Scalings for tokamak energy confinement

TLDR

Current tokamak energy‑confinement scaling laws are numerous because the key parameter combination fs varies little in the database and τE depends differently on physical parameters across devices. The study aims to reduce this multiplicity by enriching the database with data showing larger fs variation and by clarifying the physical causes of tokamak‑to‑tokamak differences in τE dependence. By combining fs with a factor fq that captures q, Ip, and ne dependence, the authors transform the new power‑law and offset‑linear scalings into forms closely matching most existing expressions.

Abstract

On the basis of an analysis of the ITER L-mode energy confinement database, two new scaling expressions for tokamak L-mode energy confinement are proposed, namely a power law scaling and an offset-linear scaling. The analysis indicates that the present multiplicity of scaling expressions for the energy confinement time τE in tokamaks (Goldston, Kaye, Odajima-Shimomura, Rebut-Lallia, etc.) is due both to the lack of variation of a key parameter combination in the database, fs = 0.32 R a−0.75 k0.5 ∼ A a0.25k0.5, and to variations in the dependence of τE on the physical parameters among the different tokamaks in the database. By combining multiples of fs and another factor, fq = 1.56 a2 kB/RIp = qeng/3.2, which partially reflects the tokamak to tokamak variation of the dependence of τE on q and therefore implicitly the dependence of τE on Ip and ne, the two proposed confinement scaling expressions can be transformed to forms very close to most of the common scaling expressions. To reduce the multiplicity of the scalings for energy confinement, the database must be improved by adding new data with significant variations in fs, and the physical reasons for the tokamak to tokamak variation of some of the dependences of the energy confinement time on tokamak parameters must be clarified.