Adding Drift Kinetics to a Global MHD Code

Abstract:

Global MHD models have generally been successful in describing the
behavior of the magnetosphere at large and meso-scales. An exception
is the inner magnetosphere where energy dependent particle drifts are
essential in the dynamics and evolution of the ring current. Even in
the tail particle drifts are a significant perturbation on the MHD
behavior of the plasma. The most common drift addition to MHD has been
inclusion of the Hall term in Faraday's Law. There have been attempts
in the space physics context to include gradient and curvature drifts
within a single fluid MHD picture. These have not been terribly
successful because the use of a single, Maxwellian distribution does
not capture the energy dependent nature of the drifts. The advent of
multi-fluid MHD codes leads to a reconsideration of this problem. The
Vlasov equation can be used to define individual ``species'' which
cover a specific energy range. Each fluid can then be treated as
having a separate evolution. We take the approach of the Rice
Convection Model (RCM) that each energy channel can be described by a
distribution that is essentially isotropic in the guiding center
picture. In the local picture, this gives rise to drifts that can be
described in terms of the energy dependent inertial and diamagnetic
drifts. By extending the MHD equations with these drifts we can get a
system which reduces to the RCM approach in the slow-flow inner
magnetosphere but is not restricted to cases where the flow speed is
small. The restriction is that the equations can be expanded in the
ratio of the Larmor radius to the gradient scale lengths. At scales
approaching d_i, the assumption of gyrotropic (or isotropic)
distributions break down. In addition to the drifts, the formalism can
also be used to include finite Larmor radius effects on the pressure
tensor (gyro-viscosity). We present some initial calculations with this method.