Magnetic Energy Relationships in the Magnetosphere

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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.