Relationships of models of the inner magnetosphere to the Rice Convection Model

Ideal magnetohydrodynamics is known to be inaccurate for the Earth's inner magnetosphere, where transport by gradient-curvature drift is nonnegligible compared to E x B drift. Most theoretical treatments of the inner plasma s heet and ring current, including the Rice Convection Model (RCM), treat the inner magnetospheric plasma in tel ms of guiding center drifts. The RCM as sumes that the distribution function is isotropic, but particles with diffe rent energy invariants are treated as separate guiding center fluids. Howev er, Peymirat and Fontaine [1994] developed a two-fluid picture of the inner magnetosphere, which utilizes modified forms of the conventional fluid equ ations, not guiding center drift equations. Heinemann [1999] argued theoret ically that for inner magnetospheric conditions the fluid energy equation s hould include a heat flux term, which, in the case of Maxwellian plasma, wa s derived by Braginskii [1965]. We have now reconciled the Heinemann [1999] fluid approach with the RCM. The fluid equations, including the Braginskii heat flux, can be derived by taking appropriate moments of the RCM equatio ns for the case of the Maxwellian distribution. The physical difference between the RCM formalism and the Heinemann [1999] fluid approach is that the RCM pretends that particles suffer elastic colli sions that maintain the isotropy of the distribution function but do not ch ange particle energies. The Heinemann [1999] fluid treatment makes a differ ent physical approximation, namely that the collisions maintain local therm al equilibrium among the ions and separately among the electrons. For some simple cases, numerical results are presented that illustrate the differenc es in the predictions of the two formalisms, along with those of MHD, guidi ng center theory, and Peymirat and Fontaine [1994].