Ionospheric and boundary contributions to the Dessler-Parker-Sckopke formula for Dst

Abstract. The Dessler-Parker-Sckopke formula for the disturbance magnetic field averaged over the Earth's surface, universally used to interpret the geomagnetic Dst index, can be generalized, by using the well known method of deriving it from the virial theorem, to include the effects of ionospheric currents. There is an added term proportional to the global integral of the vertical mechanical force that balances the vertical component of the Lorentz force J×B/c in the ionosphere; a downward mechanical force reduces, and an upward increases, the depression of the magnetic field. If the vertical component of the ionospheric Ohm's law holds exactly, the relevant force on the plasma is the collisional friction between the neutral atmosphere and the vertically flowing plasma. An equal and opposite force is exerted on the neutral atmosphere and thus appears in its virial theorem. The ionospheric effect on Dst can then be related to the changes of kinetic and gravitational energy contents of the neutral atmosphere; since these changes are brought about by energy input from the magnetosphere, there is an implied upper limit to the effect on Dst which in general is relatively small in comparison to the contribution of the plasma energy content in the magnetosphere. Hence the Dessler-Parker-Sckopke formula can be applied without major modification, even in the case of strong partial ring currents; the ionospheric closure currents implied by the local time asymmetry have only a relatively small effect on the globally averaged disturbance field, comparable to other sources of uncertainty. When derived from the virial theorem applied to a bounded volume (e.g. the magnetosphere bounded by the magnetopause and a cross-section of the magnetotail), the Dessler-Parker-Sckopke formula contains also several boundary surface terms which can be identified as contributions of the magnetopause (Chapman-Ferraro) and of the magnetotail currents.