Mathematical Analysis and Simulation of Field Models in Accelerator Circuits (Springer Theses)

✍ Scribed by Idoia Cortes Garcia

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 171
• Category: Library

✦ Synopsis

This book deals with the analysis and development of numerical methods for the time-domain analysis of multiphysical effects in superconducting circuits of particle accelerator magnets. An important challenge is the simulation of “quenching”, i.e. the transition of a material from the superconducting to the normally electrically conductive state. The book analyses complex mathematical structures and presents models to simulate such quenching events in the context of generalized circuit elements. Furthermore, it proposes efficient parallelized algorithms with guaranteed convergence properties for the simulation of multiphysical problems. Spanning from theoretical concepts to applied research, and featuring rigorous mathematical presentations on one side, as well as simplified explanations of many complex issues, on the other side, this book provides graduate students and researchers with a comprehensive introduction on the state of the art and a source of inspiration for future research. Moreover, the proposed concepts and methods can be extended to the simulation of multiphysical phenomena in different application contexts.

✦ Table of Contents

Supervisor’s Foreword
Parts of this thesis have been published in the following articles:
Acknowledgements
Contents
Abbreviations
1 Introduction
1.1 Related Work
1.2 Outline
References
2 Modelling
2.1 Maxwell's Equations
2.2 Material Relations
2.2.1 Nonlinear Materials
2.3 Boundary and Initial Conditions
2.4 Static and Quasistatic Fields
2.5 Formulations
2.5.1 Full Maxwell
2.5.2 Electroquasistatics
2.5.3 Magnetoquasistatics
2.5.4 "0245A-φ Formulation
2.5.5 "0245T-Ω Formulation
2.5.6 Duality of the Formulations
2.6 Modelling of Excitations
2.6.1 Excitation with Winding Density Functions
2.6.2 Excitation with Boundary Conditions
2.7 Modelling of Superconducting Magnets
2.7.1 2D Homogenisation Model
2.7.2 Heat Equation
2.8 Electric Circuits
2.8.1 From Maxwell to Circuits
2.8.2 Lumped Element Models
2.8.3 Modified Nodal Analysis
2.8.4 Circuit Topology
References
3 Numerical Methods and Model Analysis
3.1 Space Discretisation
3.1.1 Finite Integration Technique
3.1.2 Finite Element Method
3.1.3 Matrix Properties
3.2 Time Discretisation
3.2.1 Theoretical Fundamentals
3.2.2 Time Integration Techniques
3.2.3 Solution of Nonlinear Systems
3.3 Differential Algebraic Equations
3.3.1 Index
3.3.2 Initial Conditions
3.3.3 Numerical Methods for DAEs
References
4 Structural Analysis of the Coupled Systems
4.1 Generalised Circuit Elements
4.1.1 Definitions
4.2 Analysis of the Coupled System
4.2.1 Generalised Elements in MNA
4.2.2 DAE Index of the Circuit
4.2.3 Linearity of the Index 2 Components
4.3 Classification of Field Models
4.3.1 Discrete Gauging
4.3.2 Inductance-Like Elements
4.3.3 Capacitance-Like Element
4.3.4 Resistance-Like Element
4.4 Conclusion
References
5 Iterative Methods in Time Domain
5.1 Optimised Waveform Relaxation
5.1.1 Introduction
5.1.2 Optimised Schwarz for Accelerator Magnets
5.2 Parareal
5.2.1 Introduction
5.2.2 Parareal for Differential Algebraic Equations
5.3 Parallelised Waveform Relaxation
5.3.1 Waveform Relaxation and Parareal
5.4 Conclusions
References
6 Results
6.1 DAE Index of Refined Models
6.1.1 Inductance-Like Element
6.1.2 Capacitance-Like Element
6.1.3 Conclusions
6.2 Waveform Relaxation for Index 2 Circuit
6.3 Optimised Co-Simulation of Field-Circuit Systems
6.3.1 Transmission Condition Study
6.3.2 Conclusions
6.4 Parareal for DAEs with Implicit Euler
6.5 Parallelised Co-Simulation of Field-Circuit Systems
6.5.1 Parallelised Waveform Relaxation
6.5.2 Field-Circuit Parallelised Waveform Relaxation
6.5.3 Simulation Results
6.5.4 Conclusion
6.6 Conclusions
6.6.1 Outlook
References
Appendix Author Biography