Optimum equilibria for high performance, steady state tokamaks

The dependence of the ideal ballooning β limit on aspect ratio, A, and elongation κ is systematically explored for nearly 100% bootstrap current driven tokamak equilibria in a wide range of the shape parameters (A = 1.2–7.0, κ = 1.5–6.0 with triangularity δ = 0.5). The critical βN is shown to be optimal at κ = 3.0–4.0 for all A studied and increases as A decreases with a dependence close to A−0.5. The results obtained can be used as a theoretical basis for the choice of optimum aspect ratio and elongation equilibria for future high performance steady-state tokamaks.