[1] Empiric evidence and theoretical argument indicate that magnetospheric convection is globally sub-adiabatic. Reconciliation of the sub-adiabaticity with the underlying adiabatic particle drifts is a problem that has not been conclusively demonstrated. In this paper, through an ensemble average, we show that the Rice Convection Model contains a heat flux due to thermal inequilibrium between two adjacent flux tubes of equal volume. The averaged theory is based on field variables obeying a set of partial differential equations (Eulerian formulation), instead of conservative variables advecting with fluid elements (Langrangian formulation). We apply the theory to investigate a one-dimensional case of subadiabatic variation of thermodynamic properties in the plasma sheet.

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[1] In the long run, energy entering the magnetosphere from the solar wind must be balanced by energy dissipation in or escape from the system. It then follows that the Joule heating rate in the ionosphere statistically should be bounded from the upside by the solar wind energy input function (e.g., the Perrault-Akasofu parameter). We show that this energy constraint, coupled with some observationally motivated assumptions about the behavior of the auroral oval under escalating solar wind conditions, leads to the prediction of polar cap potential saturation.

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