Genetic programming for the data driven formulation of scaling laws: the case of the L-H and H-L transitions

Reliable scaling expressions, for the power threshold to access and leave the H mode of confinement, remain a subject of active research, because up to now no theoretical relation has proved to be general enough to interpret reliably these critical phenomena. In this contribution, reports on a series of advanced statistical methods developed to extract scaling expressions directly from the data without "a priori" assumptions on their mathematical form. They are applied to the investigation of the power to access and leave the H mode. The long term objective of this line of research is the identification of reliable scaling expressions for the planning of the experiments and the design of future devices. The developed statistical tools, which combine Symbolic Regression and Genetic Programming, are deployed to analyse all available JET discharges with the ITER Like Wall explicitly designed to address the L-H transition. The best scaling expressions for both the L-H and the H-L transitions are not power laws and depend on the pressure and plasma shape. The scalings of the same mathematical form fit quite well also the data of the previous campaigns with the carbon wall. The scalings obtained with these regressors are significantly better than the ones obtained with alternative quantities, such as the plasma current, Zeff etc. The extrapolations to ITER, even if they have to be taken with great caution given the limited amount of examples available, seem to indicate more favourable conditions for the access to the H mode than normally expected on the basis of traditional power laws. The issue of hysteresis has also been investigated in detail, trying to separate time dependent from time independent hysteresis. The obtained results, even if not absolutely conclusive, seem to indicate the presence of time independent hysteresis.