Generalized ballooning and sheath instabilities in the scrape-off layer of divertor tokamaks

Abstract

The stability of the scrape-off layer to high toroidal mode number ballooning-type instabilities is considered. The equilibrium includes a simple model of the X-point geometry, and parallel (as well as cross-field) equilibrium variations of temperature, density, and potential. The latter are computed numerically from the Braginskii form for Ohm’s law. The stability analysis includes the effects of curvature, resistivity, parallel variation of the E×B drift frequency, and sheath boundary conditions at the divertor plate. Importantly, the equilibrium model assures consistency among the possible instability drives; i.e., the pressure weighting of the curvature, the plasma potential (E×B drift), and the conditions at the divertor plate are coupled by the equilibrium model. Numerical solutions indicate two modes: (i) the curvature-driven mode with growth rate enhanced by the sheaths; and (ii) the E×B shear mode driven by equilibrium variations in the region between the X point and the plate. The latter mode is shown to be partly driven by the X-point geometry. The effect of finite Larmor radius, resistivity, and electron inertia on these modes is investigated.