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Optimal Design of the Magnet Profile for a Compact Quadrupole on Storage Ring at the Canadian Synchrotron Facility

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Optimal Design of the Magnet Profile for a Compact Quadrupole on Storage Ring at the Canadian Synchrotron Facility OPTIMAL DESIGN OF THE MAGNET PROFILE FOR A COMPACT QUADRUPOLE ON STORAGE RING AT THE CANADIAN SYNCHROTRON FACILITY A Thesis Submitted to the College of Graduate and Postdoctoral Studies in Partial Fulfillment of the Requirements for the Degree of Master of Science in the Department of Mechanical Engineering, University of Saskatchewan, Saskatoon By MD Armin Islam ©MD Armin Islam, December 2019. All rights reserved. Permission to Use In presenting this thesis in partial fulfillment of the requirements for a Postgraduate degree from the University of Saskatchewan, I agree that the Libraries of this University may make it freely available for inspection. I further agree that permission for copying of this thesis in any manner, in whole or in part, for scholarly purposes may be granted by the professors who supervised my thesis work or, in their absence, by the Head of the Department or the Dean of the College in which my thesis work was done. It is understood that any copying or publication or use of this thesis or parts thereof for financial gain shall not be allowed without my written permission. It is also understood that due recognition shall be given to me and to the University of Saskatchewan in any scholarly use which may be made of any material in my thesis. Requests for permission to copy or to make other use of the material in this thesis in whole or part should be addressed to: Dean College of Graduate and Postdoctoral Studies University of Saskatchewan 116 Thorvaldson Building, 110 Science Place Saskatoon, Saskatchewan, S7N 5C9, Canada Or Head of the Department of Mechanical Engineering College of Engineering University of Saskatchewan 57 Campus Drive, Saskatoon, SK S7N 5A9, Canada i Abstract This thesis concerns design of a quadrupole magnet for the next generation Canadian Light Source storage ring. The quality of the design is measured by the so-called width of Good Field Region (GFR) in the magnetic field generated by the magnet in a particular configuration, e.g. quadrupole configuration. The width of GFR is defined upon the multipole error in magnetic field strength, in particular the error being less than 0.1%. The design requirement for the magnet was to have the GFR at least ±1.0 cm. It is noted that the existing or preliminary design of the magnet (Dallin, 2018) has only achieved ±0.8 cm GFR. This thesis was motivated to design the magnet of the quadrupole so that the foregoing design requirement can be met. The secondary motivation of this thesis was to improve the design of the magnet so that the bad edge effect of the magnet can be reduced. Increase of the width of GFR may be achieved by reduction of the multipole errors. The shape of the magnet pole is a major factor to cause these errors. An optimal design of the shape of the magnet pole was attempted in this thesis. Specifically, a simulation-based trial-and-error procedure was taken for the optimal design partly due to some difficulty to represent the shape of the magnet pole analytically. This procedure was acceptable as a pilot try for a more sophisticated optimal design that may follow in the future. Reduction of the bad edge effect with the magnet may be reduced by careful modification of the shape of the side or edge of the magnet. The result of this thesis is very encouraging; specifically, the width of ±1.1 cm of GFR has been achieved within the field region. The result thus gives a proof of the proposed design approach with the procedure. Further, the bad edge effect was also reduced. This thesis has made a contribution in the field of synchrotron radiation machinery with the proposed design approach to the magnet. The proposed approach is simple and can be implemented in any synchrotron radiation facility. ii Acknowledgements First, I would like to express my sincere gratefulness to my supervisors Dr. Chris Zhang and Dr. Mark Boland for their constant support. Their incredible guidance and motivation helped me to successfully complete my MSc study program. Starting from the coursework, giving me a summer internship at Canadian Light Source Inc., helping me with the research proposal, guiding me through the whole research and writing the thesis, I can’t think a better supervisor than them. Also, their guidance and contribution to my attending to a conference as well as conference paper writing, opened a new door of my expertise for which I will always be grateful to them. I would also like to thank my advisory committee members, Dr. Daniel Chen and Dr. Madan M. Gupta, for their helpful advice and suggestions from the first Advisory Committee meeting. I would also like to express my gratitude to Les Dallin who is an accelerator physicist and scientist at Canadian Light Source Inc. for his extended collaboration and valuable suggestions which contributed greatly to the development of this research. Also, I would like to thank Drew Bertwistle who is also an accelerator physicist at Canadian Light Source Inc. for providing me the necessary software licenses and the software using instructions. Again, a special thank goes to the Canadian Light Source staff especially Accelerator Operations and Development (AOD) staff, for their help and co-operation without which it would be difficult to accomplish the goal of this research. Finally, I would like to express my profound gratitude to my parents and my siblings for providing me continuous encouragement and support throughout my whole study program. This accomplishment would not have been possible without their support. iii Table of Contents Permission to Use ............................................................................................................................ i Abstract ........................................................................................................................................... ii Acknowledgements ........................................................................................................................ iii Table of Contents ........................................................................................................................... iv List of Figures ............................................................................................................................... vii List of Abbreviations ..................................................................................................................... xi : Introduction .................................................................................................................. 1 1.1 Background of the Research ................................................................................................. 1 1.2 Motivation and Research Problem ........................................................................................ 6 1.3 Research Objectives and Scope............................................................................................. 9 1.4 Organization of the Thesis .................................................................................................. 10 : Background and Literature Review ........................................................................... 11 2.1 Introduction ......................................................................................................................... 11 2.2 Electromagnets in a Synchrotron ........................................................................................ 11 2.2.1 Dipole ........................................................................................................................... 11 2.2.2 Quadrupole ................................................................................................................... 12 2.2.3 Sextupole ...................................................................................................................... 13 2.3 Requirements for the Quadrupole ....................................................................................... 14 2.3.1 Magnetic requirements of the quadrupole .................................................................... 14 2.3.2 Structural requirements of the quadrupole ................................................................... 15 2.4 Design of the Pole Shape of the Quadrupole in Different Synchrotrons ............................ 18 2.6 Conclusion ........................................................................................................................... 28 : Analysis of the Quadrupole ........................................................................................ 29 iv 3.1 Introduction ......................................................................................................................... 29 3.2 Magnetic Field in a Quadrupole ..................................................................................... 29 3.3 Multipole Errors in a Quadrupole ....................................................................................... 32 3.5 Governing Equations ........................................................................................................... 34 3.6 Simulation Software ............................................................................................................ 36 3.7 Summary ............................................................................................................................. 37 : Optimal Design of the Geometry of Magnet in a Quadrupole ................................... 38 4.1 Introduction ........................................................................................................................
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