A Contribution to the Computation of the Impedance in Acceleration Resonators

This thesis is focusing on the numerical computation of the impedance in acceleration resonators and corresponding components. For this purpose, a dedicated solver based on the Finite Element Method (FEM) has been developed to compute the broadband impedance in accelerating components. In addition, various numerical approaches have been used to calculate the narrow-band impedance in superconducting radio frequency (RF) cavities. From that an overview of the calculated results as well as the comparisons between the applied numerical approaches is provided. During the design phase of superconducting RF accelerating cavities and components, a challenging and difficult task is the determination of the impedance inside the accelerators with the help of proper computer simulations. Impedance describes the electromagnetic interaction between the particle beam and the accelerators. It can affect the stability of the particle beam. For a superconducting RF accelerating cavity with waveguides (beam pipes and couplers), the narrow-band impedance, which is also called shunt impedance, corresponds to the eigenmodes of the cavity. It depends on the eigenfrequencies and its electromagnetic field distribution of the eigenmodes inside the cavity. On the other hand, the broadband impedance describes the interaction of the particle beam in the waveguides with its environment at arbitrary frequency and beam velocity. With the narrow-band and broadband impedance the detailed knowledges of the impedance for the accelerators can be given completely. In order to calculate the broadband longitudinal space charge impedance for acceleration components, a three-dimensional (3D) solver based on the FEM in frequency domain has been developed. To calculate the narrow-band impedance for superconducting RF cavities, we used various numerical approaches. Firstly, the eigenmode solver based on Finite Integration Technique (FIT) and a parallel real-valued FEM (CEM3Dr) eigenmode solver based on symmetric curvilinear tetrahedrons are applied to the Superconducting Proton Linac (SPL) cavity. Afterwards, a parallel complex-valued FEM (CEM3Dc) eigenmode solver based on curvilinear tetrahedrons is applied to the TESLA 1.3 GHz and the third harmonic 3.9 GHz superconducting cavities