Equations for the field lines of a sectorial magnetic multipole

Abstract

This paper extends an earlier investigation by Willis & Young (1987), in which an exact equation was derived for the magnetic field lines of the general axisymmetric magnetic multipole of arbitrary degree (n). Exact equations are derived for the magnetic field lines of two special non‐axisymmetric magnetic multipoles of arbitrary degree, which may be classified as either symmetric or antisymmetric sectorial multipoles. These results have applications in studies of the possible nature of solar‐terrestrial physics during geomagnetic polarity reversals. The magnetic‐field‐line configurations for these two non‐axisymmetric multipoles are discussed in detail and are illustrated for low‐degree (2 ≤ n ≤ 4) multipoles. It is shown that the existence of magnetic neutral lines is a characteristic feature of such non‐axisymmetric multipoles. These neutral lines define localized regions of space (‘magnetospheric cusps’) through which charged particles can gain access to the inner magnetosphere. Moreover, both non‐axisymmetric magnetic fields are locally perpendicular to a set of meridional planes and one is locally perpendicular to the equatorial plane. Therefore, there exist classes of charged‐particle trajectories for which motion is confined completely to these meridional planes, or the equatorial plane, and every particle executing such planar motion is scattered non‐adiabatically when it encounters a neutral line. This result emphasizes the need for a more detailed study of the motion of charged particles in both axisymmetric and non‐axisymmetric multipole magnetic fields before firm conclusions can be reached on possible changes in geomagnetically trapped radiation during polarity reversals. Copyright © 1988, Wiley Blackwell. All rights reserved