Dimitris Valougeorgis

The sub-divertor neutral gas pressure in relation to seven plasma parameters is predicted, based on the data of the Wendelstein 7-X OP1.2b experimental campaign, via two machine learning (ML) approaches, the extra trees (ET) and symbolic regression (SR) for the standard, high iota and high mirror magnetic configurations. To capture the changing behavior of moving from attached to detached conditions, the dataset in each configuration is divided into three clusters. Via a formal feature importance analysis, in all cases considered, the line integrated electron density is ranked as the most dominant parameter, while the heating power, followed by the radiated power, are always included in the key parameters. In the standard configuration, the coil control current has also been ranked very high. On the contrary, the center and edge temperatures and the toroidal current are of much less importance. The ET model yields nearly perfect predictions but it lacks interpretability and may struggle to generalize to unseen data. The two- and three-parameter expressions obtained by the SR model explicitly demonstrate the dependency of the neutral gas pressure on the plasma parameters and have greater potential for extrapolation to unseen estimates. Although SR predictions lag behind those of ET, they still remain very accurate. The present investigation provides valuable insight into the interconnection between the sub-divertor pressure and plasma parameters and may support the design and optimization of the particle and impurity exhaust system of W7-X and other fusion reactors, broadening the scope of ML applications in fusion.

A machine learning approach, namely symbolic regression (SR), is applied in the stellarator Wendelstein 7-X (W7-X), to investigate the effect of six plasma parameters (line integrated electron density, heating power, toroidal plasma current, fraction of radiated power, core and edge ion temperatures) on the sub-divertor neutral gas pressure. Based on the data from the OP1.2b experimental campaign, closed-form expressions of the neutral gas pressure in terms of the plasma parameters are deduced for the standard, high iota and high mirror magnetic configurations at three different ports of the exhaust system. While common regression schemes assume a predetermined functional form, SR autonomously discovers, via genetic programming, the functional structure of the model, purely from data. In all cases, the optimized data driven SR framework clearly points out that, in estimating the neutral gas pressure, the most dominant parameters are the electron density and the heating power, while the remaining plasma parameters have minor impact, at least from the statistical point of view and may not be included in the correlations. Balancing model generality, complexity(COMP) and accuracy for all considered magnetic configurations and ports, the proposed closed form expressions contain only the product of electron density and heating power raised at some powers, times a constant. The proposed two-parameter symbolic expressions, exhibiting low COMP and excellent accuracy metrics, provide a practical and analytical tool for the acceleration of the neutral gas pressure calculations, that are otherwise computationally very expensive and for the overall performance assessment of the W7-X exhaust system. They may also contribute to more efficient experimental design and operation. performance assessment of the W7-X exhaust system. They may also contribute to more efficient experimental design and operation.

The viscous and thermal velocity slip coefficients of various monatomic gases are computed via the linearized classical Boltzmann equation, with ab initio potential, subject to Maxwell and Cercignani–Lampis boundary conditions. Both classical and quantum interatomic interactions are considered. Comparisons with hard sphere and Lennard–Jones potentials, as well as the linearized Shakhov model are performed. The produced database is dense, covers the whole range of the accommodation coefficients and is of high accuracy. Using symbolic regression, very accurate closed form expressions of the slip coefficients, easily implemented in the future computational and experimental works, are deduced. The thermal slip coefficient depends, much more than the viscous one, on the intermolecular potential. For example, in the case of diffuse scattering, the relative differences in the viscous slip coefficient data between HS and AI potentials are less than 4%, whilst the corresponding ones in the thermal slip coefficient data are about 6% for He, reaching 15% for Xe. Quantum effects are considered for He, at temperatures 1–10⁴ K to deduce that deviations from the classical behaviour are not important in the viscous slip coefficient, but they become important in the thermal slip coefficient, where the differences between the classical and quantum approaches reach 15% at 1 K. The computational effort of solving the linearized Boltzmann equation with ab initio and Lennard–Jones potentials is the same. Since ab initio potentials do not contain any adjustable parameters, it is recommended to use them at any temperature.