A New Way to Include Inertia in the Rice Convection Model

The RCM-I model formulation published in 2019 represents a first attempt to generalize the long-standing assumptions of quasi-static slow-flow convection in the inner magnetosphere by including electrodynamic effects of the inertial drifts in the Rice Convection Model. Its most serious approximation is to assume that, when the inertial drift contribution is calculated, the mass is concentrated near the magnetospheric equatorial plane. In this paper, we present a reformulation of the model where plasma pressure and density are constant along each field line. That approximation still precludes getting the details of substorm timing right, but it is much more realistic than assuming that the all of the mass is in the equatorial plane. The constant pressure-density assumption is often used in simple plasma physics, e.g., interchange instability, which the physics that we are trying to represent closely resembles. Our new formulation of the RCM-I involves multiple coordinate systems, including a rectangular quasi-Cartesian system, a dipolar system, and a field-aligned system that is based on Euler potentials; the lattermost system it is not orthogonal, and it changes with time. We employ a Riemannian geometry to this end, for a flat space manifold. Tensor calculus is used to formulate a covariant set of self-consistent field equations with which we can easily transition between the coordinate systems with the use of metric tensors and Christoffel symbols. The covariant formulation facilitates the inclusion of inertia and allows representation of the auroral ionosphere at 1-10 km resolution and finer than 0.5 RE resolution in equatorial plane. The Riemann-tensor multi-grid approach to magnetospheric modeling might point a way to help other magnetospheric models bridge the scale gap between the ionosphere and magnetosphere.