Physics of the Magnetosphere pp 290-300 | Cite as

# Magnetic Energy Relationships in the Magnetosphere

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## Abstract

Using a more physical method of calculating magnetic energy changes, various theorems relating to geomagnetic processes have been reformulated. In particular, we have determined : (a) the energy of confinement of a magnetic dipole field by a perfectly conducting surface (e.g., the steady state containment of the Earth’s field by the solar wind); (b) the energy of transient compression of a shielded dipole field by a diamagnetic medium (such as the sudden commencement of a magnetic storm); and (c) the zero order energy of trapped particles in an undistorted dipole field (e.g., the energy of the radiation belts during quiet times or the main phase in a weak magnetic storm). In all three instances the magnetic and kinetic energies are directly proportional to **M·b**(0), where **b**(0) is the total perturbation field at the position of the dipole moment M due to sources exterior to the shielding volume (if any). A new result shows that (c) follows directly from a more general theorem which phenomenologically includes the non-linear effects of particle interactions within the belt. A simple model is developed which demonstrates that the zero order theorem (c) leads to an overestimate of the kinetic energy of the particle distribution when the non-linear magnetic distortions of the particles are important.

## Keywords

Solar Wind Magnetic Storm Magnetic Energy Radiation Belt Dipole Field## Preview

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