The role of flow shear in the ballooning stability of tokamak transport barriers

Abstract

A tokamak’s economic performance is strongly affected by the plasma pressure that it may sustain, which in turn is limited by the maximum pressure gradients that may be supported. Ballooning modes are typically driven unstable by increasing the pressure gradient, and because they can radially extend across many rational surfaces, they can seriously reduce a plasma’s energy confinement. Here an eigenmode formulation is used to study the stability of ballooning modes in internal transport barriers (“ITBs”), in which very strong pressure gradients and flow shears may be found. This extends previous studies that used an “eikonal” formulation, as it enables the study of: ballooning modes with a finite toroidal mode-number n (finite wavelength perpendicular to the magnetic field), to find new solution branches, to obtain the eigenmode structures, and to investigate the effects of a radially varying equilibrium. The structure of a finite n ballooning mode in flow shear is found to be significantly affected by a radially varying equilibrium, and at low flow shears the growth rates are increased above those of modes studied in the limit of n→∞. The different solution branches can couple as the flow shear is increased, leading to a pair of asymmetric mode structures with complex conjugate growth rates. These effects are shown to be a consequence of the mode trying to localize at the most unstable radial location, and its desire to rotate with the flow. In addition, closer to marginal stability a sufficiently strong flow-shear can (at least for some cases), destabilize a previously stable mode.