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Ann. Geophys., 24, 1085-1097, 2006
www.ann-geophys.net/24/1085/2006/
© European Geosciences Union 2006
Ionospheric and boundary contributions to the Dessler-Parker-Sckopke formula for Dst
V. M. Vasyliūnas
Max-Planck-Institut für Sonnensystemforschung, 37191 Katlenburg-Lindau, Germany
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.
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