title: Data-driven simulation of magnetic fields in accelerator magnets
Creators: name: Fleig, Luisa
Publisher: name: UNSPECIFIED
Year: 2024

description: The accelerator complex operated at the European Organization for Nuclear Research (CERN) consists of thousands of normal- and superconducting electromagnets and permanent magnets, which are guiding, focusing, and defocusing the particle beams. In this context, the magnetic field usually has to meet high quality requirements allowing relative errors of only a few units in 10000. Simulations and measurements of magnet systems and their generated fields are used for operation. Despite the improvements in numerical methods and computing power in the last decades, simulated field predictions are insufficient for the operation of accelerator magnets, because the simulations are affected by aleatory and epistemic uncertainty as well as acknowledged and unacknowledged errors. For example, the knowledge of the underlying physical processes is often limited. Measurements on the other hand are affected by random and systematic uncertainties. To predict field-related quantities of interest (interpolation and extrapolation), and to gain insight into local quantities (introspection) that are not easily measurable, system models of accelerator magnets and their generated field have been developed that combine simulations with measurement data. By the combination of both approaches, some of their respective limitations can be overcome. This strategy is also known as hybrid modeling. Even though the system models of accelerator magnets found in the literature are heterogeneous, some common methods can be identified to build and adjust them. These include deterministic and stochastic model updating, solving inverse problems, and addressing their ill-posedness.
Applying these methods, three system models of accelerator magnets in the static operation mode are derived in this thesis, focusing on different aspects. First, we use a data-driven stochastic B(H)-curve model, based on permeameter measurements of yoke material specimens and the Karhunen-Loève expansion, to regularize by low-rank approximation the updating of the yoke’s B(H)-curve. Second, the permanent magnetizations in a three-dimensional system model of the first short Halbach dipole of the FASER experiment are updated with Bayesian inference. We show that the mismatch between the measured and the predicted higher-order multipole coefficients can be explained by adjusting the magnetizations in the range of their manufacturing tolerances. The third application addresses the field description in curved magnet systems, where the classical field description based on the circular harmonic expansion fails. The toroidal harmonic expansion is a well-known alternative, but algorithms to determine its coefficients based on field observations have rarely been studied. For this purpose, we derive and evaluate an identification approach based on linear least squares fitting and an identification method based on integration.
The three derived system models follow the spirit of hybrid modeling by combining physics-based methods with data-based methods. Including knowledge obtained from measurements improves in all the studied
use cases the field predictions of the system model, even outside the regime of the training data. The validation of this methodology in the context of accelerator magnets contributes to establishing more interconnections between the models, data sets, and physical objects operated at the TE-MSC-TM section at CERN.