Field line twist and field‐aligned currents in an axially symmetric equilibrium magnetosphere

Abstract

Field‐aligned Birkeland currents and the twist of magnetic tail field lines are calculated for an axially symmetric pole‐on magnetosphere. The magnetic field components in the magnetospheric tail result from linear solutions to the MHD equilibrium problem. The field line twist angle, ε = arc tan (Bϕ/Bz), is shown to be dependent on the radial distance measured from the tail axis, on the amount of thermal plasma confined in closed magnetotail flux tubes, and on the ionospheric Pedersen conductivity. The field lines are maximally twisted in the force‐free tail configurations; they are minimally twisted if the magnetotail reaches the state of maximum plasma pressure, the so‐called Harris sheet limit. The field line twist results from the planetary rotation, which leads to the development of a toroidal magnetic Bϕ component and to differentially rotating magnetic field lines. If centrifugal forces become important, the thermal plasma pressure P(A) in the Grad‐Shafranov equation assumes the form P(A, r) which allows centrifugal forces to be included in the MHD equilibrium formalism. The equilibrium model reveals that magnetopause field lines do not rotate because the magnetopause is held in place by the solar wind stream. For a given ionospheric conductivity and a given thermal plasma content within the tail, the field line helix is twisted most near the center of the circular tail plasma sheet. The field‐aligned Birkeland currents reach their maximum strength on tail field lines that confine the plasma sheet. Thus polar aurorae are expected to appear around both the dayside and nightside magnetic poles at latitudes where the plasma sheet field lines map into the planet's ionosphere. This theoretical model was originally developed for the anticipated pole‐on magnetosphere of Uranus. Thus references to the Uranian magnetosphere that appear in this study and in the quoted literature apply to hypotheses that had been developed before the closest approach of Voyager 2 at Uranus on January 24, 1986. However, the results of this study are sufficiently general to allow their application to other rotating axially symmetric plasma‐magnetic field configurations in space.