Neoclassical transport simulations for stellarators

Abstract

The benchmarking of the thermal neoclassical transport coefficients is described using examples of the Large Helical Device (LHD) and TJ-II stellarators. The thermal coefficients are evaluated by energy convolution of the mono-energetic coefficients obtained by direct interpolation or neural network techniques from databases precalculated by different codes. The temperature profiles are calculated by a predictive transport code from the energy balance equations with the ambipolar radial electric field estimated from a diffusion equation to guarantee a unique and smooth solution although several solutions of the ambipolarity condition may exist when root-finding is invoked; the density profiles are fixed. The thermal transport coefficients as well as the ambipolar radial electric field are compared and very reasonable agreement is found for both configurations.Together with an additional W7-X case, these configurations represent very different degrees of neoclassical confinement at low collisionalities. The impact of the neoclassical optimization on the energy confinement time is evaluated and the confinement times for different devices predicted by transport modeling are compared with the standard scaling for stellarators. Finally, all configurations are scaled to the same volume for a direct comparison of the volume-averaged pressure and the neoclassical degree of optimization.

Comparison of particle trajectories and collision operators for collisional transport in nonaxisymmetric plasmas

“…It is thus expected that E * is of order E * ∼ ρ θ /L ⊥ , where ρ θ = ρ/(ιǫ) and ǫ is the inverse aspect ratio, and the ratio ρ θ /L ⊥ is typically ≪ 1. In W7-X, E * is predicted to be a few percent in normal plasma scenarios [44]. The largest E r in normal W7-X scenarios is predicted to be a few tens of kV/m, in the edge where density gradients are steep, corresponding to E * up to a few tenths [44].…”

Extended estimations of neoclassical transport for the TJ-II stellarator: The bootstrap current

“…The first set of profiles, Case 1, is the same as the one presented in Ref. [34], the second one, called Case 2, corresponds to a higher density ECRH operation. The density and temperature profiles are plotted in Fig.…”

“…4 of Ref. [34]). Only one solution with positive E r (electron root) is found in the plasma core followed by three solutions (there is always an odd number of solutions) at outer radius.…”

“…The predicted radial electric field is obtained from the solution of a diffusion equation for the radial electric field, see Ref. [34] for details. It is worth stressing the fair agreement between the results of Fig.…”

ECRH scenarios with selective heating of trapped/passing electrons in the W7-X Stellarator

“…Simulations were performed with help of the following numerical tools: 3D ray-tracing code TRAVIS [15] coupled self-consistently with the 1D-transport code NTSS [16], which is based on comprehensive neoclassical and simple turbulent transport models. The magnetic equilibriums with finite-β effects accounted were precalculated by the VMEC code [17] as well as the transport coefficients calculated by the DKES code [18].…”