臺灣博碩士論文加值系統

高亮度同步加速器光源是廿一世紀尖端科學研究不可或缺的實驗利器,NSRRC董事會於2004年7月決議推動向政府提出「台灣光子源(TPS)跨領域實驗設施興建計畫」，建造完成後，將可提供高亮度之光源，成為世界上性能最優異的同步加速器光源。在台灣光子源興建完成後，現有的台灣光源(TLS)即規畫將其能量從1.5 GeV降至1 GeV，以便提供接近繞射極限束散度的光源給VUV的用戶使用，為了提供高亮度光源，其電子束的束散度(emittance)必須要達到很小。本篇論文的研究目標是在不改變TLS儲存環的既有硬體設施前提下，重新設計使得達到最小束散度、避免三階共振和具有足夠的動力孔徑的儲存環磁格。

根據模擬的結果顯示，在不改變儲存環的既有硬體設施下，其所能夠到的最小束散度為6.12 nm-rad，且在包含了高階磁鐵誤差和插件磁鐵的考量下，其所能達到的動力孔徑大約為±20mm /±10mm(水平/垂直)。為了運作在高電流(300 mA)模式下，其電子團會因為庫倫散射而使其生命周期(Touschek lifetime)降低至只有1.5小時。即電子束生命周期將會是個議題，故未來在運作時，必須在儲存環裏新增一個Harmonic cavity以拉長電子束的長度，增長其生命周期。

After completing the construction of the Taiwan Photon Source, the existing Taiwan Light Source (TLS) could lower
its energy from 1.5 GeV to 1 GeV for VUV users. In order to
provide high-brightness light source, the emittance of electron beam must be reduced as small as possible. This thesis will explore the possibility of designing a low emittance storage ring without altering the hardware configurations.Simulation results show that the minimum emittance of TLS could be reduced to 6.12 nm-rad with good dynamic aperture. However the lifetime is less than 2 hours and it will be an issue for future operation.

Contents

中文摘要............................... ...................i
致謝.....................................................iii
英文摘要..................................................iv

1. Introduction.........................................1

2. Introduction to Accelerator Physics..................4

Transverse Motion...... ...................................4

2.1 Hamiltonian for Particle Motion in Accelerator......4
2.2 Magnet.............................................7
2.3 Betatron Motion and Linear Motion..................8
2.4 Hill Equation......................................9
2.5 Transfer Matrix and Stability of Betatron Motion..11
2.6 Courant-Snyder Parametrization....................15
2.7 Tune Shift Due to Quadrupole Field Error..........15
2.8 Action-Angle Variable.............................17
2.9 Off- Momentum Orbit And Dispersion................19
2.10 Momentum Compaction Factor........................21
2.11 Chromatic Aberration..............................22
2.12 Chromatic Correction..............................24
2.13 Nonlinear Resonances Driven by Sextupoles.........26

Synchrotron Motion .......................................30

2.14 Synchrotron Equation of Motion....................31
2.15 Phase Space and Fixed Points......................37
2.16 RF Bucket, Bucket Width and Buck High.............39

Emittance in Electron Storage Ring........................41

2.17 Emittance and H-function..........................42
2.18 Minimization of H-function with and without Achomat
..................................................43
2.19 Minimum Emittance for TLS at 1 GeV................46
2.20 Effects of Insertion Devices......................47


3. Methods and Tools for Lattice Design..............49
3.1 Methods for Attaining the Theoretical Minimum
Emittance...........................................49
3.2 Linear Lattice Design by MAD8.....................50
3.3 Frequency Map Analysis by TRACY-II................52

4. Results of Candidate Lattice........................57
4.1 Basic Parameters for Current TLS Ring.............57
4.2 Linear Lattice Design Results.....................58
4.3 Nonlinear Dynamics................................61
4.4 Multipole Error...................................63
4.5 Touschek Lifetime.................................67
4.6 Insertion Device..................................68
4.7 Test of Design Lattice ...............................72

5. Summary and Conclusion..............................77

Appendix…………………………………………………………………79
A : Model of Insertion Device.............................79
B: MAD Optical Matched File for TME...................81
B.1 : TLS Lattice for Match........................81
B.2 : Match File.................................82
C : MAD Lattice File.................................85
C.1 : Insertion Device............................85
C.2 : Lattice Input File..........................91
D: Basic Commands Used in TRACY-II...................94
E: TME and Small Dynamic Aperture without Harmonic
Sextupole........................................102

Bibliography.............................................105

Bibliography


Abstract

[a.1] for more detail on TPS projects, one can refer to
NSRRC wbsite http://www.nsrrc.org.tw/chinese/
index.aspx

Chapter 1

[1.1] The brightness of a beam is denned as the beam's
intensity divided by its space volume.
[1.2] The Fig.1.1 is adopted from S.Y.Lee, ”Accelerator \
Physics”, Chapter 1

Chapter 2

[2.1] J.B.Marion, ”Classical dynamics of system and
particle ”,3rd edition, chapter 7
[2.2] Herbert Goldstein, ”Classical Mechanics”, 3rd
edition, chapter 8
[2.3] Arfken, ” Mathematical Methods for Physicists”,
Sec. 2.2
[2.4] for more detail on magnets, one can refer to CERN
accelerator school courses
http://cas.web.cern.ch/cas/Belgium-2009/Bruges-
after.html
[2.5] for detail analysis, refer to S.Y.Lee, ”Accelerator
Physics”, Sec. I.5, Appendix A
[2.6] see S.Y.Lee, ”Accelerator Physics”, Sec. II.7,
Chapter 2
[2.7] one should see S.Y.Lee, ”Accelerator Physics”,
Sec.VII, Chapter 2 for more detail
[2.8] S.Y.Lee, ”Accelerator Physics”, Table 2.3,
Sec.VII.1, Chapter 2
[2.9] A.W.Chao, ”Synchrotron Motion”, lecture note at
NTHU,11/03/2009
http://edu.nsrrc.org.tw/lightsource/index.php
[2.10] A.W.Chao, ”Synchrotron Motion”, lecture note at
THU,11/03/2009
http://edu.nsrrc.org.tw/lightsource/index.php
[2.11] J.D.Jackson, ”Classical Electrodynamics”, 3rd
edition, Sec. 14.6,Eq. 14.81
[2.12] S.Y.Lee, ”Accelerator Physics”, Sec. II.5, Chapter
4
[2.13] for detail derivation see S.Y.Lee, ”Accelerator
Physics”, Sec.III.1.B1, Chapter 4
[2.14] for detail analysis on beam dynamics, one should
refer to S.Y.Lee, ”Accelerator Physics”,
III.2,Chapter 4
[2.15] for detail derivation see H. C. Chao, et al, “Beam
Dynamics Effects with Insertion Devices for the
Proposed 3G eV Ring in Taiwan”,APAC 2007,TUPMA058.

Chapter 3

[3.1] H. Grote,et al., The MAD programe (Methodical
Accelerator Design),ERN/SL/90-13(AP).
[3.2 ] TRACY-II, SOLEIL’s version.
[3.3]''pac.lal.in2p3.fr/2010/2011/Cours/AccConcepts/fma2011
_handout.pdf”, or refer to the reference [3.7] for
detail discussion.
[3.4] one should refer to H.Goldstein, ”Classical
Mechanics”, 3rd edition, chapter 7 for more
discussion on action angle variable.
[3.5] see Sec. 2.8 or S.Y.Lee, ”Accelerator Physics”,
Sec. II.4 ,Chapter 2 for detail analysis.
[3.6] see S.Y.Lee, ”Accelerator Physics”, Eq. (2.384),
Sec.VII.1.C, p204 for 3rd order resonance analysis.
[3.7] Laskar, J., Frequency map analysis and particle
accelerator, PAC’03, Portland (2003).

Chapter 4

[4.1] SRRC-MM-IM-92-02, NSRRC internal report
[4.2] SRRC-BD-IM-91-16, NSRRC internal report
[4.3] for the definition of Touschek life time, see
S.Y.Lee, ”Accelerator Physics”,Sec.II.8B,Chapter 4
[4.4] Note: TRACY-II first calculates the momentum
acceptance [4.5] then the Touschek life time
[4.5] Momentum acceptance and Touschek lifetime,04/08/2008,
SLS Note 18/97
[4.6] see p37,SyncLight-databook383670.pdf

Chapter 5

[5.1] see S.Y.Lee, ”Accelerator Physics”, Sec. III.3.B,
Chapter 4
[5.2] see S.Y.Lee, ”Accelerator Physics”, Sec. VIII,
Chapter 2 or reference [5.3]
[5.3] A.W.Chao, ”Physics of Collective Beam Instabilities
in High Energy Accelerators”