Showing papers on "Dipole model of the Earth's magnetic field published in 1981"

Alfven wave resonances in a realistic magnetospheric magnetic field geometry

Abstract: The notion of magnetic field line resonance has been very effective in explaining many features of long-period geomagnetic pulsations. To date the decoupled transverse wave equations have been solved in a magnetic dipole field, whereas only WKB approximate solutions have been used in more general geometries. We have developed a solution of the decoupled equations that includes both a general magnetic field geometry and the effects of density and mass composition. The aim of this paper is to isolate and examine the effect on eigenfrequencies of only the field geometry by keeping density constant along all field lines. We review the diurnal variations in wave period predicted on the ground and in space by using the recent Olson-Pfitzer magnetospheric magnetic field model in our solution. For example, on the ground at 67° magnetic latitude the diurnal variation in period caused by field geometry is larger than a factor of 2. At 6.6 RE, where the dipole field line from 67° crosses the magnetospheric equator, there is negligible diurnal variation in period. Significant diurnal variations in period (≳10%) at fixed radial distance in the equatorial plane in space occur only at distances ≳10 RE. Knowledge of the field geometry is shown to be important for the determination of mass density in space from ground pulsation observations. We discuss the impact of our results in interpretation of experimental data.

Calculation of force-free magnetic field with non-constant α

Abstract: A numerical method is developed for solving the force-free magnetic field equation, ▽ × B = α B, with spatially-varying α. The boundary conditions required are the distribution of B n (viz. normal component of the field on the photosphere) as well as the value of α in the region of positive (or negative) B n . Examples of calculations are presented for a simple model of a solar bipolar magnetic region. It is found that the field configuration and the energy stored in the field depend crucially on the distribution of α. The present method can be applied to a more complex configuration observed on the Sun by making use of actual magnetic field measurements.

Substorm signatures at synchronous altitude

Abstract: The signatures of magnetospheric substorms near 6.6 earth radii are statistically examined using data obtained on board ATS 6 by magnetic field and energetic particle measurements. It is confirmed that the configuration change toward a tail-like field in the dusk-to-midnight sector typically begins about one hour before the onset of the expansion phase of a substorm. Configuration changes before the onsets of moderate substorms are characterized by a directional change of magnetic field at magnetic latitude of approximately 10 deg, rather than by a change in the field magnitude. It is found during storm periods that the magnetic field orientation occasionally becomes almost parallel to the magnetic equator before expansion phase onsets. Here, the field magnitude usually increases above background levels. These facts are seen as strongly suggesting that a tail-like configuration is caused by an intensification and earthward motion of the cross-tail current system, often close to 6.6 earth radii, rather than by development of diamagnetic ring current.

The magnetic field of Jupiter: A generalized inverse approach

Abstract: The estimation of planetary magnetic fields from observations of the magnetic field gathered along a spacecraft flyby trajectory is examined with the aid of generalized inverse techniques, with application to the internal magnetic field of Jupiter. Model non-uniqueness resulting from the limited spatial extent of the observations and noise on the data is explored and quantitative estimates of the model parameter resolution are found. The presence of a substantial magnetic field of external origin due to the currents flowing in the Jovian magnetodisc is found to be an important source of error in estimates of the internal Jovian field, and new models explicitly incorporating these currents are proposed. New internal field models are derived using the vector helium magnetometer observations and the high field fluxgate observations of Pioneer 11, and knowledge of the external current system gained from the Pioneer 10 and Voyagers 1 and 2 encounters.

Saturn's ring current and inner magnetosphere

Abstract: The Voyager 1 magnetic field observations at Saturn are shown in a graph. The departure of the oberved magnetic field from the field of a dipole is considered. The observed field magnitude is appreciable less than that of the model dipole at small radial distances and greater than the model dipole in the more distant magnetosphere. These characteristics can be understood by introducing a model current system similar to a system originally applied to observations of the Jovian magnetic disk. Saturn's ring current has important implications for charged-particle motion in Saturn's magnetosphere, particularly the absorption of trapped radiation by its many satellites and rings. The absorption signature observed by the Voyager 1 cosmic ray experiment near the orbital position of Rhea illustrates well the effects of Saturn's ring current on charged particle trajectories.

A three dimensional MHD model of the Earth’s magnetosphere

Abstract: The results of a global MHD calculation of the steady state solar wind interaction with a dipole magnetic field are presented. The computer code used, being much faster than previous codes, makes it possible to increase the number of grid points in the system by an order of magnitude. The resulting model qualitatively reproduces many of the observed features of the quiet time magnetosphere including the bow shock, magnetopause, and plasma sheet.

A cause of solar wind speed variations observed at 1 a.u.

Abstract: An attempt is made to interpret solar wind variations observed at the earth's distance, namely the solar cycle variations, the semi-annual variations, and the 27-day variations, as well as the polarity changes of the interplanetary magnetic field, mainly in terms of two effects, a positive latitudinal gradient of the solar wind speed and a wobbling solar dipole, combined with the annual (heliospheric) latitudinal excursion of the earth. It is shown that a significant part of the solar wind variations observed at the earth's distance and the changes of polarity pattern of the interplanetary magnetic field can be reasonably well reproduced by the two effects.

Chatanika Radar observations relating to the latitudinal and local time variations of Joule heating

Abstract: Observations of plasma convection made with the Chatanika incoherent scatter radar have been analyzed to give latitude/local time plots of the electric field contribution (E squared) to thermospheric Joule heating. The data, which plan the invariant latitude range 56 deg to 75 deg, show the presence of strong heating throughout the auroral regions. Of special interest are brief interludes of intense heating (greater than 50 mW/sq m) that are observed at nearly all local times and latitudes in response to magnetospheric disturbances. Further, there seem to be particular regions of the auroral oval where Joule heating seems to be continually enhanced above the broad background. The results of six 24-hour experiments are presented to illustrate summer and winter conditions. A shorter eight hour experiment is also given to show the characteristics of cleft heating, insofar as they are visible to the Chatanika radar.

The role of particle drifts in solar modulation

Abstract: The importance of gradient and curvature drifts in the description of the transport of cosmic rays in the heliospheric magnetic field is considered. It is shown that, contrary to recent claims, the conventional expression for the drift flux (F/sub perpendicular/ = c(qB/sup 2/)/sup -1/B x delP) may not be incorporated into the interplanetary cosmic-ray transport equation to describe particle drift in static magnetic fields with arbitrary spatial variation. For magnetic field configurations satisfying the restrictions of quasi-linear theory, the conventional expression involving the average magnetic field appears to be valid, but this result may not e extended to more general configurations. For one configuration involving magnetic flux tubes containing helical magnetic fields (which may indeed occur in the solar wind), the drift transport of particles is effectively eliminated. Altogether, in spite of the possibility that the solar magnetic field exhibits a simple dipolar morphology, the role of the conventional drift flux in solar modulation may, but need not, be of importance.

A simple physical model for the terrestrial dynamo

Abstract: The strength of the earth's magnetic field results from an equilibration between rates of buoyant energy production and Ohmic dissipation. Changes in magnetic field, in particular the long term changes in dipole moment, provide an indication of changes in core energy sources, and so become critical data for understanding the evolution of both the core and deep mantle. A simple physical model is proposed to establish a connection between dipole moment behavior and production of buoyancy within the core. The model rests on two hypotheses: (1) magnetism is generated by small scale, rotation dominated turbulence consisting of a field of propagating inertial waves, and (2) the turbulence is supported by a flux of buoyancy, thermal or compositional, originating either at the core-mantle or inner core boundary. The efficiency with which wave kinetic energy is converted to magnetic energy is determined by the wave helicity—the correlation between velocity and vorticity. The wave helicity is non-zero if there exists a preferred propagation direction. Negative buoyancy generated at the mantle-core boundary leads to propagation radially inward; positive buoyancy generated at the inner core boundary leads to radially outward propagation. Using parameters appropriate for the earth's core, we find that the inertial wave dynamo dissipates 8 × 1011 W in generating a magnetic field equal to the present terrestrial field. Four energy sources are considered: decay of potassium 40, secular cooling, inner core growth, and differentiation of the core from the mantle. Any of these sources can reasonably support the turbulent dynamo for much of the earth's history.

On the spectrum of turbulent magnetic fields

Abstract: Theoretical power spectra of magnetic fields subject to turbulent fluid motions in the kinematic regime are presented, and previous theories are reviewed, with reference to magnetic fields on the sun. Magnetic field diffusion in turbulence with persistent eddies is predicted to be described by an effective negative magnetic diffusivity. It is found that observations cannot be explained on the basis of turbulent kinematic theories unless the turbulent motions are three-dimensional, and the effective diffusivities are larger than the molecular diffusivities. Lower bounds on the turbulent viscosity are derived, suggesting that dynamical processes controlling the magnetic field spectrum occur at least 15,000 km below the surface. The results, which remain consistent with the assumption that effective diffusivity is uniform, suggest that surface magnetic field observations can be used as a diagnostic for subsurface flows.

Propagation of low energy solar electrons

Abstract: Two events are reported in which 2-10 keV electrons of solar energy have undergone significant adiabatic mirroring and pitch angle scattering in large scale magnetic structures in the interplanetary medium within a distance of about 0.5 AU from the earth. Electrons of 3 keV, typical of the energies measured, have a speed of about one-tenth of the speed of light, so that their travel time from the sun at 0 deg pitch angle would be about 100 minutes. Their cyclotron radius is about 20 km for a pitch angle of 30 deg, and a field of magnitude of 5 nT, and the cyclotron period is about 7.1 milliseconds. The electrons are scattered by spatial variations in the interplanetary magnetic field. When the spatial variations are convected past a stationary spacecraft by a 500 km/sec solar wind, they are seen as temporal fluctuations at a frequency of about 3 Hz.

Dynamo theory of the earth's varying magnetic field

Abstract: Various forms of the dynamo theory are presented in a graphic manner. Each of them depends on a flow pattern of presumably thermal convection in the earth's fluid core. The conducting fluid moves in magnetic fields generated by currents induced by the motion. Each of the flow patterns includes vortices, with helicity induced by the Coriolis force, that twist the magnetic fields in such a way as to regenerate an initial field. Some of them involve also differential rotation, with the parts of the core near the axis rotating more rapidly than the outer parts. Some forms of the theory are more successful than others in accounting qualitatively for the various observed aspects of the field, particularly the westward drifts and the occasional polarity reversals. The thermal energy source may be radioactivity of heat or crystallization at the inner-core surface.

Magnetostatic atmospheres in a spherical geometry and their application to the solar corona

Abstract: The formalism for deriving ‘two-dimensional’ magnetostatic equilibria is extended to spherical coordinates and applied to magnetic fields that are functions of radius and polar angle. A family of analytic solutions is readily found. The basic properties of these solutions are displayed for a dipole magnetic field at the base of the atmosphere and for physical parameters appropriate to the solar corona. Variation of the concentration of plasma at the ‘magnetic equator’ illustrates the distortion of a simple dipole magnetic field by the electric currents required to maintain force balance in the presence of the imposed pressure gradients in the polar direction. The deviation of the magnetostatic field lines from the simple dipole configuration depends on the parameter (Peq–Ppole)/(B0²/8π), where Peq and Ppole are the equatorial and polar plasma pressures and B0 is the dipole field strength at the base of the corona. Reasonable choices of these physical quantities give a value for this parameter of about 1/2, implying deviations in the large-scale coronal magnetic field geometry from the commonly used potential field that are not negligible. These deviations lead to field lines that are more nearly vertical at the base of the corona and to more magnetic flux on open field lines than in potential field models with the same magnetic boundary conditions.

Mercury's magnetosphere and magnetotail revisited

Abstract: Magnetic observations which are not complicated by currents of trapped plasma are a good test of geomagnetopause and geomagnetotail predictions. Recent attempts to model the Hermean magnetospheric field based on a planet-centered magnetic multipole field with a quadrupole moment in addition to the planetary dipole field or a dipole field linearly displaced from planet center and no quadrupole moment have produced reasonably good fits to the Mercury magnetic field measurements. In this work we find a better fit for a dipole displacement from the planet center by making use of an improved representation of the magnetic field in the magnetotail, where many of the Mercury measurements were made. The rms deviation of the data was reduced from 10. or 11. γ to 9.3 γ by employing this new tail field representation. Also, by making use of this new tail field representation, we find a best fit for a dipole displacement of −0.0285 RM (earlier, 0.026 RM) toward the dawn in the magnetic equatorial plane and 0.17 RM (earlier, 0.189 RM (earlier, 0.189 RM) northward along the magnetic dipole axis, where RM is the planet radius. Thus with only minor adjustments in the displacement vector of the dipole from the planet center we achieve a measurable improvement in the fit of the data by using the improved magnetotail field representation.

Modelling coronal magnetic fields

Abstract: The ‘hairy ball’ model of coronal magnetic fields has a spherical source surface separating potential and radial magnetic fields. In the present model the source surface is chosen such that the wind speed equals the Alfvenic speed at selected points on the source surface. Results have been obtained for a dipole base field and an isothermal corona.

Nonlinear development of magnetic reconnection in the tearing-type and the Petschek-type field geometries

Abstract: Distinct hydromagnetic characteristics associated with the tearing-type and the Petschek-type field geometries are numerically studied. Both the tearing-type and the Petschek-type reconnections are initiated by local resistive disturbance and develop from an initially antiparallel magnetic field. In the tearing-type field geometry the current-sheet plasma, accelerated at X-type neutral points through reconnection, cannot be ejected away from the system but is confined in the resulting magnetic islands. It is found that the nonlinear saturation oscillates as a result of the interaction between the confined plasma and the surrounding magnetic field; the period of the oscillation is approximately given by the time required for an Alfven wave to cross one wavelength. On the other hand, in the Petschek-type field geometry the plasma can freely be ejected away from the system, so that the antiparallel field is allowed to collapse into the X-type neutral point.

On the magnetic field in the tail of Comet Halley

Abstract: The method of evaluation of the cometary magnetic field proposed by Podgornyet al. (1980) is shown not to be self-consistent. An alternative method is discussed.

Possible Use of (a) Solar Faculae and (b) The Interplanetary Magnetic Field as Heralds of a Solar Cycle Peak

Abstract: Two independent methods of predicting the magnitude of the peak of a forthcoming sunspot cycle are summarized. One is based on considerations of the development of spots relative to the area of the faculae within which they form during the early stages of the cycle in question, and gives a lead-time of about 2 years. The other uses measurements of the quiet-day variations of the Earth's magnetic field at the time of the preceding sunspot minimum and allows predictions to be made a half-cycle ahead. A possible extension of this technique to the use of data on the component of the interplanetary magnetic field normal to the ecliptic plane is suggested. References to fuller details of both methods are given.

Magnetospheric Magnetic Field Geometry

Abstract: In this paper we present a calculation of long-period, ultralow-frequency (ULF) magnetospheric pulsations that uses a realistic earth's magnetic field geometry rather than a simple dipole field. The calculation pertains to transverse standing wave oscillations, whether they are Pc 3, 4, or 5 continuous pulsations with periods from 10 to 600 s or the irregular Pi pulsations in the same period range. The presence of standing Alfven wave resonances of the earth's magnetic field lines has been clearly demonstrated by conjugate point and spacecraft observations [see, e.g., Nagata et al., 1963; $ugiura and Wilson, 1964; Van Chi et al., 1968; Lanzerotti et al., 1972, Lanzerotti and Fukunishi, 1974; Kokubun et al., 1976; Singer and Kivelson, 1979]. Several mechanisms have been suggested to generate these waves, but regardless of the method of generation, intrinsic interest in this fundamental magnetohydrodynamic plasma process and the possibility of using the waves to diagnose magnetospheric properties make it worthwhile to model these standing wave oscillations. In the following presentation the basic MHD equations are used to derive an equation for the period and amplitude of low-frequency transverse waves in an arbitrary field geometry. Next, the equation is numerically solved by using a field model that takes into consideration external current systems established because of the earth's interaction with the solar wind. Finally, the model results are compared to those calculated for oscillations in a dipole magnetic field. In hydromagnetics, the wave equation for low-frequency waves in an infinitely conducting, stationary, magnetized plasma with zero pressure can be derived from the following linearized equations:

A comparison of type III metric radio bursts and global solar potential field models

Abstract: Evidence of coronal magnetic fields from polarized metric type III radio bursts is compared with (1) global potential field models, (2) direct averages of the observed photospheric magnetic field, and (3) H-alpha synoptic charts. The comparison clearly indicates both that the principal aspects of type III burst radiation are understood and that global potential field models are a significantly more accurate representation of coronal magnetic field structure than either the large-scale photospheric field or H-alpha synoptic charts.

Free-Free Opacity in Strong Magnetic Fields

Abstract: A way of computing the absorption cross-section for photons on electrons undergoing free-free transitions in magnetic plasma is described. Theoretical expressions for the free-free cross sections in magnetic plasma are given in a representation in which they can be easily compared with the classical results in the absence of the magnetic field. The results of numerical computations of these cross-sections are also presented and discussed. Finally the free-free cross-sections are averaged over the electron states in magnetic plasma in thermal equilibrium, yielding the opacity coefficient as a function of photons frequency. The results of numerical computations are given in graphical form.

The Schwarzschild criterion for convection in the presence of a magnetic field

Abstract: The Schwarzschild criterion governing the onset of convective instability has been modified to include magnetic field. This may be of importance for solar variability. The revised condition suggests that the underside of field layers are stabilizing and the upper side destabilizing. Absolute instability can be reached to achieve conventional magnetic buoyancy. This may explain the inverse correlation between the time intervals between sunspot minima and sunspot maxima with the maximum values of sunspot number, which is found to be significant at the 5.5 sigma level.