A new approach to the formulation and validation of scaling expressions for plasma confinement in tokamaks

The extrapolation of the energy confinement time to the next generation of devices has been investigated both theoretically and experimentally for several decades in the tokamak community. Various scaling expressions have been proposed using dimensional and dimensionless quantities. They are all based on the assumption that the scalings are in power law form. In this paper, an innovative methodology is proposed to extract the scaling expressions for the energy confinement time in tokamaks directly from experimental databases, without any previous assumption about the mathematical form of the scalings. The approach to obtain the scaling expressions is based on genetic programming and symbolic regression. These techniques have been applied to the ITPA database of H-mode discharges and the results have been validated with a series of established statistical tools. The soundest results, using dimensional variables, are not in the form of power laws but contain a multiplicative saturation term. Also the scalings, expressed in terms of the traditional dimensionless quantities, are not in power law form and contain additive saturation terms. The extrapolation to ITER of both dimensional and dimensionless quantities indicate that the saturation effects are quite significant and could imply a non-negligible reduction in the confinement time to be expected in the next generation of devices. The results obtained with the proposed techniques therefore motivate a systematic revisiting of the scaling expressions for plasma confinement in tokamaks.