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Description
Superconducting radio frequency (SRF) cavities used for accelerating charged particle beams are commonly used in accelerator facilities around the world. The design and optimization of modern SRF cavities requires intensive numerical simulations. Vast number of operational parameters must be calculated to ensure appropriate functioning of the accelerating structures.
The increased demand for complicated simulations of SRF structures brought into focus a concatenation procedure that allows to speed up computations. The State-Space Concatenation (SSC) scheme makes use of model order reduction to speed up numerical simulations. It allows to break the long SRF structure into separate segments, proceed with relevant simulations for these segments and to perform the concatenation into a full structure at the end. Afterwards, vital parameters, like resonance frequencies, external quality factors, and geometrical longitudinal and transverse impedances, can be extracted for the modes of the full structure in the frequency range of interest.
In this study, we primarily focus on estimation and behavior of higher order modes (HOMs). In the elliptical cavities discussed in this work, used to accelerate electron beams, the HOMs have frequencies higher than the fundamental accelerating mode. Charged particle beams traversing such cavities lose part of their energy. The lost energy is manifested in form of electromagnetic resonant HOMs characteristic of a given cavity. Due to low intrinsic losses in SRF cavities the HOMs decay very slowly and interact destructively with the beam. Thus it is crucial to dampen HOMs to ensure beam stability.
The analysis of HOMs in large SRF structures is discussed on an example of a module of three 1.3 GHz cavities, being designed for the bERLinPro energy recovery linac. The second example used in this work is the planned upgrade to BESSY-VSR, where four new cavities will be installed. The new BESSY-VSR SRF cavities will be operating at two different accelerating frequencies of 1.5 GHz and 1.75 GHz. This gives a rare opportunity to investigate a chain of mixed cavities and their interaction.
