Ballooning-mode stability of shaped high-β tokamaks

The effect of elongation and triangularity of flux surfaces on the local and global stability of high-n ideal ballooning modes in a high-β tokamak are investigated. The equilibrium surfaces are obtained by a numerical solution of the Grad-Shafranov equation using an efficient algorithm based on a generalized variational technique. A marginal stability analysis of these surfaces is carried out in which the equilibrium shift, elongation, triangularity, and their radial variations are taken into account. The influence of the cylindrical safety factor (qc), as well as the variations in the shape of β and q profiles, on the maximum attainable beta value (βc) are also considered. Detailed numerical results, over a wide range of parameter space, show that the effect of boundary elongation κa is always stabilizing while the effect of boundary triangularity δa depends on the values of κa and qc. It is found that for elongated cross section (κa≥1.6), the effect of δa is always stabilizing. We present an alternative scaling law that effectively captures these features of the shape parameter dependences. For a JET (Joint European Torus) -type plasma, broad β profiles and q profiles that tend to be flat in the interior are found to be favorable for achieving a high βc value