Determination of Beam Coupling Impedance in the Frequency Domain

• Main Author: Niedermayer, Uwe
• Format: Others
• Language: German; en
• Published: 2016
• Online Access: https://tuprints.ulb.tu-darmstadt.de/5157/1/main%20-%20Kopie.pdf; Niedermayer, Uwe <http://tuprints.ulb.tu-darmstadt.de/view/person/Niedermayer=3AUwe=3A=3A.html> (2016): Determination of Beam Coupling Impedance in the Frequency Domain.Darmstadt, Technische Universität, [Online-Edition: http://tuprints.ulb.tu-darmstadt.de/5157 <http://tuprints.ulb.tu-darmstadt.de/5157> <official_url>],[Ph.D. Thesis]

The concept of beam coupling impedance describes the electromagnetic interaction of uniformly moving charged particles with their surrounding structures in the Frequency Domain (FD). In synchrotron accelerators, beam coupling impedances can lead to beam induced component heating and coherent beam instabilities. Thus, in order to ensure the stable operation of a synchrotron, its impedances have to be quantified and their effects have to be controlled. Nowadays, beam coupling impedances are mostly obtained by Fourier transform of wake potentials, which are the results of Time Domain (TD) simulations. However, at low frequencies, low beam velocity, or for dispersive materials, TD simulations become unhandy. In this area, analytical calculations of beam coupling impedance in the FD, combined with geometry approximations, are still widely used. This thesis describes the development of two electromagnetic field solvers to obtain the beam coupling impedance directly in the FD, where the beam velocity is only a parameter and dispersive materials can be included easily. One solver is based on the Finite Integration Technique (FIT) on a staircase mesh. It is implemented both in 2D and 3D. However, the staircase mesh is inefficient on curved structures, which is particularly problematic for the modeling of a dipole source, that is required for the computation of the transverse beam coupling impedance. This issue is overcome by the second solver developed in this thesis, which is based on the Finite Element Method (FEM) on an unstructured triangular mesh. It is implemented in 2D and includes an optional Surface Impedance Boundary Condition (SIBC). Thus, it is well suited for the computation of longitudinal and transverse impedances of long beam pipe structures of arbitrary cross-section. Besides arbitrary frequency and beam velocity, also dispersive materials can be chosen, which is crucial for the computation of the impedance of ferrite kicker magnets. Numerical impedance simulations always contain simplifications, therefore they have to be confirmed by dedicated measurements. However, the beam coupling impedance of a single accelerator component cannot be measured directly. Therefore, a dedicated RF-laboratory was established at GSI, in order to measure broadband beam coupling impedances on the bench by means of the wire method, i.e. without beam. A detailed analysis of measurement methods is given by comparison of analytical, numerical, and measurement results for simplified accelerator devices. One conclusion is, that also the bench measurements have to be validated by dedicated electromagnetic simulations. The thesis closes with selected impedance induced effects on the beam revolving in the synchrotron and relevant impedance results for the future SIS-100 synchrotron for the FAIR project at GSI.