Eccentric Dipole Research Articles

The geomagnetic eccentric dipole: facts and fallacies

The geomagnetic field is sometimes approximated as that of a single dipole displaced from the geocentre, i.e. by an eccentric dipole. By investigating how the field can be represented exactly by a spherical harmonic (multipole) series at a displaced origin, it is shown how this eccentric dipole depends on the choice of criterion of best fit. In particular it is explained how, in some approximations, the ‘best’ eccentric dipole need not be parallel to, or have the same magnitude as, the geocentric dipole, despite the physical invariance of the true dipole moment to change of origin. Finally, the reader is warned about attempts to give physical significance to the position of the eccentric dipole.

Simultaneous observation of a traveling vortex structure in the morning sector and a field line resonance in the postnoon sector

Radar observations suggesting ULF field line resonances impulsively excited via a cavity or waveguide mode were obtained simultaneously in the dawn (Bistatic Auroral Radar System (BARS)) and postnoon (Sweden and Britain Radar‐Auroral Experiment (SABRE)) sectors. The primary data used to study this event are from both the European Incoherent Scatter magnetometer cross and Subauroral Magnetometer Network magnetometer arrays in the postnoon sector and from the Canadian Auroral Network for the Origin of Plasmas in the Earth's Neighborhood Program Unified Study (CANOPUS), MAgnetometer, RIometer and tellurics Array (MARIA), the GOES 7 magnetometer, and the neural network classification of Defense Meteorological Satellite Program (DMSP) particle data in the dawn sector. In the postnoon sector (Scandinavia) a decaying field line resonance was observed following a more complicated initial interval. The resonance period was 326 s (3.07 mHz). However, in the dawn sector the response was dominated by the initial interval in which the characteristics of a traveling vortex system were observed. The subsequent disturbance in this sector was of lesser amplitude and without discerned pattern. The field‐aligned current(s) of the traveling vortex structure was (were) at about 65° Eccentric Dipole Field Line (EDFL) latitude (approximately 68° International Geomagnetic Reference Field (IGRF)). The DMSP neural network data, however, indicate this position to have been well within the magnetosphere. GOES 7 was on a field line which was connected to the ionosphere near the MARIA meridian line at about 62.5° EDFL latitude (approximately 65.5° IGRF), just equatorward of the traveling vortex structure. It observed a magnetic disturbance which was initially driven and followed directly by a damped sinusoid signature of the azimuthal component. The frequency during this decay was 4.45 mHz (225‐s period). Values of ∑p, the height‐integrated Pedersen conductivity for both the postnoon and GOES 7 damped segments were deduced. These were low, particularly if the disturbances were in the second harmonic along the field line as suggested by GOES 7 data, and perhaps imply an additional loss mechanism. Although substantially understood, this pulsation event had distinctly different characteristics in the two time sectors and displayed many puzzling features. In particular, it was significantly more complicated than our initial anticipation of global excitation of field line resonances via a cavity or waveguide mode.

Secular variation in the geographic location of the dip equator

The geographic location of the dip equator on the globe has been determined for several epochs between 1550 and 1990 A.D. It is shown that two regions near 165°E and 285°E are devoid of migratory changes whereas between 300 and 0°E there is a large northward movement. The period between 1945 and 1990 is marked by a nearly linear change in the latitude of the dip equator while earlier epochs show more complex trends. Consistent with the earlier observations of the movement of the magnetic center towards or away from the centre of the earth, before and after 1800 A.D., the secular curves in certain longitude zones indicate a clear change in pattern. The observed secular variations in the vertical cornponent at several low latitude stations are generally in agreement with the direction of the movement of the dip equator. Examples of unexpected behaviour are highlighted. The eccentric dipole model appears to be adequate to delineate the dip equator for any epoch.

Geographic asymmetries of the Viking auroral distribution: Implications for ionospheric coordinate systems

Viking images of the auroral distribution have been used to investigate the relevance of various ionospheric coordinate systems. An important aspect of the large‐scale auroral shape is its dependence on the asymmetries of the Earth's internal field. Model predictions of where the aurora occurs, using the equatorial plane's volume current density, agree with observations and imply that the internal field plays a more important role than generally believed. Historically, the belief that the internal field has only small effects seems to stem from the widespread use of the corrected geomagnetic and invariant coordinate systems. These systems involve the mapping of field lines and have advantages in statistical studies and comparisons; less sophisticated systems such as the eccentric dipole coordinate system should be used in individual studies and in studies involving the differentiation or integration of some observational parameters. Observations of the auroral distribution are given to illustrate the universal time, tilt angle, and Kp variability in different coordinate systems and demonstrate that the dominant variability of the aurora is due to internal field asymmetries. A new set of coordinate systems are briefly developed as examples of how to incorporate external field models into studies of auroral images. It is proposed that one of these coordinate systems can be used as a test of how well an external field model can match observed auroral distributions.

Photometric studies of the great red aurora March 13 and 14, 1989

Extended photometric coverage of the great red aurora of March 13–14, 1989 was obtained at the Rabbit Lake observatory located in northern Saskatchewan, at an eccentric dipole latitude of 65.3°. The red aurora first appeared there about 0311 UT on March 13 and appeared to have run its course by about 0700 UT on March 14. During much of the two nights the observatory was near the poleward edge of the display; the aurora was active much of the time and its brightenings were accompanied by poleward expansions to as far north as the observatory. Combining these observations with those at low latitudes suggest a large auroral expanse from an equatorward edge of about 30° to a poleward edge of about 65° magnetic latitude. One key value of the optical data was the semicontinuous monitoring of major auroral emission intensities. The 01D emission at 630 nm reached 130 kR intensity shortly after onset, at about 0347 UT on March 13. Its intensity the following night was typically 35 kR or below. A HILAT satellite pass around 0415 UT March 14 indicated an electron influx of average energies varying between 150 and 800 eV. The excitation efficiency for the 630 nm emission, neglecting any collisional deactivation, was approximately 1 kR per erg cm−2 s−1 (1 erg = 10−7 J) of precipitating electron energy. These measurements along with related worldwide observations will assist in gaining a better understanding of the magnetospheric conditions producing such major widespread auroras.

New definitions of an eccentric dipole for the geomagnetic field

Optimum eccentric dipoles are calculated from the geomagnetic field models using several different minimum conditions in the least-squares method. In this calculation the three components of the dipole moment vector as well as its location are determined. The higher harmonics above the quadrupole, which have been neglected in the conventional definition, are also taken into account. The dipoles thus defined are named ‘the LSM-dipoles’ in this paper. By definition, these LSM-dipoles are not necessarily parallel to the conventional eccentric dipole whose vector dipole moment is the same as that of the centered dipole. This circumstance is not inconsistent with the fact that the vector dipole moment of a given distribution of magnetic field is independent of the choice of the origin of the coordinate system. Derivations based on four different minimum conditions are presented; for example, the total magnetic energy integrated over the whole space outside the Earth's core is minimized. The four LSM-dipoles determined are located 4–23° south of and 4–12° north of the ordinary eccentric dipole position, and migrate with speeds a little larger than for the latter. Differences are also found between the radial distances from the Earth's center of these dipoles and that of the ordinary eccentric dipole, but these differences are small relative to the differences in the longitudinal and latitudinal directions. However, these dipoles (including the conventional eccentric dipole) follow traces that are qualitatively similar to each other in spite of the differences in their location and drift rate. This suggests that although the position of an LSM-dipole is dependent on the (centered) quadrupole and higher terms, the time variation in its position is mainly controlled by the quadrupole.

Seasonal and longitudinal effects on plasmaspheric tube content

A mathematical model of the ionosphere and plasmasphere that includes an eccentric dipole geomagnetic field has been constructed to model, in the first instance, whistler results at L = 2.5. Observations show that there is a pronounced annual variation in plasmaspheric tube content at mid-latitudes and that this effect is modulated by longitude. The model results indicate that the geometry of the magnetic field (in terms of geographic coordinates) is a major factor in determining the magnitude of the annual variation, with neutral air winds and the degree of plasmaspheric refilling also important. A global variation in neutral atomic hydrogen abundance appears to have little influence.

Polar cusp topology and position as a function of interplanetary magnetic field and magnetic activity: Comparison of a model with Viking and other observations

A family of quantitative magnetospheric models is used to determine the cusp position in the ionosphere and to analyze the field topology around the outer cusp. It is demonstrated that the “cusp proper” (∼1° × 2 hours), observed in particle precipitation patterns, can be defined as the footprint of the magnetopause current layer with field lines connected to the interplanetary medium via a normal magnetic field component. A wider magnetic local time extent of the cleft (∼8–16 hours MLT) can be associated with field lines connected to the low‐latitude boundary layer between XGSM = 0 and 20 RE downtail and extending 1–2 RE inward from the magnetopause layer. It is suggested that the finite‐sized physical cusp originates as a result of gyroviscous erosion at the magnetopause current layer that enlarges the topologically singular magnetic cusp. The model‐predicted magnetic latitude (MLAT) of the ionospheric footprint of the cusp is 79° during quiet conditions and 74° during active periods. The latitude of the cusp varies also with universal time and with season, due to variation of the dipole tilt angle. The corrected magnetic coordinates are found to exhibit the smallest amplitude of diurnal variation of the cusp position and are recommended for mapping of auroral phenomena. Other coordinate systems produce artificial diurnal variations of the cusp position. These artificial effects have an amplitude of ±2.5 (±1) hours MLT and ±4° (±2°) MLAT for dipole (eccentric dipole) coordinates, respectively. An interplanetary magnetic field (IMF) By component linearly superposed with the magnetospheric field can shift the magnetic local time of the cusp by a maximum of 0.07–0.15 hour/nT. A negative (positive) IMF Bz component can shift equatorward (poleward) the position of the cusp by a maximum of 0.1°–0.2° /nT. A similar effect is obtained with a positive (negative) Bz component. These results imply that the instantaneous effect of a negative Bz component on the equatorward shift of the cusp is smaller than an indirect effect due to increased magnetic activity. Some of the model predictions are compared with cusp observations made on board the Swedish Viking satellite. Both the Viking and other observations can be quantitatively explained by the model predictions.

Model plasmasphere calculations for L-values near 2.5 at the longitude of Argentine Islands, Antarctica

A model of the terrestrial plasmasphere that includes an eccentric dipole geomagnetic field has been developed. Calculations are carried out for tubes of plasma at the longitude of Argentine Islands, Antarctica (64°W). Results for L-values around 2.5 are compared with those obtained in VLF experiments at Faraday that detect whistler signals from NAA and NSS stations in the north east U.S.A. Calculated group delay and Doppler shift of whistler signals are analysed by the usual technique employed by experimenters at Faraday to deduce meridional E × B plasma drift and rate of change of plasma tube content (i.e. ionosphere-plasmasphere flux). The deduced drifts and fluxes are compared with those from the model.

A Best-Fit Eccentric Dipole and the Invariance of the Earth's Dipole Moment.

It is demonstrated by a simple example and an elementary calculation that under certain conditions the moment of a dipole fitted to a distribution of magnetic potential is not necessarily the same as the dipole moment in the original magnetic potential. The dipole moment of the original magnetic potential which is a vector quantity specified by the first three coefficients in the spherical harmonic expansion is invariant, that is, independent of the choice of the origin of the coordinate system. Despite this, the moment of the fitted dipole can be different from the dipole moment in the original magnetic potential, depending on the choice of the optimum condition for the fitting. The optimum condition used here differs from that adopted in Schmidt's definition in that in the present definition coefficients of all degree and order are considered. The present definition becomes identical with Schmidt's definition when the harmonics of degrees higher than the quadrupole are truncated. When all the higher harmonics are included in the definition, we obtain a moment and location of the dipole different from those obtained from the classical method of Schmidt. Moreover, the obtained dipole moment and location are different from those deduced from a generalization of Schmidt's definition by inclusion of all harmonics to the infinite degree. For the present geomagnetic field, this method of analysis gives a dipole position shifted from the conventional eccentric dipole position roughly by 80km, and a moment reduced roughly by 20nT.

The geomagnetic time and position of a terrestrial station

The concepts of geomagnetic time and position of a station on Earth are reviewed on the basis of the centred dipole, and the eccentric dipole, magnetic field approximations. Equations are presented from which the centred dipole coordinates can be computed as a special case of the eccentric dipole coordinates. It is also shown that several aspects relating to geomagnetism appear to vary nearly linearly with time and are well represented by linear regression equations which can significantly simplify subsequent computations. Sufficient information is included so that magnetic time and position for any station on Earth may be calculated. Sample results are presented which specifically relate to Scott Base, Antarctica.

Eccentric dipole sources in fluid-filled boreholes: Numerical and experimental results

A frequency-wavenumber (ω−k) representation is given for the response of eccentric multipole sensors in a fluid-filled borehole. Specializing to eccentric dipole sensors, synthetic time-domain waveforms from an array of receivers deployed along the axis of the borehole are displayed for a range of eccentricity magnitude and orientation, formation slowness, and borehole radius. Flexural wave slowness estimates within several frequency bands are extracted from the synthetic waveforms using a semblance technique. For eccentricity small relative to the borehole radius, the character of dipole waveforms and the estimated flexural slowness are little changed. When the eccentricity is a substantial fraction of the borehole radius, flexural wave amplitude is greatly increased, and strong nonmonotonic trends are introduced due to interference with other modes. If eccentricity is not parallel to the transmitting dipole axis, substantial signals are detected on cross-dipole receivers, perpendicular to that of the transmitting dipole. Eccentricity effects decrease with frequency. Even for large eccentricity, flexural slowness estimates are affected only slightly. Scaled laboratory experiments confirm the numerical results. Comparison of the experimental and numerical waveforms is made for both centered and eccentric dipoles in several model formations. The predicted increase and nonmonotonic variation of flexural wave amplitude versus receiver offset for eccentric sensors is observed. Experimental and numerical waveforms overlay with excellent agreement.

Effects of quiet time plasmaspheric electric fields on electron and proton precipitation

The effect of the corotation and the quiet time ionospheric dynamo electric fields on the dynamics of energetic electrons and protons (with energies between 50 keV and 1 MeV), inside the inner magnetosphere, is investigated, using the concept of drift paths of constant effective potential. The quiet time ionospheric dynamo electric field is given by an analytic empirical model based on scatter radar observations. The corotation electric field and the Earth's magnetic field are given by analytic expressions corresponding to a centered and an eccentric dipole model. The main conclusion is that the quiet time electric fields cause a diurnal modulation of the electron and proton precipitation. At low L values the locus in longitude of the maximum precipitation is shown to be energy dependent.

Vector analysis of three-dimensional evoked potentials: eccentric dipoles.

The quantitative description of three-dimensional cerebral evoked potentials is extended to include eccentric dipolar sources. Eccentricity-related distortions in dipole orientation and magnitude are assessed. The use of nonstandard montages, the prediction of topographic surface maps, dynamic analysis, and theoretical mechanisms of planar segment formation are discussed.

SAMA: For how long?

The South Atlantic Magnetic Anomaly (SAMA) has been studied since the beginning of the sixties. This region of low field intensity in the South Adantic near Brazil is known to have important consequences in radiationbelt physics “e.g., Pinto and Gonzalez, 1986”. This feature of the field can be explained by the concept of an eccentric dipole. This concept, specified by the dipole and quadrupole terms of the multipole expansion of the geomagnetic field, account for about 90% of the surface field “Parkinson, 1983”.

On IGRF models for 1945–1985

Several candidate models for 1945 are compared and models for 1945–1990 are estimated in terms of the eccentric dipole.

Centered and eccentric geomagnetic dipoles and their poles, 1600–1985

Using a unified approach, expressions are derived for the various pole positions and other dipole parameters for the centered and eccentric dipole models of the earth's magnetic field. The pole positions and other parameters are then calculated using the 1945–1985 International Geomagnetic Reference Field Gauss coefficients and coefficients from models of the earth's field for earlier epochs. Comparison is made between (1) the recent pole positions and those pertaining since 1600 and (2) the various theoretical pole positions and the observed dip pole positions.

World Magnetic Charts for 1985 - spherical harmonic models of the geomagnetic field and its secular variation

The 1985 World Magnetic Charts, published by the UK Hydrographic Department and by the US Defence Mapping Agency, have been produced jointly They are based on spherical harmonic models of the main geomagnetic field (168 coefficients) and of the secular variation (80 coefficients). These models are presented here with a discussion of the data on which they are based and of the methods used to derive them. Positions of the dip-poles, the geomagnetic poles and the eccentric dipole, together with their rates of change, are derived from the models.

Experimental foundation of the Gabor-Nelson theory applied to boundaries which are non-insulating

In order to found the application of the Gabor-Nelson theory to non-insulating boundaries, we have used a network which we have divided into two parts: a core energized by a source sink pair and an appendage, the conductivity of which may or may not differ from that of the core. By ignoring the appendage and by applying the Gabor-Nelson method to the restricted perimeter as if it were totally insulating, we stress the errors made in computing the dipole strength, orientation and position and how they are influenced by the dipole eccentricity, by its orientation with respect to the junction between the added portion and the core, and by a change in conductivity between the same compartments. Finally, we restore the dipole characteristics by using the appropriate correction derived from theory. Comparing the later results to those obtained by applying the Gabor-Nelson method to the whole insulating boundary leads to the conclusion that the correction is founded and must be taken into account.

Complete calculation of the electric potential produced by a pair of current source and sink energizing a circular finite-length cylinder

Green’s function for the solution of Poisson’s equation in cylindrical coordinates is calculated using the underlying Sturm–Liouville problem. The potential distribution produced by an arbitrarily oriented eccentric dipole located in a homogeneous conducting circular finite-length cylinder is given; three alternative forms are presented, which enable us to compute the potential everywhere in the cylinder. Previous works devoted to this subject were incomplete in the sense that the formulas which were presented there do not converge everywhere. For our expressions of the Green function,we show that Gabor and Nelson’s theorem applies for the present geometry. We also consider the case where the current source and sink are remote from each other in order to check the consistency between Gabor and Nelson’s theorem and Helmholtz’s principle. Applications of our formulas are presented in a situation which is representative of the human trunk activated by the heart and discussion of the results is made in relation with electrocardiology. It is shown that the eccentricity of the dipole is responsible for curving the line of the greatest potentials and for wrapping the zero equipotential plane.