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 nighttime 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°, 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 along 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 Sq fields.

A quantitative model of the external magnetospheric field has. been derived by making least squares fits to magnetic field measurements from four Imp satellites. The data set consists of 12,616 vector field averages over half-earth radii intervals between 4 and 17 Re, taken from 451 satellite orbits between 1966 and 1972. The data were fit to a power series expansion in the solar magnetic coordinates and the solar wind-dipole tilt angle, and thus the model contains the effects of seasonal north-south asymmetries. The expansion is divergence free, but unlike the usual scalar potential expansion, the model contains a nonzero curl representing currents distributed within the magnetosphere. The model includes four sets of coefficients, representing different degrees of magnetic disturbance as determined by the range of Kp values. The latitude at the earth separating open polar cap field lines from field lines closing on the day side is about 5 ø lower than that determined by previous theoretically derived models. At times of high Kp, additional high-latitude field lines extend back into the tail. Near solstice, the separation latitude can be as low as 75 ø in the winter hemisphere. The average northward component of the external field is much smaller than that predicted by theoretical models; this finding indicates the important effects of distributed currents in the magnetosphere. Current densities implied by the model are of the order of 10 -9 A/m: across the magnetotail.Quantitative models of the geomagnetic field generally fall into two types: those that describe the field due to sources inside the earth (internal models) and those that attempt to describe the effect of currents located above the earth's surface (external models). Internal models are derived from direct measurements of one or more components of the field. Since the time of Gauss, spherical harmonic expansions of a scalar potential have been used to fit these measurements, Similar techniques have been used to model the overhead current systems responsible for the diurnal and lunar variations in the surface field. However, up until now, quantitative models of the external magnetospheric field have not been based on field measurements or were based only indirectly on them. Calculations of the contribution of magnetopause currents[Mead, 1964; Midgley, 1964; Choe and Beard, 1974] have been based on theoretical solutions to the traditional Chapman-Ferraro problem of an unmagnetized plasma incident upon a magnetic dipole [e.g., Mead and Beard, 1964; Olson, 1969; Choe et al., 1973]. In these calculations the resulting external field is expressed in terms of a scalar potential expanded in spherical harmonics and modified to reflect.the fact that the current sources are external to the region of the expansion. Other models [Hones, 1963; Taylor and Hones, 1965; Williams and Mead, 1965; Antonova and Shabanskiy, 1968; Sugiura and Poros, 1973; Olson and Pfitzer, 1974; Olson, 1974] have been based partly on theory and partly on known characteristics of the exte...

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.

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Using data from the polar orbiting satellite 1963 38C, we have obtained the diurnal variation of trapped electrons of energies Ee≥280 kev and ≥1.2 Mev during magnetic quiet. This diurnal variation is measured as a latitude shift for constant electron intensity and is obtained as a function of invariant magnetic latitude. All the data were obtained for dipole orientations within ±12° from the normal to the earth‐sun line and for satellite positions within 8° of the noon‐midnight meridian. Assuming conservation of the adiabatic invariants as these trapped electrons drift in the magnetosphere, it has been possible to obtain a nightside magnetic field configuration that fits the observed diurnal variations. A dayside configuration that agrees with experimental observations was used. The nightside configuration so determined displays an extended field line geometry and a current sheet in the magnetic equatorial plane. The field due to this current sheet is found to range from 20 to 40 gammas adjacent to the sheet, depending upon the radial extent of the sheet. A field line configuration in the noon‐midnight meridian is presented. The nightside trapping boundary as defined by field line closure was found to occur at 1100 km at 67°, in agreement with observed boundaries at 1100 km of ∼67° for both ≥40‐ and ≥280‐kev electrons. The situation on the dayside is different and is discussed.