The relationship between magnetospheric convection and ionospheric heating

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Abstract
Treating the magnetic stress introduced into the magnetosphere by the solar wind at the magnetopause, we show the direct relation between the magnetospheric convection pattern and the field perturbations. The Birkeland currents are caused by the field perturbations and follow directly from Ampere's law, of course. The ionospheric heating is given by the rate at which the stress in the convecting field does work on the ionosphere. The parallel electric fields may then be deduced from the plasma microphysics and the established currents if desired.