近年來因應在各領域的應用需求，如:極紫外光蝕刻(lithography)、結構生物學、時間解析科學等等，使短波長高增益自由電子雷射日益受到重視。高增益自由電子雷射是利用高電荷密度的電子束在聚頻磁鐵之中與輻射場交互作用而將電子束能量轉換成電磁波能量。其中對電子束的高峰值電流、短束團長度、發射度、能散等條件有嚴格的要求。但由於一般低發射度電子源系統所能提供的束流強度尚未達到要求，因而需要進一步對電子束的長度進行壓縮，由於束團壓縮的過程中受射頻加速場的曲率(rf curvature)等非線性效應所影響使得束流壓縮器效能不佳。為修正此一缺點，最常見的方式為諧波補償方案(harmonic compensation)。此方法是在將電子束團進行壓縮以前先進行能量啁啾修正。但由於需要成本昂貴的諧波直線加速器系統，因此較不具成本效益。本論文將探討一種具成本效益、利用非線性電子光學所設計稱為S型彎道束團壓縮器。
由國家同步輻射中心所設計使用於極紫外光自由電子雷射系統上的S型彎道束團壓縮器就是利用電子光學元件的非線性的特性進行非線性效應之補償。但由於電子源系統的射頻操作相位所產生不同程度的能量啁啾對束團壓縮器的性能造成極大的影響。因此，本研究主要為探討在不同光陰極注射器系統中之線性加速器L0加速相位中對束團壓縮之影響進行分析研究。

In recent years, in response to the application requirements in various fields, such as extreme ultraviolet lithography (EUVL), structural biology, time-resolved scientific research, etc., short-wavelength high-gain free electron lasers (FELs) have drawn much attention, FEL of this kind employs electron beam with high charge density to interact with the radiation field in the undulator such that the electron beam energy can be transferred into electromagnetic wave energy. However, strict requirements for high peak current, short bunch length, low-emittance, and small energy spread of the electron beam have to be fulfilled. Since the beam intensity provided by common low-emittance electron sources are still far below the specification, it is therefore necessary to further compress the length of the electron beam to achieve high current.
Nonlinear effects such as rf curvature make the beam compression inefficient. In order to correct this deficiency, the most common method is the harmonic compensation scheme, in which the energy chirp correction is performed before sending the beam through the dispersive beamline where the beam is being compressed. However, this scheme requires installation of an expensive harmonic linear accelerator system. In this study, a cost-effective bunch compressor called ‘‘double dogleg’’ using nonlinear electron optics will be discussed.
This double dogleg bunch compressor, is designed at National Synchrotron Radiation Research Center (NSRRC), It used as a bunch compressor for the proposed NSRRC EUV free electron laser. The compressor uses the nonlinear characteristics of optical components such as quadrupoles, sextupoles etc. to compensate for nonlinear effects. However, the energy chirp of beams generated by the photoinjector when operated at different rf phases have a great impact on the performance of the bunch compressor. Therefore, this study is mainly focus on the analysis of the effect of operation phase of photoinjector booster linac on bunch compression.

摘要 i
Abstract ii
目錄 iv
圖目錄 vii
表目錄 xi
第一章 簡介 1
1.1 研究背景 1
1.2 研究目的與方法 5
第二章 基本原理 6
2.1 高增益自由電子雷射原理 7
2.1.1 高增益自由電子雷射主要參數 7
2.1.2 高增益自由電子雷射相關參數修正方法 9
2.2 束團壓縮非線性動力學 10
2.2.1 非線性能量啁啾 10
2.2.2 束團壓縮器原理 11
2.3 C型彎道束團壓縮器與諧波補償方案 14
2.3.1 C型彎道束團壓縮器 14
2.3.2 諧波補償方案 15
2.4 S型彎道束團壓縮器操作原理 19
2.4.1 非線性效應之補償 19
2.4.2 二階色散係數調整 20
第三章 國家同步輻射中心之極紫外光自由電子雷射系統設計 22
3.1 EUV-FEL光束線設計 22
3.2 NSRRC EUV-FEL束團壓縮器設計 24
3.2.1 NSRRC光陰極電子槍設計及模擬 24
3.2.2 NSRRC S型彎道束團壓縮器設計及模擬 29
第四章 模擬結果 32
4.1 光陰極注射器系統追蹤模擬 32
4.1.1 光陰極注射器系統參數選擇 32
4.1.2 光陰極注射器系統束團追蹤模擬結果 35
4.2 S型彎道束團壓縮器模擬結果 39
4.2.1 能量啁啾計算 39
4.2.2 補償所需色散係數計算 41
4.2.3 補償所需參數匹配 42
4.2.4 ELEGANT追蹤模擬結果 45
4.3 光陰極注射器系統中之線性加速器L0操作相位對S型彎道束團壓縮器之影響 51
4.3.1 光陰極注射器系統出口之電子束團參數擬合與計算 51
4.3.2 光學元件操作參數匹配及影響分析 54
4.3.3 不同注射器操作相位對最終束團之影響分析 58
第五章 結論與未來工作 67
參考文獻 69
附錄 71
A 研究使用軟體介紹 71
A-1 ASTRA (電子槍追蹤優化) 71
A-2 ELEGANT (束團壓縮器電子追蹤) 74
A-3 MAD (束團壓縮器結構參數設計) 76
B 模擬輸入檔 77
B-1 ASTRA 77
B-2 MAD 80
B-3 ELEGANT 83

[1] J. Madey, "Stimulated Emission of Bremsstrahlung in a Periodic Magnetic Field," Journal of Applied Physics, vol. 42, no. 5, pp. 1906-1913, 1971.
[2] P. Emma et al., "First lasing and operation of an ångstrom-wavelength free-electron laser," Nature Photonics, vol. 4, pp. 641-647, 2010.
[3] F. Stephan et al., "High Brightness Photo Injectors for Brilliant Light Sources," Synchrotron Light Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation and Science Applications, pp. 561-604, 2016.
[4] L. W. K. et al., "Emittance control and RF bunch compression in the NSRRC photoinjector," Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 637, no. 1, Supplement, pp. S91-S94, 2011.
[5] F. Stulle et al., "Designing a bunch compressor chicane for a multi-TeV linear collider," Physical Review Special Topics - Accelerators and Beams, vol. 10, no. 3, 2007.
[6] P. Emma, "X-Band RF Harmonic Compensation for Linear Bunch Compression in the LCLS," Office of Scientific and Technical Information (OSTI), 2005.
[7] S. Boutet et al., "The Coherent X-ray Imaging (CXI) instrument at the Linac Coherent Light Source (LCLS)," NEW JOURNAL OF PHYSICS, vol. 12, MAR 31 2010.
[8] D. Pile, "X-RAYS First light from SACLA," NATURE PHOTONICS, vol. 5, no. 8, pp. 456-457, AUG 2011.
[9] I. S. Ko et al., "Construction and Commissioning of PAL-XFEL Facility," APPLIED SCIENCES-BASEL, vol. 7, no. 5, MAY 2017.
[10] T. Tschentscher et al., "Photon Beam Transport and Scientific Instruments at the European XFEL," APPLIED SCIENCES-BASEL, vol. 7, no. 6, JUN 2017.
[11] C. J. Milne et al., "SwissFEL: The Swiss X-ray Free Electron Laser," APPLIED SCIENCES-BASEL, vol. 7, no. 7, JUL 2017.
[12] A. Halavanau et al., "Very high brightness and power LCLS-II hard X-ray pulses," Journal of Synchrotron Radiation, vol. 26, pp. 635-646, May 2019.
[13] N. Huang et al., "Features and futures of X-ray free-electron lasers," The Innovation, vol. 2, no. 2, p. 100097, 2021.
[14] P. H. Williams et al., "Arclike variable bunch compressors," Physical Review Accelerators and Beams, vol. 23, no. 10, p. 100701, 10/13/ 2020.
[15] Y. Sun et al., "X-band rf driven free electron laser driver with optics linearization," Physical Review Special Topics - Accelerators and Beams, vol. 17, no. 11, p. 110703, 2014.
[16] 邱琬婷, "用於高重複率EUV自由電子雷射中之2998 MHz雷射激發光陰極電子槍之設計研究," 國立清華大學, 新竹市, 2019.
[17] 謝景安, "雷射激發光陰極電子槍直線加速器之束流動力學研究," 碩士, 物理學系, 國立清華大學, 新竹市, 2020.
[18] W. Lau et al., "DESIGN OF A DOGLEG BUNCH COMPRESSOR WITH TUNABLE FIRST-ORDER LONGITUDINAL DISPERSION," 2018.
[19] N. Sudar et al., "Octupole based current horn suppression in multistage bunch compression with emittance growth correction," Physical Review Accelerators and Beams, vol. 23, no. 11, p. 112802, 2020.
[20] Z. Zhu et al., "Inhibition of current-spike formation based on longitudinal phase space manipulation for high-repetition-rate X-ray FEL," Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 1026, p. 166172, 2022/03/01/ 2022.
[21] U. van Rienen et al., "3D SPACE CHARGE CALCULATIONS FOR BUNCHES IN THE TRACKING CODE ASTRA," Physics, pp. 2203-2205, 01/01 2006.
[22] G. Pöplau et al., THE PERFORMANCE OF 3D SPACE CHARGE MODELS FOR HIGH BRIGHTNESS ELECTRON BUNCHES. 2008.
[23] K.-J. Kim, "Rf and space-charge effects in laser-driven rf electron guns," Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 275, no. 2, pp. 201-218, 1989/02/15/ 1989.
[24] A. Xiao et al., "Direct space-charge calculation in elegant and its application to the ilc damping ring," 2007 IEEE Particle Accelerator Conference (PAC), pp. 3456-3458, 2007.