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High-$\langle \beta \rangle$ operations require a fast and robust inference of plasma parameters with a self-consistent MHD equilibrium. Precalculated MHD equilibria are usually employed at W7-X due to the high computational cost. To address this, we couple a physics-regularized NN model that approximates the ideal-MHD equilibrium with the Bayesian modeling framework Minerva. We show the fast and robust inference of plasma profiles (electron temperature and density) with a self-consistent MHD equilibrium approximated by the NN model. We investigate the robustness of the inference across diverse synthetic W7-X plasma scenarios. The inferred plasma parameters and their uncertainties are compatible with the parameters inferred using the VMEC, and the inference time is reduced by more than two orders of magnitude. This work suggests that MHD self-consistent inferences of plasma parameters can be performed between shots., Comment: 18 pages, 6 figures

The electron density and temperature profiles measured with Thomson scattering at the stellarator Wendelstein 7-X show features which seem to be unphysical, but so far could not be associated with any source of error considered in the data processing. A detailed Bayesian analysis reveals that errors in the spectral calibration cannot explain the features observed in the profiles. Rather, it seems that small fluctuations in the laser position are sufficient to affect the profile substantially. The impact of these fluctuations depends on the laser position itself, which, in turn, provides a method to find the optimum laser alignment in the future.

In magnetic confinement fusion research, the achievement of high plasma pressure is key to reaching the goal of net energy production. The magnetohydrodynamic (MHD) model is used to self-consistently calculate the effects the plasma pressure induces on the magnetic field used to confine the plasma. Such MHD calculations serve as input for the assessment of a number of important physics questions. The VMEC code is the most widely used to evaluate 3D ideal-MHD equilibria, as prominently present in stellarators. However, considering the computational cost, it is rarely used in large-scale or online applications. Access to fast MHD equilbria is a challenging problem in fusion research, one which machine learning could effectively address. In this paper, we present artificial neural network (NN) models able to quickly compute the equilibrium magnetic field of W7-X. Magnetic configurations that extensively cover the device operational space, and plasma profiles with volume averaged normalized plasma pressure $\langle \beta \rangle$ ($\beta$ = $\frac{2 \mu_0 p}{B^2}$) up to 5% and non-zero net toroidal current are included in the data set. By using convolutional layers, the spectral representation of the magnetic flux surfaces can be efficiently computed with a single network. To discover better models, a Bayesian hyper-parameter search is carried out, and 3D convolutional neural networks are found to outperform feed-forward fully-connected neural networks. The achieved normalized root-mean-squared error ranges from 1% to 20% across the different scenarios. The model inference time for a single equilibrium is on the order of milliseconds. Finally, this work shows the feasibility of a fast NN drop-in surrogate model for VMEC, and it opens up new operational scenarios where target applications could make use of magnetic equilibria at unprecedented scales., Comment: 24 pages, 16 figures. Accepted for publication to Nuclear Fusion