Fast recovery of vacuum magnetic configuration of the W7-X stellarator using function parametrization and artificial neural networks

Abstract

W7-X, a five-period, fully optimized stellarator, currently under construction at IPP-Greifswald, Germany, is built with superconducting coils to show the steady state capability of stellarators. However, the steady state needs continuous equilibrium information for monitoring and controlling the discharge. Although the timescales are long compared with tokamaks, the computational effort for calculating three-dimensional magnetohydrodynamic equilibria is also orders of magnitude higher. This has led us to start the development of a fast equilibrium recovery for W7-X. As a starting point and also for investigating the richness of magnetic configurations, of which only nine physically interesting examples have been examined till now, a fast recovery of vacuum magnetic configurations, described by the flux surface geometry and profile parameters, is carried out using the function parametrization (FP) and artificial neural networks (ANN) methods. Additionally, we parametrize the detectable major magnetic island chains (5/6, 5/5, 5/4) in the form of their locations, , and their width, w(is). The quality of FP recovery is compared with ANN, where the vacuum parameters are non-linearly regressed in terms of linear combinations of the coil currents. The results show that a quadratic FP model is generally sufficient for a good recovery of the parameters which are related to the magnetic axis. However, a cubic model is necessary for modelling accurately the magnetic island-related parameters. ANN models offer no improvement over the cubic FP model.