Vol. 33 - Compact State-Space Models for Complex Superconducting Radio-Frequency Structures Based on Model Order Reduction and Concatenation Methods

The modeling of large chains of superconducting cavities with couplers is a challeng- ing task in computational electrical engineering. The direct numerical treatment of these structures can easily lead to problems with more than ten million degrees of freedom. Problems of this complexity are typically solved with the help of parallel programs running on supercomputing infrastructures. However, these infrastructures are expensive to purchase, to operate, and to maintain. The aim of this thesis is to introduce and to validate an approach which allows for modeling large structures on a standard workstation. The novel technique is called State-Space Concatena- tions and is based on the decomposition of the complete structure into individual segments. The radio-frequency properties of the generated segments are described by a set of state-space equations which either emerge from analytical considera- tions or from numerical discretization schemes. The model order of these equations is reduced using dedicated model order reduction techniques. In a nal step, the reduced-order state-space models of the segments are concatenated in accordance with the topology of the complete structure. The concatenation is based on alge- braic continuity constraints of electric and magnetic elds on the decomposition planes and results in a compact state-space system of the complete radio-frequency structure. Compared to the original problem, the number of degrees of freedom is drastically reduced, i.e. a problem with more than ten million degrees of freedom can be reduced on a standard workstation to a problem with less than one thousand degrees of freedom. The nal state-space system allows for determining frequency- domain transfer functions, eld distributions, resonances, and quality factors of the complete structure in a convenient manner. This thesis presents the theory of the state-space concatenation approach and discusses several validation and application examples. The examples show that the resulting compact state-space models accu- rately describe the radio-frequency properties of the full structure and that the error introduced by the model order reduction and the concatenation of the segments is smaller than the error arising from the numerical treatment of the segments. In conclusion, the state-space concatenation scheme enables the investigation of radio- frequency properties of large structures without the application of supercomputers