Tokamak elongation: how much is too much? II Numerical results

TL;DR

This paper develops a numerical code to analyze the maximum achievable elongation in tokamaks, revealing how it scales with various parameters and highlighting the importance of confinement time in high-performance discharges.

Contribution

It provides numerical scaling relations for tokamak elongation and triangularity based on experimental parameters, extending theoretical predictions with practical computational tools.

Findings

Maximum elongation scales with inverse aspect ratio and other parameters.

Optimized triangularity decreases as elongation increases.

High performance involves both MHD stability and confinement time considerations.

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. Numerically obtained scaling relations of maximum achievable elongation versus inverse aspect ratio are obtained for various values of poloidal beta, wall radius and feedback capability parameter in ranges near the reference values. It is also shown that each value of maximum elongation occurs at a corresponding value of optimized triangularity, whose scaling is also determined as a function of inverse aspect ratio. The results show that the theoretical predictions of maximum elongation are slightly higher than experimental observations for high performance discharges as measured by high average pressure. The theoretical optimized triangularity values are noticeably lower. We suggest that the explanation is associated with the observation that high performance involves not only MHD considerations, but also transport as characterized by confinement time. Operation away from the MHD optimum may still lead to higher performance if there are more than compensatory gains in the confinement time. Unfortunately, while the empirical scaling of the confinement time with the elongation has been determined, the dependence on the triangularity has still not been quantified. This information is needed in order to perform more accurate overall optimizations in future experimental designs.