period from 1955 to 1960

The isoporic charts of X, Y and Z of geomagnetic secular variation during the period from 1955 to 1960 are constructed based on data observed at 99 stations over the earth's surface including the Antarctic region, and illustrated in Figs. 1-9. Equivalent current system of the variation on the earth's core's surface is shown in Figs. 11-13.From the results of the spherical harmonic analyses of these isoporic charts, it is concluded that (a) the earth's magnetic dipole is decreasing in moment with the rate of -4.4×1022emu/yr, magnitude of the moment at 1960.0 being 8.046×1025emu; (b) the eccentric dipole is drifting westwards by 18′/yr, northwards by 12′/yr, and outwards by 3.4×10-4× the earth's radius/yr. It is shown that the other harmonics, are drifting mostly westwards also with the rate of several decimals of a degree per year.On the other hand, very intense foci of isopors are found in the Antarctic region, amounting to about 200γ/yr in Z. The current change on the earth's core's surface equivalent to the foci amount to about 0.1Amp/cm/yr. This value is strikingly large compared with intensity of the equivalent current of the earth's magnetic dipole, which is about 0.5Ampere/cm in this region.

The secular variation and the geomagnetic theory of cosmic radiation

This paper discusses the effect of the secular variation of the geomagnetic field on the elements of the eccentric dipole and eccentric dipole-quadripole models. It studies the migration during the period between 1845 and 1955 of geomagnetically equivalent points and examines the conditions for the invariance of the differential equation of motion of charged particles in the geomagnetic field. Formulas and practical rules are given for adapting calculations of cones, cutoff momenta and energies, and directions of incidence, valid for any arbitrary year to any specific year of observation. Time corrections for the curves of cutoff momenta vs. geomagnetic latitude were calculated for the period 1845–1955 for points of observation distributed over the southern and northern hemispheres.

Eccentric dipoles and spherical harmonic analysis

Eccentric dipoles and spherical harmonic analysis

The Cosmic Ray Equator and the Geomagnetism

It was formerly thought that the disagreement of the position of geomagnetic dipole equator with that of the cosmic ray equator was caused by 45 deg westward shifting of the latter. Referring to the theory of geomagnetic effect on cosmic rays, it was determined whether such westward shifting could be existent or not. It was found that the deviation of the cosmic ray equator from the geomagnetic dipole equator is negligible even if the magnetic cavity is present around the earth's outer atmosphere. Taking into account such results, the origin of the cosmic ray equator was investigated. It was found that this equater could be produced by the higher harmonic components combined with the dipole component of geomagnetism. The relation of the origin of the cosmic ray equater to the eccentric dipoles, near the outer pant of the earth's core, contributing to the secular variation of geomagnetism was considered. (auth)