Showing papers on "Dipole model of the Earth's magnetic field published in 1964"

Deformation of the geomagnetic field by the solar wind

Abstract: From the three-dimensional numerical solution to the Chapman-Ferraro problem of a steady solar wind perpendicularly incident upon a dipole field, a simple spherical harmonic description of the distorted field is obtained. From this, a three-dimensional picture of the field line configuration within the magnetosphere is given. The field lines are found to be compressed on both the daytime and nightiime sides. The behavior of the field lines on the daylight side changes abruptly as one approaches a critical latitude, which ranges between 80 and 85 deg , depending on the intensity of the solar wind. Above this latitude, lines originating along the noon meridian pass over the north pole and cross the equator alorg the midnight meridian. The behavior of conjugate-point phenomena and trapped particles near this critical latitude is discussed. Magnetic changes at the earth's surface due to an increase in the solar wind intensity are calculated. The diurnal variations due to a steady solar wind are also calculated; they are found to be small compared with observed S/sub q/ fields. (auth)

Initial results of the imp 1 magnetic field experiment

Abstract: The interplanetary monitoring platform Imp 1, or Explorer 18, launched on November 27, 1963, has provided the first accurate measurements of interplanetary magnetic fields. The initial apogee of the satellite was 197,616 km on the sunlit side of the earth, with an apogee-earth-sun angle of 26°. This paper presents the initial results of the detailed measurements of the interplanetary magnetic field and the interaction of the solar wind with the geomagnetic field. The strength of the interplanetary magnetic field is found to vary between 4 and 7 γ, with extreme values as low as 1 and as high as 10 γ. The magnitude, however, is extremely stable over times of hours, although changes of direction are significant. The average direction of the interplanetary magnetic field is slightly below the plane of the ecliptic and approximately along the streaming angle predicted for a steady-state solar wind. A significant feature of the magnetic field measurements is the discovery of fields pointed diametrically opposite the streaming angle, indicating filamentary structure of the interplanetary field. Associated with the fields of opposite direction are null surfaces between the filaments and in the over-all field structure. The complex interaction of the solar wind and the geomagnetic field shows a variety of magnetic field fluctuations and transition characteristics. The detection of the collisionless magnetohydrodynamic shock wave at 13.4Re at the stagnation point associated with the super Alfvenic flow of solar plasma is one of the major results of this experiment. Details of the fluctuations are discussed, as well as the gross structure and shape of the magnetospheric surface (10.2Re at the subsolar point) and the shock wave from the subsolar point to the nighttime geomagnetic tail. The transition region between the shock wave and the magnetopause is one of high turbulence in the magnetic field. A unique aspect of the magnetic field data is the detection of the magnetohydrodynamic wake of the moon during the fifth orbit, when the satellite was eclipsed by the moon's magnetosphere while in interplanetary space. The implications of this experimental discovery are discussed.

Shape of the geomagnetic field solar wind boundary

Abstract: The shape of the boundary of the geomagnetic field in a solar wind has been calculated by a self-consistent method in which, in first order, approximate magnetic fields are used to calculate a boundary surface. The electric currents in this boundary produce magnetic fields, which can be calculated once the first surface is known. These are added to the dipole field to give more accurate fields, which are then used to compute a new surface. This iterative procedure converges rapidly, and the final surface may be tested by finding how close the total fields outside the boundary are to the required value of zero. The result of this stringent test is that the magnetic fields in the plasma outside the fourth surface and within twice the distance to the boundary on the solar side are everywhere less than 1 per cent of the geomagnetic dipole field in the absence of a solar wind. This surface has been used to calculate the perturbation of the geomagnetic field by the solar wind; the results of these calculations, plus a number of applications, are given in an accompanying paper.

A diffusive model for the initial phase of a solar proton event

Abstract: The presence of an interplanetary magnetic field in the vicinity of the earth is now fairly well established, and several authors have proposed that the long duration of solar proton events is due to the storage of protons in the tubes of force of this field, which we shall assume to be of solar origin. According to one model, protons emitted by a flare diffuse through the solar atmosphere, gradually leaking off into the interplanetary field where they are stored for comparatively long periods. The early anisotropic phase of a solar proton event presumably represents the filling of the earth's local tube of force by this mechanism. An attempt is made to treat the diffusion through the solar atmosphere in a quantitative fashion, and the results are applied to measurements carried out by Explorer 12 on September 28, 1961. These data appear to fit the theory and permit a determination of the diffusion constant. Application of classical diffusion theory, though admittedly of dubious validity, yields a mean free path of about 600 km for protons of a few hundred Mev energy.

Effect of oblique interplanetary magnetic field on shape and behavior of the magnetosphere

Abstract: The oblique angle made by the spiral interplanetary magnetic field with the radially expanding solar wind is shown to result in an easterly deflection of the solar wind as it traverses the standing hydromagnetic shock wave a few earth radii upstream of the magnetosphere. A quantitative estimate of the deflection angle can be obtained from the plasma shock relations, which are solved generally to yield the particle density, temperature, magnetic field, and plasma flow field immediately behind the shock front in terms of the corresponding interplanetary (preshock) parameters. For typical values of the interplanetary plasma and magnetic field parameters, the calculated deflection angle lies between 5° and 20°. The earth's orbital velocity relative to the radial solar wind direction contributes approximately an additional 5° deflection. The two effects combined cause the axis of symmetry of the magnetosphere, on the average, to be tilted away from the earth-sun line as if the solar wind came from an apparent direction between 10° and 25° to the west of the sun. These conclusions are consistent with a considerable body of experimental data and also suggest an alternate explanation for Explorer 10's numerous encounters with the magnetospheric boundary.

A statistical model of the geomagnetic field

Abstract: A statistical model of the geomagnetic field is derived, based on the assumption of an axial geocentric dipole field of strengthHe at the equator perturbed by randomly directed components of constant magnitudeh. The model fits the dispersions found from an analysis of the 1945 field, and the ratioh/He obtained for this field and from the palaeomagnetic data both average to about 0.4. The model predicts that during reversal of the dipole field, the field intensity falls to between 0.2 and 0.4 of the steady field intensity, and this agrees with estimates made from the palaeomagnetic observations.

Radial dipoles as the sources of the Earth's main magnetic field

Abstract: It is assumed that magnetic dipoles are useful as a first approximation to the electrical currents in the core that produce the earth's main magnetic field. For simplicity the model is restricted to a central dipole and several additional radial dipoles at equal distances from the center of the earth. A least-squares method is used to adjust the amplitude, latitude, and longitude of each dipole for a best fit to the observed field components on the earth's surface. In the first of four studies the observed field was the field of the United States 1945 world charts. Originally 11 dipoles, 10 of them at the core-mantle interface at 0.54 earth radii, were used. Progressively better fits were obtained as the dipoles were placed deeper, and two of the dipoles were eliminated at greater depths. The 29-parameter, 9-dipole model, with the radial dipoles at 0.28 earth radii, produced nearly as good a fit to the 1945 field as Vestine's 48 spherical harmonic coefficients. Models were also fitted to the United States 1955 world chart field, to the British Admiralty 1955 world chart field, and to the field synthesized from the Finch-Leaton spherical harmonic coefficients for 1955. The last model produced the best fit. In all cases the radial dipoles are surprisingly deep and the central dipole is considerably stronger than the centered dipole given by the first three spherical harmonic coefficients. The great depth of the radial dipoles is qualitatively explained by a shielding effect from currents in the mantle and core. The spherical harmonic coefficients from the analyses of Vestine and of Finch and Leaton are compared with the spherical harmonic coefficients computed from the dipole parameters.

The solar wind geomagnetic field boundary

Abstract: The theory of the boundary of the cavity surrounding a magnetic dipole immersed in a steadily flowing stream of plasma is reviewed, and the various results are compared with satellite observations of the termination of the geomagnetic field. The shape on the solar side as roughly hemispherical with an indentation near the poles; the shape on the antisolar side is probably that of a raindrop, but it depends critically on the direction and relative magnitude of the interplanetary magnetic field and possible nonadiabatic processes in the boundary transition layer.

Interaction of a supersonic plasma stream with a dipole magnetic field

Abstract: A laboratory experiment is described which simulates some aspects of the interaction of the solar wind and the geomagnetic field. In this experiment, a Mach 2 hydrogen plasma stream from a pulsed coaxial gun was directed against a dipole magnetic field. The shape of the windward side of the magnetic cavity and the circulation of the sheet currents in the boundary were found to be in general agreement with results based on the single-particle model. But the supersonic-fluid model is appropriate for the interpretation of further results. A nonluminous arc-shaped region resembling a bow shock wave appeared upstream from the nose of the cavity, and the plasma was observed to flow irreversibly through this region and around the cavity. Time-resolved photographs depict the dynamics of the interaction, revealing drifts of the plasma near the interface layer and penetration of the plasma into the magnetic cavity. At times following the impact of the plasma on the field, the field near the magnet was found to be asymmetric and generally lower than the normal dipole field. The recovery time of the field to the dipole value was long in comparison with the decay time of the plasma pulse from the gun.

The effect of an interplanetary magnetic field on the solar wind

Abstract: A weak interplanetary magnetic field is shown to be compressed into a boundary layer of high magnetic-field intensity several earth radii deep at the surface of the magnetosphere. Thus, if the solar wind consisted of streams of plasma interspersed with an interplanetary magnetic field, magnetic intensity beyond the magnetopause would be expected to fluctuate for several earth radii from zero to as high as the value at the boundary of the magnetosphere. The compressed field is tangential to the boundary and, in general, unrelated in direction to the field inside the boundary. Both conclusions are in agreement with satellite measurements. Particles in the solar wind travel smoothly around to the dark side of the earth where their pressure and the compressed interplanetary magnetic pressure may be expected to close the hollow the geomagnetic field creates in the solar wind.

Trapped particles in a distorted dipole field

Abstract: A dipole magnetic field is analytically compressed and extended to represent a possible effect of the solar wind on the earth's magnetic field on the day and night side of the earth in the earth-sun meridian plane. The first and second adiabatic invariants of particle motion are used to calculate the mirror points of constant energy particles in the compressed and extended fields. The results support and clarify work by previous investigators, showing that shifts in mirror points of particles moving from one field to the other are large at large distances and smaller at lower altitudes. The results are compared to the experimental findings of recent satellites. It is concluded that field distortion may be a major cause of the observed shift in mirror points, but that final resolution of the problem will depend on further determination of the magnetic field on the night side of the earth.

The Energy of Magnetic Storms

Abstract: Summary The extra magnetic energy present in the magnetosphere during a magnetic storm is shown to be the same as if the disturbing field existed without the main field of the Earth: that is, the “joint” energy of the two fields is zero. The disturbance field energy is considered for both the first and the main phase of a storm, on the basis of idealized models of the electric currents that cause the disturbance. The currents, actually distributed throughout volumes, are taken to flow only on surfaces. Numerical estimates of the field energy are given, for a weak storm and for a great storm. The magnetic moment of the field of the ring current is also considered; it is inferred that it is only a small fraction of the Earth's dipole moment. The field energy of magnetic storms is found to be less than the kinetic energy associated with the ring current at the peak of the main phase.

Ionospheric focusing in the presence of the earth's magnetic field

Abstract: A new technique has been developed for application to problems of radio wave propagation in magnetoionic mediums. This method is based on a mathematical formulation of Poeverlein's graphical solution. The mathematical formulation is made possible by assuming that the index of refraction surfaces are ellipsoids of revolution. Complicated problems can be solved in terms of the semiaxes, a and b, of these ellipsoids, which can be evaluated as continuously varying elements by means of the Appleton-Hartree equation. The results obtained through the application of this method are as exact as that equation. The problem of focusing in the terrestrial ionosphere has been investigated in complete generality through an application of this new technique. The general equations obtained have the same structure as those previously derived by neglecting the terrestrial magnetic field. The corresponding radiation patterns are substantially different, however, when the effects of the earth's magnetic field are included. The effects of the earth's magnetic field are very pronounced and cannot be ignored as X approaches unity and Y becomes relatively large. This is the domain of interest to radio astronomy in space.

Interaction of a Streaming Plasma with the Magnetic Field of a Two‐Dimensional Dipole

Abstract: The flow of an infinitely conducting plasma past a two‐dimensional magnetic dipole oriented parallel to the flow has been considered by Hurley, among others. The problem consists of finding a vacuum magnetic field such that along a bounding field line whose location is to be found, the magnetic pressure balances the Newtonian dynamic pressure appropriate to the local slope of the boundary. A related problem has been solved by Cole and Huth; in their case there is no flow, but an isotropic static plasma surrounding the magnetic field region which exerts a constant pressure on the boundary. In the actual flow problem we would expect there to be a stagnant (trapped) region near the front. The stagnant flow would be at nearly constant pressure. Away from this region the Newtonian pressure would again be applicable. This problem, which is a mixture of those cited above, has been solved by an approximate technique due to Cockcroft. The solution is shown to have features of both the cited problems, as appropriate.

Magnetostatic Measurement of Spacecraft Magnetic Dipole Moment

Abstract: This paper describes a technique for determining the magnetic dipole moment of a spacecraft by sampling its magnetic field at constant radius. Integral equations relating magnetic field samples to the three-axis dipole components are derived from a multipole expansion of the distributed magnetic source. Included in this paper are a description of a magnetic test facility and a sample calculation demonstrating the above theory.

Penetration through the magnetopause and trapping in its vicinity

Abstract: In recent years the magnetic field of the earth has been measured at large distances from the earth's surface by means of magnetometers mounted in satellites [Cahill, 1963]. It has been found that the geomagnetic field lies within the magnetosphere, limited and shaped by the interaction of the solar wind [Parker, 1963] with the earth's field. The field on the sunward side is now fairly well known, the magnetopause lying at a distance of approximately ten earth radii from the earth's center. The field corresponds quite well up to about six earth radii to that of a dipole. At larger distances the field lines are compressed, and the external field due to magnetopause currents becomes important. A harmonic analysis of this external field for a zero temperature, field-free solar wind has been made by Mead [1964].

The interaction between the solar wind and the earth's magnetic field.

Abstract: : The report consists of a study of the interaction between the solar wind and the earth's magnetic field, which takes into account: (1) the presence of an interplanetary magnetic field within the solar wind, and (2) the possibility that the solar wind may be penetrated by field lines emanating from the earth. The first part of the report (Chapters I-IV) contains a qualitative discussion of the field and flow patterns which may develop under the conditions stated above. The second part of the report explores two methods for the treatment of the MHD equations which govern the interaction, namely, expansion in spatial coordinates, and parametric expansions. The first method, which is suitable for local studies of the flow, is applied to the region in the immediate vicinity of the stagnation line behind the bow shock. The results of this treatment are embodied in a local field-flow pattern, which reveals several features which can be attributed directly to the presence of an interplanetary field within the solar wind, weak as those fields may be.