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

Abstract

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 (epsilon) are obtained numerically for various values of poloidal beta (beta(p)), wall radius (b/a) and feedback capability parameter (gamma tau(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 (delta), whose scaling is also determined as a function of epsilon. 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 delta 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 beta(N) in the Troyon limit and transport as characterized by tau(E). Operation away from the n = 0 MHD optimum may still lead to higher performance if there are more than compensatory gains in beta N and tau E. Unfortunately, while the empirical scaling of beta(N) and tau(E) with the elongation (kappa) has been determined, the dependence on delta has still not been quantified. This information is needed in order to perform more accurate overall optimizations in future experimental designs.