Tokamak elongation - How much is too much? Part 2. Numerical results

The analytic theory presented in Paper I is converted into a form convenient for numerical analysis. A fast and accurate code has been written using this numerical formulation. The results are presented by first defining a reference set of physical parameters based on experimental data from high performance discharges. Scaling relations of maximum achievable elongation (K_max) versus inverse aspect ratio (ϵ) are obtained numerically for various values of poloidal beta (β_p), wall radius (b/a) and feedback capability parameter (γτ_w) in ranges near the reference values. It is also shown that each value of K_max occurs at a corresponding value of optimized triangularity (δ), whose scaling is also determined as a function of ϵ. The results show that the theoretical predictions of K_max are slightly higher than experimental observations for high performance discharges, as measured by high average pressure. The theoretical δ values are noticeably lower. We suggest that the explanation is associated with the observation that high performance involves not only n = 0 MHD stability, but also n ≥ 1 MHD modes described by β_N in the Troyon limit and transport as characterized by τ_E. Operation away from the n=0 MHD optimum may still lead to higher performance if there are more than compensatory gains in β_N and τ_E. Unfortunately, while the empirical scaling of β_N and τ_E with the elongation (K) has been determined, the dependence on δ has still not been quantified. This information is needed in order to perform more accurate overall optimizations in future experimental designs.