TU Darmstadt / ULB / TUbiblio

Numerical methods for the simulation of particle motion in electromagnetic fields

Simona, Abele (2020):
Numerical methods for the simulation of particle motion in electromagnetic fields.
Milano, Darmstadt, Politecnico di Milano, Technische Universität Darmstadt,
DOI: 10.25534/tuprints-00011687,
[Ph.D. Thesis]

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
Erschienen: 2020
Creators: Simona, Abele
Title: Numerical methods for the simulation of particle motion in electromagnetic fields
Language: English
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.
Place of Publication: Milano, Darmstadt
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
Date Deposited: 13 Aug 2020 13:23
DOI: 10.25534/tuprints-00011687
URL / URN: https://tuprints.ulb.tu-darmstadt.de/11687
URN: urn:nbn:de:tuda-tuprints-116876
Referees: Schöps, Prof. Dr. Sebastian ; Russenschuck, Dr.-Ing Stephan ; Vázquez, Dr. Rafael
Refereed / Verteidigung / mdl. Prüfung: 13 March 2020
Alternative Abstract:
Alternative abstract Language

In dieser Arbeit untersuchen wir numerische Methoden zur näherungsweisen Lösung von elektromagnetischen Feldern. Die Hauptmotivation ist die Anwendung in Teilchenbeschleunigern. In diesem Rahmen vergleichen wir zunächst die Effizienz verschiedener numerischer Methoden für die Berechnung von Partikeltrajektorien beim Entwurf eines magnetischen Quadrupols für das High-Luminosity LHC-Projekt und wir analysieren die Verwendung eines spezifischen Vektorpotentials zur Reduzierung der Berechnungskosten. Die Ergebnisse dieses ersten Vergleichs motivieren die anschließende Untersuchung der Genauigkeit der numerischen Näherungen der Felder. Wir entwickeln ein neues Verfahren zur Diskretisierung des magnetischen Skalarpotentials in zylindrischen Gebieten und verwenden sie zur Feldrekonstruktion mittels Daten eines realistischen Messverfahrens basierend auf dem Satz von Bayes. Wir vergleichen die neue Methode mit der Rekonstruktion, die durch eine klassischeren Ansatz, der auf der Trennung der Variablen basiert, erhalten wurde. Wir diskutieren die Vorteile der neuen Diskretisierung und ihrer Anwendbarkeit auf den Rekonstruktionsprozess. Motiviert durch den Bedarf an effizienten Methoden zur Beschreibung elektromagnetischer Felder, dehnen wir die Studie auf weitere achsensymmetrische Probleme aus, die eine hohe praktische Relevanz in der Anwendung von Teilchenbeschleunigern haben. In diesem Zusammenhang schlagen wir die Verwendung einer Methode vor, die auf der Fourier-Basis und der IsoGeometrischen Analyse (IGA) basiert. Sie nutzt zum einen die durch die Symmetrie der Domäne erzielbare Recheneffizienz und zum anderen die exakte Darstellung der Geometrie und die guten Approximationseigenschaften, die durch IGA erreichbar sind. Darüber hinaus folgt die vorgeschlagene Methode dem de Rham-Komplex, der es garantiert, eine stabile Methode zu erhalten, die physikalisch korrekte Näherungen liefert. Wir wenden die Methode schließlich auf die Berechnung von Resonanzmoden eines beschleunigenden TESLA-Resonators an.

German
Export:
Suche nach Titel in: TUfind oder in Google
Send an inquiry Send an inquiry

Options (only for editors)
Show editorial Details Show editorial Details
OAI 2.0-Basis-URL: https://tubiblio.ulb.tu-darmstadt.de/cgi/oai2 TUbiblio verwendet EPrints 3.
Drucken | Impressum | Datenschutzerklärung