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A Directionally Dispersion-free Algorithm for the Calculation of Wake Potentials

Hampel, Robert (2009):
A Directionally Dispersion-free Algorithm for the Calculation of Wake Potentials.
Darmstadt, Technische Universität, TU Darmstadt, [Online-Edition: urn:nbn:de:tuda-tuprints-13550],
[Ph.D. Thesis]

Abstract

The numerical simulation of electromagnetic fields excited by moving charged particles is a particularly difficult problem. The frequency spectrum of the excited fields ranges up to the terahertz regime. In order to resolve the very short wavelengths, a fine computational grid is required. Consequently, a large number of time steps has to be performed, making the results sensitive to error accumulation. In this thesis an algorithm is presented which allows for the accurate simulation of high-frequency fields along dedicated directions. The Finite Integration Technique (FIT) is a discretization method for the computer simulation of electromagnetic fields. The propagation of waves in the discrete space shows directionally dependent dispersion properties and vanishing dispersion errors for certain directions. The presented algorithm exploits these directions in order to avoid the accumulation of errors in long-term simulations. The algorithm is developed followed by a theoretical analysis of its dispersion properties. Furthermore, it is verified in comparisons with analytical solutions. The implementation of the algorithm was applied to the simulation of electromagnetic fields excited in particle accelerator components. These are currently subject to optimization studies.

Item Type: Ph.D. Thesis
Erschienen: 2009
Creators: Hampel, Robert
Title: A Directionally Dispersion-free Algorithm for the Calculation of Wake Potentials
Language: English
Abstract:

The numerical simulation of electromagnetic fields excited by moving charged particles is a particularly difficult problem. The frequency spectrum of the excited fields ranges up to the terahertz regime. In order to resolve the very short wavelengths, a fine computational grid is required. Consequently, a large number of time steps has to be performed, making the results sensitive to error accumulation. In this thesis an algorithm is presented which allows for the accurate simulation of high-frequency fields along dedicated directions. The Finite Integration Technique (FIT) is a discretization method for the computer simulation of electromagnetic fields. The propagation of waves in the discrete space shows directionally dependent dispersion properties and vanishing dispersion errors for certain directions. The presented algorithm exploits these directions in order to avoid the accumulation of errors in long-term simulations. The algorithm is developed followed by a theoretical analysis of its dispersion properties. Furthermore, it is verified in comparisons with analytical solutions. The implementation of the algorithm was applied to the simulation of electromagnetic fields excited in particle accelerator components. These are currently subject to optimization studies.

Place of Publication: Darmstadt
Publisher: Technische Universität
Uncontrolled Keywords: FIT, Finite Integration Technique, CEM, Accelerator, Computational Electromagnetics, Wake Field, Wake Potential, Numerical Dispersion
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute of Electromagnetic Field Theory (from 01.01.2019 renamed Institute for Accelerator Science and Electromagnetic Fields)
Date Deposited: 01 Apr 2009 12:03
Official URL: urn:nbn:de:tuda-tuprints-13550
License: Creative Commons: Attribution-Noncommercial-No Derivative Works 3.0
Referees: Weiland, Prof. Dr.- Thomas and Klinkenbusch, Prof. Dr.- Ludger
Refereed / Verteidigung / mdl. Prüfung: 31 October 2008
Alternative Abstract:
Alternative abstract Language
Die numerische Simulation von elektromagnetischen Feldern, die durch bewegte elektrische Ladungen angeregt werden, stellt eine besonders schwierige Aufgabenstellung dar. Das Frequenzspektrum der angeregten Felder erstreckt sich bis in den Bereich von Terahertz. Die daraus resultierenden kurzen Wellenlängen können nur mit einem sehr feinen Gitter aufgelöst werden. Daraus ergibt sich eine hohe Zahl von benötigten Zeitschritten für die Simulation. Dies macht die Ergebnisse besonders anfällig für die Akkumulation von Fehlern. In dieser Arbeit wird ein Algorithmus vorgestellt, der es erlaubt, hochfrequente Felder entlang bevorzugter Richtungen zu simulieren. Die Methode der Finiten Integration (engl. \glqq Finite Integration Technique\grqq, FIT) stellt eine Diskretisierungsmethode für die Simulation elektromagnetischer Felder dar. Die Ausbreitung von Wellen im diskretisierten Raum weisen richtungsabhängige Dispersionseigenschaften auf. Für einige bestimmte Richtungen verschwinden die Dispersionsfehler völlig. Der vorgestellte Algorithmus nutzt diese Richtungen aus, um die Akkumulation von Fehlern in lang andauernden Simulationen zu vermeiden. Nach der Entwicklung des Algorithmus werden seine Dispersionseigenschaften untersucht und eine Verifikation mit analytischen Lösungen folgt. Schließlich wird der Algorithmus nach seiner Implementierung für die Simulation elektromagnetischer Felder in Bauteilen von Teilchenbeschleunigern angewandt, die Gegenstand aktueller Optimierungsstudien sind.German
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