# Uncertainty Modeling and Analysis of the European X-ray Free Electron Laser Cavities Manufacturing Process

## TL;DR

This paper presents a comprehensive uncertainty quantification and sensitivity analysis of the manufacturing process for TESLA-shaped superconducting cavities used in the European X-ray Free Electron Laser, combining measurements and advanced simulation techniques.

## Contribution

It introduces a detailed comparison and integration of measurement data with simulation-based uncertainty analysis for accelerator cavities.

## Key findings

- Identified key sensitivities in cavity manufacturing process.
- Validated simulation models against measurement data.
- Enhanced surrogate modeling techniques for uncertainty quantification.

## Abstract

This paper reports on comprehensive efforts on uncertainty quantification and global sensitivity analysis for accelerator cavity design. As a case study object the TESLA shaped superconducting cavities, as produced for the European X-ray Free Electron Laser (EXFEL), are selected. The choice for these cavities is explained by the available measurement data that can be leveraged to substantiate the simulation model. Each step of the manufacturing chain is documented together with the involved uncertainties. Several of these steps are mimicked on the simulation side, e.g. by introducing a random eigenvalue problem. The uncertainties are then quantified numerically and in particular the sensitivities give valuable insight into the systems behavior. We also compare these findings to purely statistical studies carried out for the manufactured cavities. More advanced, adaptive, surrogate modeling techniques are adopted, which are crucial to incorporate a large number of uncertain parameters. The main contribution is the detailed comparison and fusion of measurement results for the EXFEL cavities on the one hand and simulation based uncertainty studies on the other hand. After introducing the quantities of physical interest for accelerator cavities and the Maxwell eigenvalue problem, the details on the manufacturing of the EXFEL cavities and measurements are reported. This is followed by uncertainty modeling with quantification studies.