Possible con®gurations of the magnetic ®eld in the outer magnetosphere during geomagnetic polarity reversals

Possible con®gurations of the magnetic ®eld in the outer magnetosphere during geomagnetic polarity reversals are investigated by considering the idealized problem of a magnetic multipole of order m and degree n located at the centre of a spherical cavity surrounded by a boundless perfect diamagnetic medium. In this illustrative idealization, the ®xed spherical (magnetopause) boundary layer behaves as a perfectly conducting surface that shields the external diamagnetic medium from the compressed multipole magnetic ®eld, which is therefore con®ned within the spherical cavity. For a general magnetic multipole of degree n, the non-radial components of magnetic induction just inside the magnetopause are increased by the factor f1‡ ‰…n‡ 1†=nŠg relative to their corresponding values in the absence of the perfectly conducting spherical magnetopause. An exact equation is derived for the magnetic ®eld lines of an individual zonal …m ˆ 0†, or axisymmetric, magnetic multipole of arbitrary degree n located at the centre of the magnetospheric cavity. For such a zonal magnetic multipole, there are always two neutral points and nÿ 1 neutral rings on the spherical magnetopause surface. The two neutral points are located at the poles of the spherical magnetopause. If n is even, one of the neutral rings is coincident with the equator; otherwise, the neutral rings are located symmetrically with respect to the equator. The actual existence of idealized higher-degree …n > 1† axisymmetric magnetospheres would necessarily imply multiple …n‡ 1† magnetospheric cusps and multiple …n† ring currents. Exact equations are also derived for the magnetic ®eld lines of an individual non-axisymmetric magnetic multipole, con®ned by a perfectly conducting spherical magnetopause, in two special cases; namely, a symmetric sectorial multipole …m ˆ n† and an antisymmetric sectorial multipole …m ˆ nÿ 1†. For both these non-axisymmetric magnetic multipoles, there exists on the spherical magnetopause surface a set of neutral points linked by a network of magnetic ®eld lines. Novel magnetospheric processes are likely to arise from the existence of magnetic neutral lines that extend from the magnetopause to the surface of the Earth. Finally, magnetic ®eld lines that are con®ned to, or perpendicular to, either special meridional planes or the equatorial plane, when the multipole is in free space, continue to be con®ned to, or perpendicular to, these same planes when the perfectly conducting magnetopause is present.