Analysis of Classical Transport Equations for the Tokamak Edge Plasma

The classical fluid transport equations for a magnet-plasma as given, for example, by Braginskii [1], are complicated in their most general form. Here we obtain the simplest reduced set which contains the essential physics of the tokamak edge problem in slab geometry by systematically applying a parameter ordering and making use of specific symmetries. An important ingredient is a consistent set of boundary conditions as described elsewhere [2]. This model clearly resolves some important issues concerning diamagnetic drifts, high parallel viscosity, and the ambipolarity constraint. The final equations can also serve as a model for understanding the structure of the equations in the presence of anomalous transport terms arising from fluctuations. In fact, Braginskii-like equations are the basis of a number of scrape-off layer (SOL) transport codes [3]. However, all of these codes contain ad hoc radial diffusion terms and often neglect some classical terms, both of which make the self-consistency of the models questionable. Braginskii's equations [1] have been derived from the first principles via the kinetic equations and, thereby, contain such ''built-in'' features as the symmetry of kinetic coefficients, and automatic quasineutrality of a cross-field diffusion in a system with toroidal symmetry such as a tokamak. Our model thus maintains these properties.