Efficient Shape Uncertainty Quantification for the TESLA Cavity

In our contribution, we present an efficient shape uncertainty quantification method based on closed-form shape derivatives for the Maxwell eigenvalue problem. We demonstrate our algorithm for the 9-cell TESLA cavity which is subject to misalignment due to imperfections in the manufacturing process and compare the performance of our approach to the classic Monte Carlo method. In this comparison, we observe a drastic increase in efficiency.

I. Introduction

The eigenfrequency of an accelerator cavity and hence the efficiency of the particle acceleration depend sensitively on the geometry of the device. One source for deviations from the ideal cavity shape are manufacturing imperfections due to, e.g., misalignment of the cavity cells in the welding process. Two examples of misaligned TESLA cavities, where the cell centers deviate from the ideal central axis (for visualization purposes to an exaggerated extent) are displayed in Fig. 1. In order to state the influence on the critical quantities, i.e., the eigenpair, we are interested in an uncertainty quantification, which however may be computationally very expensive. As an alternative to classic sampling methods, we propose a derivative-based uncertainty quantification method.