MHD and Fluid Instabilities at the Plasma Edge in the Presence of a Separatrix and X-Point

The effect of an X-point and separatrix on unstable modes is considered within the context of MHD and fluid models. We begin by reviewing the magnetic flux geometry in the vicinity of the X-point and the effect it has on wave behavior. We then consider fluid models for the edge and SOL lasma based on the reduced Braginskii equations, and subsets thereof. For parameters typical of tokamak boundary plasmas, the models support a variety of low frequency instabilities including ideal and resistive MHD modes, drift-Alfvén instabilities, and instabilities driven by sheath and neutral physics. The physics of these modes and the role of X-point geometry on them is elucidated. Recent results of turbulence simulations of the boundary plasma in X-point geometry are also discussed.