Tokamak equilibria and stability with arbitrary flows

The topic of plasma flows and their influence on the equilibrium and stability properties of tokamak discharges is briefly reviewed. The stability of high-n ballooning modes in the presence of sheared toroidal rotation is discussed to highlight recent advances in our understanding of the spatial structure and temporal evolution of these modes. The eikonal solution, which is mathematically equivalent to the normal mode solutions at the lowest order in 1/n, may not be physically relevant for a variety of reasons. An analytic formulation of the normal mode problem for high-n ballooning modes in the presence of sheared toroidal flow in the high-beta large-aspect-ratio limit is presented. In contrast to earlier studies, the present formulation allows for large plasma shifts as well as accounting for changes in the shape of flux surface due to rotation effects. (Author)