Simona, Abele (2020)
Numerical methods for the simulation of particle motion in electromagnetic fields.
Politecnico di Milano; Technische Universität Darmstadt
doi: 10.25534/tuprints-00011687
Ph.D. Thesis, Primary publication
Abstract
In this thesis we study numerical methods for the approximate solution of problems arising in electromagnetism. Its main motivations come from applications to the modelling of high-energy particle accelerators. In this framework, we first compare the efficiency of several numerical methods for the omputation of particle trajectories in the design of a magnetic quadrupole for the High Luminosity - Large Hadron Collider (HL-LHC) project and we analyse the use of a specific vector potential gauge to reduce the computational cost. The results from this first comparison motivate the subsequent investigation of the accuracy of the numerical approximation of the field. We therefore develop a new type of discretization for the reconstruction of the magnetic scalar potential in cylindrical domains and we apply it to the field reconstruction from a realistic measurement process in a Bayesian framework. We compare this method with the reconstruction obtained by a more classical method based on the separation of variables, highlighting the benefits of the new type of discretization and its applicability to the reconstruction process. Motivated by the need of efficient methods for the description of electromagnetic fields, we extend the study to other types of problems for axisymmetric domains, which have a high practical relevance in particle accelerator applications. In this context, we propose the use of a method based on the Fourier basis and IsoGeometric Analysis (IGA) to exploit, on one hand, the computational efficiency that can be achieved thanks to the symmetry of the domain and, on the other, the exact representation of the geometry and the good approximation properties achievable in a IGA framework. Moreover, the proposed method forms a de Rham complex, which is a crucial property that allows to obtain a stable method which produces physically correct approximations. We finally apply the method to the computation of resonant modes of an accelerating TESLA cavity.
Item Type: | Ph.D. Thesis | ||||
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Erschienen: | 2020 | ||||
Creators: | Simona, Abele | ||||
Type of entry: | Primary publication | ||||
Title: | Numerical methods for the simulation of particle motion in electromagnetic fields | ||||
Language: | English | ||||
Referees: | Schöps, Prof. Dr. Sebastian ; Russenschuck, Dr.-Ing Stephan ; Vázquez, Dr. Rafael | ||||
Date: | 3 March 2020 | ||||
Place of Publication: | Darmstadt | ||||
Refereed: | 13 March 2020 | ||||
DOI: | 10.25534/tuprints-00011687 | ||||
URL / URN: | https://tuprints.ulb.tu-darmstadt.de/11687 | ||||
Abstract: | In this thesis we study numerical methods for the approximate solution of problems arising in electromagnetism. Its main motivations come from applications to the modelling of high-energy particle accelerators. In this framework, we first compare the efficiency of several numerical methods for the omputation of particle trajectories in the design of a magnetic quadrupole for the High Luminosity - Large Hadron Collider (HL-LHC) project and we analyse the use of a specific vector potential gauge to reduce the computational cost. The results from this first comparison motivate the subsequent investigation of the accuracy of the numerical approximation of the field. We therefore develop a new type of discretization for the reconstruction of the magnetic scalar potential in cylindrical domains and we apply it to the field reconstruction from a realistic measurement process in a Bayesian framework. We compare this method with the reconstruction obtained by a more classical method based on the separation of variables, highlighting the benefits of the new type of discretization and its applicability to the reconstruction process. Motivated by the need of efficient methods for the description of electromagnetic fields, we extend the study to other types of problems for axisymmetric domains, which have a high practical relevance in particle accelerator applications. In this context, we propose the use of a method based on the Fourier basis and IsoGeometric Analysis (IGA) to exploit, on one hand, the computational efficiency that can be achieved thanks to the symmetry of the domain and, on the other, the exact representation of the geometry and the good approximation properties achievable in a IGA framework. Moreover, the proposed method forms a de Rham complex, which is a crucial property that allows to obtain a stable method which produces physically correct approximations. We finally apply the method to the computation of resonant modes of an accelerating TESLA cavity. |
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URN: | urn:nbn:de:tuda-tuprints-116876 | ||||
Classification DDC: | 500 Science and mathematics > 510 Mathematics 600 Technology, medicine, applied sciences > 600 Technology 600 Technology, medicine, applied sciences > 620 Engineering and machine engineering |
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Divisions: | 18 Department of Electrical Engineering and Information Technology 18 Department of Electrical Engineering and Information Technology > Institute for Accelerator Science and Electromagnetic Fields > Computational Electromagnetics 18 Department of Electrical Engineering and Information Technology > Institute for Accelerator Science and Electromagnetic Fields |
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Date Deposited: | 13 Aug 2020 13:23 | ||||
Last Modified: | 01 Dec 2023 07:56 | ||||
PPN: | |||||
Referees: | Schöps, Prof. Dr. Sebastian ; Russenschuck, Dr.-Ing Stephan ; Vázquez, Dr. Rafael | ||||
Refereed / Verteidigung / mdl. Prüfung: | 13 March 2020 | ||||
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