Speaker
Description
Making use of a large experimental database of pedestals of H-mode ELMy JET-ILW pulses [1], we propose several approaches to systematic prediction of the height of the electron-temperature pedestal and of the electron temperature at the top of the density pedestal, with the engineering parameters and the density profiles as inputs. Simulations of ETG turbulence in steep-gradient regions of the pedestals of JET and other large tokamaks suggest that a simple scaling exists between the (gyroBohm-normalised) heat flux and the the local values of the electron density ($R/L_{n_e}$) and temperature ($R/L_{T_e}$) gradients [2]. This has previously been checked on a small subset of this database, and we now confirm that testing it against the entire database leads to consistent prediction of the electron temperature within 50% of the experimental values. The scaling proposed in [2] includes departures from the marginal stability, presumed to be achieved at $R/L_{T_e} = \eta_{e,NL} R/L_{n_e}$, where $\eta_{e,NL} $ is generally speaking a fitting parameter. Taking a simpler approach that assumes a definite local relationship between the gradients, we find that a range of power law scalings $R/L_{T_e} = A( R/L_{n_e})^\alpha$ with $\alpha$ between 0.33 and 1 correctly capture the behaviour of the electron temperature at the density-pedestal top. For $\alpha = 1$, $A\equiv \eta_{e,cr} $, which governs the turbulence saturation in the standard picture of slab-ETG modes. Measuring it halfway between the pedestal-density top and the separatrix yields a distribution of values (Figure 1) that lie considerably above the linear threshold $\eta_{e,lin} = 0.8$ [3]. This implies either that a nonlinear effect analogous to Dimits shift lifts $\eta_{e,cr}$ to an effective value just above 2 or that turbulent transport predominantly occurs in an order-unity-supercritical regime, characterised by this higher-than-marginal gradient ratio.
Figure 1: distribution calculated between top of electron density pedestal and separatrix for 1148 pulses.
Finally, we present a simple machine learning algorithm which, given the same experimental inputs as theory-based modelling, is able to predict the electron temperature within similar error bars for 20% of the database after being trained on the other 80%. This result confirms the conceptual possibility of accurate prediction and offers a baseline quality benchmark for improved models that rely on traditional theoretical understanding of turbulent transport.
References:
[1] L. Frassinetti et al. 2021 Nucl. Fusion 61, 016001.
[2] A.R. Field et al. 2023 Phil. Trans. R. Soc. A 381, 2021022.
[3] F. Jenko, W. Dorland, G. W. Hammett 2001 Phys. Plasmas 8, 4096.
