Energy and momentum theorems in magnetospheric processes

Abstract

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 condi. tions; 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 substorms.

Ring Current Energy Input and Decay

“…The derivation of (2) is for an arbitrarily-distributed plasma (in both real space and velocity space) in a dipole magnetic field, and it only takes into consideration the cross-magnetic-field currents in the magnetosphere (see the discussion by Carovillano and Siscoe (1973)). If this current is spatially (azimuthally) asymmetric, then there will be field-aligned and ionospheric closure currents to complete the circuit that are not accounted for in (2).…”

“…Dst * , the global perturbation from near-Earth currents, is obtained by correcting the Dst index for magnetopause current contributions and for induced currents in the solid earth. A number of recent studies using in situ satellite data have presented observational tests showing that the ring current contribution (partial and symmetric) dominates the Dst * index (e.g., Greenspan and Hamilton, 2000), while other current systems are estimated to contribute only a few tens of nT at most (e.g., Carovillano and Siscoe, 1973;Crooker and Siscoe, 1974;Turner et al, 2000). Considerable uncertainty still exists over the non-ring current contributions to Dst * which some models predict to be substantial (Alexeev et al, 1996).…”

On storm weakening during substorm expansion phase

“…Olbert et al (1968), Siscoe (1970), and Carovillano and Siscoe (1973) extended the approach to obtain a generalized form of the Dessler-Parker-Sckopke equation, which relates Dst to various global magnetospheric energies (Dessler and Parker, 1959;Sckopke, 1966). To address the Iyemori and Rao question, we use the generalized form of the DPS equation.…”

Ionospheric and boundary contributions to the Dessler-Parker-Sckopke formula for <i>Dst</i>

“…The entire development has been definitively reviewed by Carovillano and Siscoe (1973). Although the Dessler-Parker-Sckopke theorem might thus seem to be a closed chapter at least as far as theory is concerned, there still are some outstanding issues which are addressed in this paper:…”