The mechanical advantage of the magnetosphere: solar-wind-related forces in the magnetosphere-ionosphere-Earth system

Abstract. Magnetosphere-ionosphere interactions involve electric currents that circulate between the two regions; the associated Lorentz forces, existing in both regions as matched opposite pairs, are generally viewed as the primary mechanism by which linear momentum, derived ultimately from solar wind flow, is transferred from the magnetosphere to the ionosphere, where it is further transferred by collisions to the neutral atmosphere. For a given total amount of current, however, the total force is proportional to ℒB and in general, since ℒ²B~ constant by flux conservation, is much larger in the ionosphere than in the magnetosphere (ℒ = effective length, B = magnetic field). The magnetosphere may be described as possesing a mechanical advantage: the Lorentz force in it is coupled with a Lorentz force in the ionosphere that has been amplified by a factor given approximately by the square root of magnetic field magnitude ratio (~20 to 40 on field lines connected to the outer magnetosphere). The linear momentum transferred to the ionosphere (and thence to the atmosphere) as the result of magnetic stresses applied by the magnetosphere can thus be much larger than the momentum supplied by the solar wind through tangential stress. The added linear momentum comes from within the Earth, extracted by the Lorentz force on currents that arise as a consequence of magnetic perturbation fields from the ionosphere (specifically, the shielding currents within the Earth that keep out the time-varying external fields). This implies at once that Fukushima's theorem on the vanishing of ground-level magnetic perturbations cannot be fully applicable, a conclusion confirmed by re-examining the assumptions from which the theorem is derived. To balance the inferred Lorentz force within the Earth's interior, there must exist an antisunward mechanical stress there, only a small part of which is the acceleration of the entire Earth system by the net force exerted on it by the solar wind. The solar-wind interaction can thus give rise to internal forces, significantly larger than the force exerted by the solar wind itself, between the ionosphere and the neutral atmosphere as well as within the current-carrying regions of the Earth's interior.