Scaling Laws For Confinement Time Research Articles

Application of symbolic regression to the derivation of scaling laws for tokamak energy confinement time in terms of dimensionless quantities

In many scientific applications, it is important to investigate how certain properties scale with the parameters of the systems. The experimental studies of scalings have traditionally been addressed with log regression, which limits the results to power laws and to theoretical and not data-driven dimensionless quantities. This has also been the case in nuclear fusion, in which the scaling of the energy confinement time is a crucial aspect in understanding the physics of transport and in the design of future devices. Traditionally two main assumptions are at the basis of the most widely accepted empirical scaling laws for the confinement time: (a) the dimensionless variables used are the ones derived from the symmetries of the Vlasov equation; (b) the final scalings have the mathematical form of power laws. In this paper, it is shown how symbolic regression (SR), implemented with genetic programming (GP) techniques, can be used to test these hypotheses. Neither assumption is confirmed by the available data of the multi-machine International Tokamak Physics Activity (ITPA) of validated tokamak discharges. The statistically soundest expressions are not power laws and cannot be formulated in terms of the traditional dimensionless quantities. The consequences of the data-driven scaling laws obtained are both practical and theoretical: the confinement time for the ITER can be significantly shorter than foreseen by power laws and different dimensionless variables should be considered for theoretical investigations. On the other hand, higher quality databases should be built to reduce the uncertainties in the extrapolations. It is also worth emphasising that the proposed methodology is fully general and therefore can be applied to any field of science.

Electron heat transport in ASDEX Upgrade: experiment and modelling

The electron heat transport is investigated in ASDEX Upgrade using electron cyclotron heating (ECH) combining steady-state and power modulation schemes. Experiments in which the electron heat flux has been varied in the confinement region while the edge was kept constant were performed. They demonstrate that ∇ Te and ∇ Te/Te can be varied by a factor of 3 and 2, respectively. They allow a detailed determination of the transport characteristics by comparing steady-state and modulation data with modelling. The analyses clearly show the existence of a threshold (∇ Te/Te)crit above which transport increases. Both steady-state and modulation experiments agree with such a transport model. The experiments have been carried out at low density in the L-mode to ensure low electron–ion coupling and good conditions for studying electron heat transport. The experiments were carried out at two different values of plasma current and show that transport increases at low current, as well-known from global scaling laws for confinement time. In the pure off-axis cases the region inside the ECH deposition is just at the (∇ Te/Te)crit threshold, which allows it to be measured directly from the profile of ∇ Te/Te deduced from the experimental Te profile. Using this technique, it appears that the turbulence threshold agrees with that expected from the trapped electron mode driven turbulence. It has the correct absolute value and seems to have the correct radial dependence that is determined by the trapped electron fraction and by the density gradient. It almost does not vary with other plasma parameters. In contrast, the threshold calculated for electron temperature gradient modes is higher than the experimental values of ∇ Te/Te and this turbulence is therefore not expected to be excited under these experimental conditions.