The influence of centrifugal forces on the B field structure of an axially symmetric equilibrium magnetosphere

Abstract

We investigate a stationary model of a rotating, axially symmetric “pole‐on” magnetosphere in MHD force balance. In this model both the planet's rotational and dipole axes are aligned with the magnetotail axis, which is the axis of symmetry in a cylindrical (r, ϕ, z) coordinate system. For mathematical convenience the magnetosphere is confined on the nightside by a cylindrical magnetopause with constant radius. On the sunward side, the magnetosphere is closed by an appropriate image dipole. Inside the magnetospheric cavity we assume isotropic thermal plasma pressure. We assume further that, in general, planetary rotation leads to differentially rotating magnetotail field lines causing field‐aligned Birkeland currents and a corresponding toroidal magnetic Bϕ component which leads to twisted magnetotail field lines. We calculate the deformation of magnetotail field lines under the influence of both thermal plasma pressure and centrifugal forces. We present “linear” (analytic) solutions to the Grad‐Shafranov equation which include the centrifugal force term. In the linear model, two free physical parameters, k and ω, measure the plasma thermal pressure and the ratio between plasma rotational and thermal energy densities, respectively. Low ω and high k values indicate the plasma‐dominated case. Conversely, low k and high ω values indicate the rotation‐dominated case. One limiting case, k = ω = 0, generates a simple vacuum magnetic field of a dipole confined within the magnetospheric cavity. The nonrotational magnetosphere with hot thermal plasma leads to a field configuration without a toroidal Bϕ component and without field‐aligned Birkeland currents. The other extreme, namely, a rapidly rotating magnetosphere with cold plasma, leads to a configuration in which the plasma must be confined within a thin disk in a plane where the radial magnetic field component Br vanishes locally. Utmost stretched magnetotail configurations can be achieved by increasing either the plasma thermal pressure or the rotation frequency of the magnetosphere, or both. In the rotation‐dominated case we found the plasma sheet thinner and located closer to the magnetopause than in the purely plasma‐dominated case. This implies that hypothetical polar aurorae, under the influence of magnetospheric rotation, appear at higher magnetic latitudes on both the dayside and the nightside. This also implies that the size of the polar oval shrinks under the influence of magnetospheric rotation. A “pole‐on” magnetosphere can be expected at Uranus in the year 2014 twice during a Uranian day.