A simplified model to estimate nonlinear turbulent transport only by linear calculations is proposed, where the turbulent heat diffusivity in tokamak ion temperature gradient(ITG) driven turbulence is reproduced for a wide parameter range including near- and far-marginal ITG stability. The optimal nonlinear functional relation(NFR) between the turbulent diffusivity, the turbulence intensity $$\mathcal{T}$$
T
, and the zonal-flow intensity $$\mathcal{Z}$$
Z
is determined by means of mathematical optimization methods. Then, an extended modeling for $$\mathcal{T}$$
T
and $$\mathcal{Z}$$
Z
to incorporate the turbulence suppression effects and the temperature gradient dependence is carried out. The simplified transport model is expressed as a modified nonlinear function composed of the linear growth rate and the linear zonal-flow decay time. Good accuracy and wide applicability of the model are demonstrated, where the regression error of $$\sigma _{\textrm{model}} = 0.157$$
σ
model
=
0.157
indicates improvement by a factor of about 1/4 in comparison to that in the previous works.
A novel nonlinear functional relation of turbulence potential intensity, zonal flow potential intensity, and ion thermal diffusivity that accurately reproduces nonlinear gyrokinetic simulations of toroidal ion temperature gradient (ITG) driven turbulence is proposed. Applying mathematical optimization techniques to find extremal solutions in high dimensional parameter space, the optimal regression parameters in the functional form are determined to be valid for both near- and far-marginal regime of the ITG stability including the Dimits-shift. Then, the regression error of ∼5% is accomplished. In addition, it is clarified that the intensity ratio of the zonal flow and turbulence potential intensity is a crucial factor to determine the reproduction accuracy.
A machine learning‐based semi‐empirical turbulent transport model DeKANIS has been modified to apply it independently of the device. DeKANIS predicts particle and heat fluxes, distinguishing diffusive and non‐diffusive transport processes. DeKANIS consists of a neural network (NN) model, which computes coefficients of the non‐diffusive terms and the ratio of the fluxes based on the gyrokinetic calculations, and a scaling formula, which estimates the turbulent saturation level founded on empirical fluxes. The datasets used for NN training have been prepared based on JT‐60U plasmas so far, but by exploiting JET plasmas, the datasets have been expanded and the parameter ranges covered by the NN models have become wider. The scaling formula has been rebuilt considering the decrease in the residual zonal flow level due to collisions. The new DeKANIS has demonstrated a reasonable profile prediction of an ITER plasma in the pre‐fusion power operation 1 phase with an integrated model GOTRESS+. In validating the prediction results with the gyrokinetic calculations, transport processes causing the fluxes have been exhibited.
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