Adding Drift Kinetics to a Global MHD Code

Global MHD models have generally been successful in describing thebehavior of the magnetosphere at large and meso-scales. An exceptionis the inner magnetosphere where energy dependent particle drifts areessential in the dynamics and evolution of the ring current. Even inthe tail particle drifts are a significant perturbation on the MHDbehavior of the plasma. The most common drift addition to MHD has beeninclusion of the Hall term in Faraday's Law. There have been attemptsin the space physics context to include gradient and curvature driftswithin a single fluid MHD picture. These have not been terriblysuccessful because the use of a single, Maxwellian distribution doesnot capture the energy dependent nature of the drifts. The advent ofmulti-fluid MHD codes leads to a reconsideration of this problem. TheVlasov equation can be used to define individual ``species'' whichcover a specific energy range. Each fluid can then be treated ashaving a separate evolution. We take the approach of the RiceConvection Model (RCM) that each energy channel can be described by adistribution that is essentially isotropic in the guiding centerpicture. In the local picture, this gives rise to drifts that can bedescribed in terms of the energy dependent inertial and diamagneticdrifts. By extending the MHD equations with these drifts we can get asystem which reduces to the RCM approach in the slow-flow innermagnetosphere but is not restricted to cases where the flow speed issmall. The restriction is that the equations can be expanded in theratio of the Larmor radius to the gradient scale lengths. At scalesapproaching di, the assumption of gyrotropic (or isotropic)distributions break down. In addition to the drifts, the formalism canalso be used to include finite Larmor radius effects on the pressuretensor (gyro-viscosity). We present some initial calculations with this method.