Energy and momentum theorems in magnetospheric processes

This review deals with the several energy and momentum theorems that relate to magnetospheric processes that have been developed. The region of primary consideration in this paper is the magnetospheric domain that extends between the ionosphere and the interplanetary medium, although, for studying certain phenomena, ionospheric and solar wind properties are of central importance and must be included. Both energy theorems and momentum theorems with their applications are presented. Since energy is an integral property of the system variables, analytical results can be found without knowledge of detailed dynamical processes. Thus, relations are derived between particle and magnetic system energies, and application is made to the shape of the magnetopause and various phases of a magnetic storm. Particular attention is given to symmetric and asymmetric ring currents, including energy and momentum equilibrium conditions; a review of nonlinear self‐consistent models and a discussion of how charge exchange and energy diffusion participate in the recovery phase are presented. Comprehensive expressions for the storm time disturbance field are given in terms of both ring current and boundary current energies, and changes that occur during magnetospheric compressions are discussed. The momentum theorems center around the requirement of static force balance during geomagnetically quiet intervals. Whereas the energy theorems give expressions for the average disturbance field over the earth, the momentum theorems give the gradient in the disturbance field across the earth. The forces between earth and the boundary current, the ring current, and the tail current are derived for various models. It is noted that existing vacuum models of the geomagnetic tail are deficient in meeting the combined requirements of energetics and dynamics of the quiet time tail. Introducing the plasma sheet removes the difficulty by allowing an extra degree of freedom in adjusting the force between the earth and the tail. The role of the plasma sheet in making force adjustments is shown to be consistent with the observed thinning of the plasma sheet before sub storms.