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Abstract

Wakes and impedances of single accelerator elements can be obtained by means of theoretical calculation, electromagnetic (EM) simulations or bench measurements. Since theoretical calculations apply only to simple structures and bench measurements have some intrinsic limitations, EM simulations can be used as a reliable tool to determine wakes and impedances. This thesis will focus on the use of time domain 3D CST Particle Studio EM simulations to calculate wakes and/or impedances. First, the results of the EM simulations are compared with the known analytical solutions and other codes. In this exercise, the driving and the detuning terms of the wakes/impedances, in the transverse plane, are disentangled for both symmetric and asymmetric geometries. The sensitivity of the simulations results to the numerical parameters is discussed, as well as the limits of validity of the wake formalism and its extension to the nonlinear regime. Using the CST Wakefield Solver, the SPS kicker impedance contribution is then estimated. The simulation model was improved step by step, and successfully benchmarked with existing and new theoretical models, giving confidence in the numerical results and allowing a better understanding of the EM problems. In the case of the resistive wall impedance of simple chamber geometries a handy theoretical model has been proposed. In order to calculate the resistive wall impedance of a round chamber, a theoretical approach based on the transmission line (TL) theory, is demonstrated to be valid and practical to use. By means of appropriate form factors the method is then extended to rectangular or elliptical chambers. Moreover the method was successfully benchmarked with the most recent codes based on the field matching technique developed at CERN and was used to construct the SPS wall impedance model. For more complicated geometries (asymmetries, small inserts, holes etc.), a theoretical estimation without involving EM simulation becomes unworkable. An example of interest is the LHC beam-screen, for which CST 3D simulations were used to estimate the impedance. In order to allow the simulator to cover the whole frequency range of interest (few KHz to several tens of MHz) a novel scaling technique was developed and applied. Where possible, the EM models developed throughout this thesis were also successfully benchmarked with bench measurements (wire methods) and observations with beam. On the specific subject of bench measurements, a numerical investigation of coaxial wire measurements has been also presented. Finally, in order to verify the adopted EM models of the materials both in theoretical calculations and 3D simulations, an experimental setup for measuring EM properties (permittivity and permeability) of materials has been presented. The method is based on fitting the measured reflection transmission coefficients through a coaxial line filled with the material to be probed, with the outcome of EM simulations or theoretical models. It was successfully applied for measuring NiZn ferrites and dielectric material (e.g. SiC).

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