| The force exerted by the external perturbation magnetic field on the magnetic moment of a
planet is related to various aspects of stress balance in the magnetosphere and its interaction
with the solar wind. The total force applied by the solar wind must ultimately be exerted on
the planet itself, which contains essentially all the mass of the entire system (the mass
fraction in the Earth’s magnetosphere is less than ~ 10-20 of the total). The force is
transmitted through the magnetosphere primarily (and near the planet almost exclusively) by
the magnetic field. In the simplest approximation (Siscoe, 1966), the force is applied directly
as the gradient of the external perturbation field at the dipole. More recently (Siscoe and
Siebert, 2006; Vasyliunas, 2007), it has been recognized that coupling by Birkeland
currents between the ionosphere and the magnetosphere allows the external force to be
transmitted also as a J Ã B-c force in the ionosphere; further transmission to the planet
itself then has to proceed as a mechanical stress. Because of the converging dipole
field, the force in the ionosphere is greatly amplified and much stronger than the
initially imposed force from the magnetosphere or solar wind, an effect sometimes
described as the mechanical advantage of the magnetosphere (Vasyliunas, 2007).
Empirical estimates of the force thus provide a sensitive (albeit indirect and imprecise)
indicator of stresses in the outer magnetosphere, as well as a direct measure of the
global input of linear momentum into the atmosphere. The total magnetic force
on the planet can be calculated from measurements of magnetic perturbations by
integrating the Maxwell stress tensor over the surface. I derive the formula for the three
vector components of the force in terms of the conventional geomagnetic quantities,
integrated over latitude and longitude with appropriate weighting factors (which are not
always intuitively obvious and in some cases reverse sign between low and high
latitudes). |