Rostock University, Faculty of Computer Science and Electrical Engineering, Rostock, Germany
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 polynomial chaos (PC) 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 PC 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.
Rostock University, Faculty of Computer Science and Electrical Engineering, Rostock, Germany
The computation of eigenmodes for complex accelerating structures is a challenging and important task for the design and operation of particle accelerators. Discretizing long and complex structures to determine its eigenmodes leads to demanding computations typically performed on super computers. This contribution presents an application example of a method to compute eigenmodes and other parameters derived from these eigenmodes for long and complex structures using standard workstation computers. This is accomplished by the decomposition of the complex structure into several single segments. In a next step, the electromagnetic properties of the segments are described in terms of a compact state space model. Subsequently, the state space models of the single structures are concatenated to the full structure. The results of direct calculations are compared with results obtained by the concatenation scheme in terms of computational time and accuracy.
