Radial anomalous diffusion coefficients are among the largest sources of uncertainty in mean‐field plasma‐edge codes such as SOLPS‐ITER. These coefficients are machine, scenario, and space‐dependent, ...thus hampering the predictive and interpretive capability of these codes. In fact, modellers usually adjust these coefficients manually, based on expert judgement or on large, computationally expensive, parameter scans. Matching data from various diagnostics, each with their own experimental uncertainties, additionally complicates the problem of finding a good parameter set. In addition, standard non‐linear regression techniques have shown to become prohibitive for expensive plasma‐edge simulations with many unknown parameters, as gradient calculation was based on finite differences. In this paper, we apply algorithmic differentiation (AD) as an efficient and more accurate alternative for gradient calculation in large, continuously developed codes as SOLPS‐ITER. In addition, the lack of uncertainty information and danger of data overfitting, key limitations of regression techniques, are overcome by combining data and uncertainties from different diagnostics in a Bayesian framework. We implement for the first time such a Bayesian inference framework into SOLPS‐ITER, using gradient‐based optimization with gradients obtained through tangent AD to find the maximum a posteriori (MAP) values of the parameters. The recently developed κ turbulence model is employed to limit the number of unknown parameters compared to full spatial profiles of diffusion coefficients. The Bayesian MAP‐estimation is compared to standard regression techniques on a small‐scale tokamak. We adopt fictitious experimental data obtained from a reference SOLPS‐ITER solution with artificial measurement noise.
A new hybrid fluid‐kinetic approach for the hydrogenic neutrals (atoms and molecules) in the plasma edge is presented. The hybrid approach combines a fully kinetic model for the atoms in the ...low‐collisional regions near the vessel wall, and for the molecules in the whole plasma edge domain, with a micro–macro approach for atoms originating from recycling at the divertor targets, volumetric recombination, and dissociation of molecules. With the micro–macro approach, the originally scattering‐dominated collision term due to charge‐exchange collisions in the kinetic equation is transformed to an absorption‐dominated term, while a large part of the neutral population is treated through a fluid approach. For JET L‐mode plasmas, the premature termination of Monte Carlo particle trajectories in the hybrid approach leads to a reduction of the CPU time by approximately a factor 3 for a high‐recycling case and by approximately a factor 11 for a partially detached case compared with a simulation with fully kinetic neutrals and the same amount of particles. For coupled fluid plasma – hybrid neutral simulations – the hybrid approach predicts the plasma divertor target profiles with a maximum hybrid‐kinetic discrepancy of approximately 30%.
In plasma edge transport codes for nuclear fusion devices, fluid‐neutral models offer an interesting alternative to the currently used kinetic Monte Carlo simulations, especially for cases of high ...ion‐neutral collisionality. In this paper, we elaborate a separate neutral energy equation in the state‐of‐the‐art SOLPS‐ITER code suite, which previously assumed perfect ion‐neutral temperature equilibration. Furthermore, we study the coupled plasma‐neutral solutions for a range of divertor operating regimes, proving the validity of these fluid‐neutral models for high‐recycling and detached regimes.
The performance of advanced fluid neutral models for the simulation of deuterium atoms in the plasma edge of magnetically confined fusion devices is tested for the first time on cases that include ...drifts and currents in the plasma model, on a simplified Alcator C-mod case. The unadapted advanced fluid neutral model already gives quantitative agreement, with 5–30% fluid-kinetic discrepancy in the broad vicinity of the strikepoint. A new advective perpendicular transport term is proposed, which further reduces the fluid-kinetic discrepancies for cases with drifts. It is also shown that the ion-neutral current can be calculated consistently for fluid or kinetic neutrals, at least when only atoms are considered. However, its effect on the solution is very small for the studied case.
•Simplified Alcator C-mod case with drifts.•Assessment of advanced fluid neutral models.•Drift-compatibility of fluid neutral models.•Compare fluid neutrals with EIRENE in SOLPS-ITER.•Comparison of ion-neutral current.
Abstract
A grid refinement study is performed for mean‐field plasma boundary simulations with fluid neutrals in an EU‐DEMO geometry. In general, grid convergence of the simulations is achieved, with ...differences between the finest and second‐finest grid of <5% for the majority of the quantities of interest. The estimated discretization errors for the original 96 × 36 grid are mostly in the 4%–25% range. However, it is also shown that exceptions are possible due to the non‐linear nature of plasma boundary codes. Hence, it is advised to regularly perform grid refinement studies on subsets of cases.
Van Uytven Raymond, Blockmans W. Constitutions and their Application in the Netherlands during the Middle Ages. In: Revue belge de philologie et d'histoire, tome 47, fasc. 2, 1969. Histoire (depuis ...l'Antiquité) — Geschiedenis (sedert de Oudheid) pp. 399-424.
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