Quantification of Geometric Uncertainties in Single Cell Cavities for BESSY VSR Using Polynomial Chaos

The electromagnetic properties of SRF cavities are mostly determined by their shape. Due to fabrication tolerances, tuning and limited resolution of measurement systems, the exact shape remains uncertain. In order to make assessments for the real life behaviour it is important to quantify how these geometrical uncertainties propagate through the mathematical system and influence certain electromagnetic properties, like the resonant frequencies of the structure’s eigenmodes. This can be done by using non-intrusive straightforward methods like Monte Carlo (MC) simulations. However, such simulations require a large number of deterministic problem solutions to obtain a sufficient accuracy. In order to avoid this scaling behaviour, the so-called generalized polynomial chaos (gPC) expansion is used. This technique allows for the relatively fast computation of uncertainty propagation for few uncertain parameters in the case of computationally expensive deterministic models. In this paper we use the gPC expansion to quantify the propagation of uncertain geometry on the example of single cell cavities used for BESSY VSR as well as to compare the obtained results with the MC simulation.