增能環設計｜國立清華大學博碩士論文庫

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研究生：	張嘉麟 Chang, Chia-Lin
論文名稱：	增能環設計 The Design of Booster Synchrotron for Taiwan Photon Source
指導教授：	周炳榮 Chou, Ping-Jung 唐述中 Tang, Shu-Jung
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2009
畢業學年度：	97
語文別：	英文
論文頁數：	83
中文關鍵詞：	增能環、加速器
外文關鍵詞：	Booster, Synchrotron
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同步輻射光源的目的在於提供高亮度的光束供科學研究使用，而小發散度的電子束方能提供高亮度的同步輻射光。發散度的定義是電子束在象空間中所佔據的面積。為了能夠提供高亮度光源，小發散度的電子束是非常重要得。為了提供儲存環小發散度的電子束，增能環內部的電子束也理當擁有小發散度。
我將設計一個週長不超過150公尺的小型增能環，能夠將電子的能量從150MeV增加到3GeV。我使用綜合功能FODO磁格設計來縮小這個增能環的週長，另外使用六極磁鐵來矯正色散和渦流效應。為了提高射束穩定度，我盡量降低高階磁場並且避免工作點觸碰到共振線。工作點的掃描和六極磁鐵的配置能夠確保這個增能環擁有足夠的動力孔徑。因為工程上不可避免的誤差導致的閉合軌道變形也同時得到修正，讓電子軌道更加穩定。
在增能環的引出過程中，我使用了一個脈衝衝擊磁鐵、四個軌道提昇磁鐵與兩個脈衝二極磁鐵來完成射束的引出，並且設計了一條傳輸線來輸送引出的射束到達儲存環，最後我完成了一套符合設計目標的增能環與傳輸線。

Accelerator is an instrument that accelerates charged particle to a desired energy. In general a circular accelerator has three main parts: booster, storage ring and transfer line. A booster is a synchrotron. Which accelerates the electron beam to a desired energy and then extract these electrons to the storage ring through a transfer line. Synchrotron light source is a circular accelerator, which stores electron beam and creates photons by the centrifugal acceleration of electrons at the bending magnets.
The goal of a synchrotron light source is to provide high brilliance photon beam for scientific research. High brilliance photon beam can only be generated by electron beam of small emittance. Beam emittance is the area occupied by particles in the phase space. Thus, making the beam emittance of the storage ring as small as possible is very important in designing a storage ring. To provide small emittance beam in the storage
ring, the booster also needs to be designed with a small beam emittance.
I try to design a small booster with circumference about 150m. The electron beam would be accelerated from 150MeV to 3GeV. Combined function FODO lattice is used for the booster to reduce the circumference. Nature chromaticity and eddy current effect are corrected by the sextupole field in combined function magnets. For beam stability the higher order magnetic fields should be keep small and the working tune should stay away from the resonance line. I scan the working tune and track the electron dynamics in phase space and find a solution with good dynamic aperture. The closed orbit distortion due to engineering imperfection could be corrected to make the particle trajectory stable.
After ramping to the desired energy, the electron beams will be extracted and delivered to the storage ring. There are a fast kicker, four bumpers and two septum magnets in the design to extract electron beams from the booster. The extracted beam traverses through a transfer line, which connects the booster and the storage ring. The closed orbit distortion in the transfer line is corrected by correction magnets. Then, the electron beams are injected to the storage ring. The design of a booster and a transverse line which meet the design requirement of storage ring has been achieved.

摘要 . . . . i
Abstract . . . . iii
誌謝 . . . . v
1 Introduction 1
1.1 Subject . . . . . . . . . . . . . . . . . . . . . . .  . . . . . . . 1
1.2 Research method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Thesis content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Accelerator Physics 3
2.1 Transverse Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Equation of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Matrix formalism for Linear beam dynamics . . . . . . . . . . . . . 5
2.2 Courant-Snyder Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Hill’a equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Transfer Matrix from β-function . . . . . . . . . . . . . . . . . . . . 8
2.2.3 Courant-Snyder transformation (Floquet’s transformation). . . . . . 9
2.3 Field error and transverse resonances . . . . . . . . . . . . . . . . . . . . . 10
2.4 Dispersion function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.1 The difinition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4.2 Momentum compaction factor . . . . . . . . . . . . . . . . . . . . . 12
2.5 Chromaticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.1 The difinition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.2 Cromaticity correction . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.3 Eddy current effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Closed orbit distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Booster Design 17
3.1 Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Engineering Limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.1 Circumference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2.2 Magnets spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.3 Magnet Iron Core Saturation . . . . . . . . . . . . . . . . . . . . . 21
3.3 Booster Extraction to Storage Ring . . . . . . . . . . . . . . . . . . . . . . 22
3.3.1 The first step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.2 The second step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.3 The third step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4 The booster 27
4.1 Booster parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Non-linear dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2.1 Sextupole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2.2 Eddy current effect . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2.3 Phase Space Diagram and Dynamic Aperture . . . . . . . . . . . . 33
4.3 Close Orbit Distortion and Correction . . . . . . . . . . . . . . . . . . . . 40
4.3.1 Correction scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3.2 Beam Stay Clear area (BSC) . . . . . . . . . . . . . . . . . . . . . . 42
5 Booster Extraction Scheme 45
5.1 Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2 Booster to Storage Ring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2.1 The BTS matching . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.2.2 COD and COD correction in BTS . . . . . . . . . . . . . . . . . . . 48
5.3 Injection to the Storage Ring . . . . . . . . . . . . . . . . . . . . . . . . . 50
6 Summary 55
A Booster design using the MAD program 57
A.1 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
A.2 MAD input file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
A.2.1 The initial FODO lattice . . . . . . . . . . . . . . . . . . . . . . . . 58
A.2.2 Find a better FODO lattice . . . . . . . . . . . . . . . . . . . . . . 59
A.2.3 Find the solution for the super period . . . . . . . . . . . . . . . . . 60
B Booster COD correction 63
B.1 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
B.2 MAD file . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
C Booster phase space and dynamic aperture tracking 65
D BTS lattice design procedures 67
D.1 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
D.2 MAD matching code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
E BTS orbit correction procedures 71
E.1 procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
E.2 MAD-X code for BTS COD correction . . . . . . . . . . . . . . . . . . . . 71
F Booster extraction procedures 75
F.1 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
F.2 MAD code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
G Storage ring injection tracking(preliminary work) 79
G.1 Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
G.2 MAD code-preliminary . . . . . . . . . . .

                                

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(1998)
[2] S. Friis-Nielsen, S. P. Møller, Beam dynamics aspectes of the ASP booster, PAC ’05
[3] S.Y.Lee, Accelerator Physics, 2nd ed. (World Scientific, 2004)
[4] H.Wiedemann, Particle Accelerator Physics I, 2nd ed. (Springer, 2003)
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part I
[6] R. K. Pathria, Statistical mechanics,2nd ed. (Elsevier, 1996)
[7] K. Wille, The Physics of Particle Accelerators (Oxford, 2000)
[8] D. A. Edwards and M. J. Syphers, An Introduction to the Physics of High Energy
Accelerators (Willey, 1993), p. 112
[9] M. Sands, The Physics of Electron Storage Rings-An introduction, SLAC-121 (1970),
Chapter 4
[10] A. Hofmann and B. Zotter, Combined-function electron storage ring, IEEE NS-24
(1977) 1875
[11] J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998), Sec. 14.7
[12] MAD-X program, http://mad.web.cern.ch/mad
[13] LHC, http://lhc.web.cern.ch/lhc/
[14] A.W. Chao, M. Tigner (eds.),Handbook of Accelerator Physics and Engineering,
(World Scientific, 1999), sec. 6.3.
[15] W.R. Leo, Techniques for Nuclear and Particle Physics Experiments,2nd revised ed.
(Springer, 1994), sec 2.5
[16] S. Tazzari, Apertures for Injection, ESRP ’83, Internal Report

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