The shape of the tilted magnetopause

A model for the determination of the shape of the magnetopause is developed that permits the inclusion of cases where the solar wind is directed obliquely toward the geomagnetic dipole axis. The solar wind is assumed to have no motions perpendicular to its (constant) velocity vector (zero temperature approximation) and to be free of magnetic fields. The region within the magnetopause is characterized as having only one magnetic source and as being free of plasma. The procedure used here is in many ways similar to the self-consistent field method developed by Mead and Beard to calculate the shape of the magnetopause when the solar wind flow is perpendicular to the dipole axis. They were able to find the surface shape (for perpendicular incidence) at one point at a time. In the present study, however, it is necessary to determine the position of the surface at several points at a time. The geocentric distance to the subsolar point is found to be largest for perpendicular incidence of the solar wind on the dipole axis. The cross sections of the tail of the magnetopause given by the model are not cylindrical but elongated in the direction perpendicular to the ecliptic plane. Generally, the boundary is very dependent upon the wind-dipole angle in the region of the neutral points but exhibits very little dependence on this angle in ‘equatorial’ regions.