ADS强流质子加速器低β超导HWR腔结构稳定性分析与调谐研究
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摘要
超导半波长谐振腔（half-wave resonator, HWR）在二十世纪九十年代由美国阿贡国家实验室首次研制成功。超导HWR腔具有结构紧凑，无横向束流偏转效应等优点，已经逐渐发展成为中低能直线加速器的主要加速结构之一。它是基于TEM电磁场模式的二分之一波长的同轴型加速结构。中国科学院先导科技专项ADS嬗变系统计划研制流强达到10mA，能量达到50MeV的超导直线质子加速器，其直线注入器II中2.1~10MeV加速器采用两种不同β的超导HWR腔。对于超导腔而言，Q值一般较高，论文研究的超导HWR腔工作在162.5MHz，有载品质因数较高，工作带宽窄，通常仅有几十赫兹，因此超导腔工作的稳定性是国际上的难点课题。
本论文研究了用于直线注入器II中频率为162.5MHz，最优β为0.10的Squeezed型HWR腔的结构稳定性。基于有限元法的多物理场耦合分析计算了HWR腔的各失谐因素，包括氦压敏感度系数计算，洛仑兹失谐效应分析，颤噪效应分析，以及腔体降温频漂等。论文引入弹性边界作为超导腔约束条件，提高了仿真计算与超导腔垂直测试、水平测试的结果的符合程度。此外，根据失谐分析结果，对Squeezed型HWR腔体进行了结构上的优化设计，提出了有效提高腔体结构稳定性的设计方案，确保超导HWR腔运行的稳定。
直线注入器II5~10MeV超导段拟采用频率162.5MHz，最优β为0.151的Taper型HWR腔。论文分析腔体的电场和磁场分别对氦压敏感度系数K P的贡献量。鉴于HWR腔体的电磁场模式和Taper型腔结构的特殊性，提出一种氦压敏感度系数为零的设计方法。通过对提高腔体磁场区的结构稳定性和降低腔体电场区的结构稳定性两方面的深入探讨，最终确定了腔体氦压敏感度系数为零的设计方案。
论文研究了低β超导HWR腔频率调谐方法。首先从理论上分析HWR腔体的调谐参数，包括腔体的调谐敏感度、调谐范围、调谐精度、幅值相位稳定度要求等。根据超导HWR腔对频率调谐的要求，结合HWR超导腔的结构特点，设计并研制了一套由步进电机驱动的慢调谐装置，通过超导HWR腔常温测试和水平测试结果表明调谐器能够稳定运行。此外，论文提出常温运行下和低温运行下的piezo快调谐器两种设计方案，提高了调谐器的调谐性能，抑制回程滞后等现象，实现对氦压波动、洛仑兹失谐等因素引起超导HWR腔频漂漂移的快速响应与调整。
The superconducting (SC) half-wave resonator (HWR) was firstly proposed andfabricated at Argonne National Laboratory in1990s. It has a compact structure. Themain advantage of HWR cavity is that there is no vertical beam steering effect becauseof the geometry symmetry in vertical direction. Considering the advantage, it has beendeveloped as one of the primary choice of accelerating structures in low and medialbeta sections. The SC HWR is a coaxial type element based on the TEM mode. Thesuperconducting linac of China ADS (Accelerator Driven sub-critical System) is about10mA of current and50MeV of energy. Two different types of superconductingHWR are employed by injector-II in ADS project, which is in the charge of Institute ofModern Physics. However, because the load quality factor of SC cavity usually isextremely higher than that of room temperature cavity, its bandwidth is quite narrow(generally scores of Hz). Furthermore, the resonant frequency of the SC HWR ishighly sensitive to mechanical deformations. Therefore, the study on mechanicalstability of a superconducting cavity is an important and difficult issue around theworld.
Mechanical stability of the HWR (optimum beta=0.10and the frequency162.5MHz) is studied in the thesis. Mainly, the multi-physics coupled analysis basedon the finite element method is used to calculate the detuning effects of the HWR. Generally, it includes the helium pressure coefficient, the Lorentz force detuningcoefficient, microphonics and the cooling down. A novel analysis method of the elasticboundary condition effect is adopted during the cavity detuning study, which makes asuperposition between the simulation and the measurement. According to thesimulation results, the structure optimization for a squeezed HWR cavity has beenfinished and a new design for higher mechanical stability is obtained. In addition, theinitial test results show that the improvement of the cavity is highly effective.
Based on the design of a162.5MHz and beta=0.15taper HWR, the contributionof electric field and magnet field to the helium pressure coefficient are analyzedrespectively. Then a new conceptual design, which the helium pressure coefficientequals zero, is introduced in the thesis.
The frequency tuning for the low beta HWR is also focused by the thesis. Firstly,the parameters of the tuning are all introduced such as frequency sensitivity, range,resolution and the stability of amplitude and phase and so on. A slow tuner driven bystep motor is designed based on the studies above. The results of the measurementduring room temperature and horizontal test prove the tuner can operate stably. Animprovement plan for the mechanical tuner is proposed after many tests. Finally, theHWR can operate at the correct frequency and suitable accelerating voltage range withthe slow tuner and fast tuner, which are controlled by low level RF. Also two kinds ofpiezo tuner design, operating at room temperature and low temperature, are achieved.The fast tuning systems, which meet the requirement of fast response, improve theperformance of the tuner and reduce the backlash effect.
本论文研究了用于直线注入器II中频率为162.5MHz，最优β为0.10的Squeezed型HWR腔的结构稳定性。基于有限元法的多物理场耦合分析计算了HWR腔的各失谐因素，包括氦压敏感度系数计算，洛仑兹失谐效应分析，颤噪效应分析，以及腔体降温频漂等。论文引入弹性边界作为超导腔约束条件，提高了仿真计算与超导腔垂直测试、水平测试的结果的符合程度。此外，根据失谐分析结果，对Squeezed型HWR腔体进行了结构上的优化设计，提出了有效提高腔体结构稳定性的设计方案，确保超导HWR腔运行的稳定。
直线注入器II5~10MeV超导段拟采用频率162.5MHz，最优β为0.151的Taper型HWR腔。论文分析腔体的电场和磁场分别对氦压敏感度系数K P的贡献量。鉴于HWR腔体的电磁场模式和Taper型腔结构的特殊性，提出一种氦压敏感度系数为零的设计方法。通过对提高腔体磁场区的结构稳定性和降低腔体电场区的结构稳定性两方面的深入探讨，最终确定了腔体氦压敏感度系数为零的设计方案。
论文研究了低β超导HWR腔频率调谐方法。首先从理论上分析HWR腔体的调谐参数，包括腔体的调谐敏感度、调谐范围、调谐精度、幅值相位稳定度要求等。根据超导HWR腔对频率调谐的要求，结合HWR超导腔的结构特点，设计并研制了一套由步进电机驱动的慢调谐装置，通过超导HWR腔常温测试和水平测试结果表明调谐器能够稳定运行。此外，论文提出常温运行下和低温运行下的piezo快调谐器两种设计方案，提高了调谐器的调谐性能，抑制回程滞后等现象，实现对氦压波动、洛仑兹失谐等因素引起超导HWR腔频漂漂移的快速响应与调整。
The superconducting (SC) half-wave resonator (HWR) was firstly proposed andfabricated at Argonne National Laboratory in1990s. It has a compact structure. Themain advantage of HWR cavity is that there is no vertical beam steering effect becauseof the geometry symmetry in vertical direction. Considering the advantage, it has beendeveloped as one of the primary choice of accelerating structures in low and medialbeta sections. The SC HWR is a coaxial type element based on the TEM mode. Thesuperconducting linac of China ADS (Accelerator Driven sub-critical System) is about10mA of current and50MeV of energy. Two different types of superconductingHWR are employed by injector-II in ADS project, which is in the charge of Institute ofModern Physics. However, because the load quality factor of SC cavity usually isextremely higher than that of room temperature cavity, its bandwidth is quite narrow(generally scores of Hz). Furthermore, the resonant frequency of the SC HWR ishighly sensitive to mechanical deformations. Therefore, the study on mechanicalstability of a superconducting cavity is an important and difficult issue around theworld.
Mechanical stability of the HWR (optimum beta=0.10and the frequency162.5MHz) is studied in the thesis. Mainly, the multi-physics coupled analysis basedon the finite element method is used to calculate the detuning effects of the HWR. Generally, it includes the helium pressure coefficient, the Lorentz force detuningcoefficient, microphonics and the cooling down. A novel analysis method of the elasticboundary condition effect is adopted during the cavity detuning study, which makes asuperposition between the simulation and the measurement. According to thesimulation results, the structure optimization for a squeezed HWR cavity has beenfinished and a new design for higher mechanical stability is obtained. In addition, theinitial test results show that the improvement of the cavity is highly effective.
Based on the design of a162.5MHz and beta=0.15taper HWR, the contributionof electric field and magnet field to the helium pressure coefficient are analyzedrespectively. Then a new conceptual design, which the helium pressure coefficientequals zero, is introduced in the thesis.
The frequency tuning for the low beta HWR is also focused by the thesis. Firstly,the parameters of the tuning are all introduced such as frequency sensitivity, range,resolution and the stability of amplitude and phase and so on. A slow tuner driven bystep motor is designed based on the studies above. The results of the measurementduring room temperature and horizontal test prove the tuner can operate stably. Animprovement plan for the mechanical tuner is proposed after many tests. Finally, theHWR can operate at the correct frequency and suitable accelerating voltage range withthe slow tuner and fast tuner, which are controlled by low level RF. Also two kinds ofpiezo tuner design, operating at room temperature and low temperature, are achieved.The fast tuning systems, which meet the requirement of fast response, improve theperformance of the tuner and reduce the backlash effect.
引文
[1] H. A t Abderrahimh, J. Galambosd, Y. Gohara and et al. Accelerator and TargetTechnology for Accelerator Driven Transmutation and Energy Production.http://staff.ustc.edu.cn/~qunwang/temp/ADS_White_Paper_final.pdf
[2] http://cerncourier.com/cws/article/cern/47513
[3]傅世年，强流质子加速器物理与技术关键问题，中国核科技报告，2001.06.15
[4]詹文龙，徐瑚珊，未来先进核裂变能——ADS嬗变系统，中国科学院院刊，第27卷第3期，2012，p.365-381
[5] P. Bosland, Proceedings of superconducting RF2009, Berlin, Germany,902-906
[6] N. Bazin, P. Bosland, S. Chel and et al. Proceedings of LINAC2012, Tel-Aviv,Israel.351-353
[7] A. Mosnier, P.Y. Beauvais, B. Branas and et al. Proceedings of IPAC’10, Kyoto,Japan.588-590
[8] F. Orsini, N. Bazin, P. Bosland and et al. Proceedings of SRF2011, Chicago, ILUSA.667-673
[9] A. Mosnier, P. Cara, R. Heidinger. Proceedings of IPAC2012, New Orleans,Louisiana, USA.3910-3912
[10]I. Mardor, D. Berkovits, I. Gertz and et al. Proceedings of SRF2009, Berlin,Germany.74-80
[11]A. Nagler, I. Mardor, D. Berkovits and et al. Proceedings of LINAC2006,Knoxville, Tennessee USA.168-170
[12] L. Weissman, D. Berkovits, A. Arenshtam and et al. Proceedings of RUPAC2012,Saint|-|Petersburg, Russia.103-105
[13] A. Shor, D. Berkovits, I. Fishman. and et al. Proceedings of LINAC2012,Tel-Aviv, Israel.1038-1040.
[14] L. Weissman, D. Berkovits, I. Eliyahu and et al. Proceedings of LinearAccelerator Conference LINAC2010, Tsukuba, Japan.679-683.
[15] B. Mustapha, P.N. Ostroumov and Z.A. Conway. Proceedings of IPAC2012,New Orleans, Louisiana, USA.2289-2291.
[16] S. D. Holmes, M. Kaducak, R. Kephart and et al. Proceedings of PAC2013,Pasadena, CA USA.315-317.
[17] Robert Kephart. Proceedings of HB2012, Beijing, China.541-545.
[18] Z.A. Conway, R.L. Fischer, M.J. Kedzie and et al. Proceedings of IPAC2012,New Orleans, Louisiana, USA.3865-3867.
[19] Robin FERDINAND, Patrick BERTRAND. Proceedings of Linear AcceleratorConference LINAC2010, Tsukuba, Japan.16-20.
[20] G. Olry, D. Longuevergne, H. Saugnac and et al. Proceedings of SRF2009,Berlin, Germany.495-501.
[21] H. Saugnac, C. Commeaux, C. Joly and et al. Proceedings of LINAC08, Victoria,BC, Canada.792-794.
[22] G. Olry, J-L. Biarrotte, S. Blivet and et al. Proceedings of the12th InternationalWorkshop on RF Superconductivity, Cornell University, Ithaca, New York, USA.323-327.
[23] E. Petit. Proceedings of IPAC2011, San Sebastián, Spain.1912-1916.
[24] J.L. Biarrotte, A.C. Mueller. Proceedings of Linear Accelerator ConferenceLINAC2010, Tsukuba, Japan.440-442.
[25] H. Podlech, M. Amberg, H. Klein and et al. Proceedings of IPAC2011, SanSebastián, Spain.2574-2576.
[26] D. Vandeplassche. Proceedings of IPAC2011, San Sebastián, Spain.2718-2720.
[27] WANG Zhi-Jun, HE Yuan, LIU Yong and et al. The design simulation of thesuperconducting section in the ADS injectorII. Chinese physics C201236(3):256-260
[28] WANG Zhi-Jun, HE Yuan, WANG Wang-Sheng and et al. End-to-end simulationof the C-ADS Injector Ⅱ with a3-D field map.201337(4):047003
[29] Y. He, Z.J. Wang, B. Zhang and et al. Progress of One of10MeVSuperconducting Proton Linear Injectors for C-ADS. Proceedings of LINAC2012,Tel-Aviv, Israel.909-911
[30] Y. He, Z.J. Wang, Y. Liu and et al. The Conceptual Design of Injector II of ADSin China. Proceedings of IPAC2011, San Sebastián, Spain.2613-2615
[31] J. R. Delayen, C. L. Bohn and C. T. Roche. IEEE Trans.Magn.1991,27:1924.
[32] A. Mosnier. Proceedings of LINAC2012, Tel-Aviv, Israel.407-411.
[33] M. Pekeler, S. Bauer, K. Dunkel. Proceedings of the12th International Workshopon RF Superconductivity, Cornell University, Ithaca, New York, USA.331-333.
[34] R. Stassen, W. Br utigam, R. Eichhorn. and et al. Proceedings of the11thWorkshop on RF Superconductivity, Lübeck/Travemünder, Germany.52-56.
[35] P.N. Ostroumov, B. Mustapha, Z.A. Conway and et al. Proceedings of IPAC2012,New Orleans, Louisiana, USA.2295-2297.
[36] P. N. Ostroumov and K.W. Shepard. Phys. Rev. ST Accel. Beams4,2001,110101.
[37] A.Palczewski, H.Tian,and R.L.Geng，Optimizing Centrifugal Barrel Polishingfor Mirror Finish SRFCavity and Rf Tests at Jefferson Lab, IPAC2012, p2435.
[38] K. Watanabe, H. Hayano，Cavity Inspection and Repair Techniques, SRF2011，p598-590.
[39] E. Zaplatin, P. Bosland, Ph. Bredy and et al. Proceedings of PAC09, Vancouver,BC, Canada.981-983
[40] A. Perry, D. Berkovits, I. Gertz. Proceedings of SRF2009, Berlin, Germany.263-267.
[41] E. Zaplatin, R. Eichhorn, F.M.Esser and et al. Proceedings of the11th Workshopon RF Superconductivity, Lübeck/Travemünder, Germany.437-441.
[42]李永明博士论文.射频超导加速腔性能相关物理与技术问题研究.北京：北京大学，2013.
[43]K. Schulze, Proceedings of the International Symposium, edited by H. Stuart, SanFrancsico, The Metallurgical Society of AIME, p163(981).
[44]G. Ciovati， HIGH FIELD Q-SLOPE AND THE BAKING EFFECT，SRF2009，Berlin, Germany，p88-94.
[45]J. Knobloch, R. L. Geng, M. Liepe and et al. Proceedings of SRF1999, Santa Fe,New Mexico, USA.77-91.
[46] J. Wilks. The Properties of Liquid and Solid Helium. Oxford: ClarendonPress.1967.
[47] D. Berkovits, L. Weissman, A. Arenshtam and et al. Operational Experience andFuture Goals of the SARAF Proton/Deuteron Linac. Proceedings of LINAC2012,Tel-Aviv, Israel.100-104.
[48] P.N. Ostroumov, Z.A. Conway, M.P. Kelly and et al. SARAF Phase II P/D40MeV Linac Design Studies. Proceedings of LINAC2012, Tel-Aviv, Israel.1064-1068.
[49] Axel Neumann. Compensating Microphonics in SRF Cavities to Ensure BeamStability for Future Free-Electron-Lasers. PH.D thesis. Humboldt-Universit t zuBerlin.2008.
[50] http://www.bnl.gov/magnets/Staff/Gupta/cryogenic-data-handbook/Section9.pdf
[51] Chao A W.Physics of collective beam instabilities in high energy accelerators,John Wiley&Sons Inc.,1993
[52] Padamsee H.,Knobloch J.,Hays T. RF Superconductivity for Accelerators.Ithaca,New York: John Wiley&Sons, Inc.,1998.
[53]刘乃泉，加速器理论，清华大学出版社.2004年第3版.
[54] David M.Pozar. Microwave Engineering Third Edition. New York: John Wiley&Sons,2006.259-260.
[55]模态分析理论与应用.上海交通大学出版社，2000年.
[56]弹性和塑形力学中的有限单元法.机械工业出版社.1981年.
[57]电磁场有限元方法.西安电子科技大学出版社.1998年.
[58]王勖成编著.有限单元法.清华大学出版社.2003年第一版.
[59]梁醒培，王辉编著.应用有限元分析.清华大学出版社.2010年第1版.
[60]梁醒培，王辉编著.基于有限元法的结构优化设计.清华大学出版社.2010年第1版.
[61]杨柳博士论文，用于高平均流强质子加速的超导QWR腔研究.北京：北京大学，2013.
[62] Weiming Yue, Yuan He, S.H.Zhang et al. Proc. of the26th LINAC. Tel-Aviv,Israel2012,600
[63] ANSYS, Inc., Canonsburg, Pennsylvania, USA. Www. ansys.com
[64] Yuan HE. Limits for peak fields and gradient in low-beta cavities for highintensity projects. TTC Meeting report. DESY Hamburg. March24-27,2014
[65]张生虎，HWR水平测试总结，近代物理所直线加速器室内部报告.
[66]高郑，HWR颤噪效应测试报告，近代物理所直线加速器室内部报告.
[67] Sam Posen and Matthias Liepe. PHYSICAL REVIEW SPECIAL TOPICS-ACCELERATORS AND BEAMS15,022002(2012)
[68]苟文选主编，材料力学I.科学出版社.2010年第二版.
[69] Y. HE, W.M. YUE,ect. SRF CAVITIES FOR ADS PROJECT IN CHINA,Proceedings of SRF2013, Paris, France
[70]岳伟明，Taper HWR EM design.近代物理所直线加速器室内部报告.
[71]许哲，CSR实验环高频系统的研制.中科院近物所博士学位论文.2008
[72]清华大学通信教研组编.高频电路（上）（下）.北京：人民邮电出版社，1979.
[73] M. Aberg, M.L. Ainalem, R. Ainsworth and et al. ESS Technical Design Report.2012. release1.
[74] Yuriy Pischalnikov. Overview of Slow and Fast Tuners for SuperconductingCavities.LLRF2011International Workshop, DESY, Germany, October17-20,2011
[75] S. Simrock. Review of Slow and Fast Tuners.12th International Workshop onSRF Superconductivity, Cornell University, Ithaca, New York,2005
[76] D. Longuevergne, S. Blivet, G. Martinet and et al. Proceedings of LINAC2008,Victoria, BC, Canada.789-791.
[2] http://cerncourier.com/cws/article/cern/47513
[3]傅世年，强流质子加速器物理与技术关键问题，中国核科技报告，2001.06.15
[4]詹文龙，徐瑚珊，未来先进核裂变能——ADS嬗变系统，中国科学院院刊，第27卷第3期，2012，p.365-381
[5] P. Bosland, Proceedings of superconducting RF2009, Berlin, Germany,902-906
[6] N. Bazin, P. Bosland, S. Chel and et al. Proceedings of LINAC2012, Tel-Aviv,Israel.351-353
[7] A. Mosnier, P.Y. Beauvais, B. Branas and et al. Proceedings of IPAC’10, Kyoto,Japan.588-590
[8] F. Orsini, N. Bazin, P. Bosland and et al. Proceedings of SRF2011, Chicago, ILUSA.667-673
[9] A. Mosnier, P. Cara, R. Heidinger. Proceedings of IPAC2012, New Orleans,Louisiana, USA.3910-3912
[10]I. Mardor, D. Berkovits, I. Gertz and et al. Proceedings of SRF2009, Berlin,Germany.74-80
[11]A. Nagler, I. Mardor, D. Berkovits and et al. Proceedings of LINAC2006,Knoxville, Tennessee USA.168-170
[12] L. Weissman, D. Berkovits, A. Arenshtam and et al. Proceedings of RUPAC2012,Saint|-|Petersburg, Russia.103-105
[13] A. Shor, D. Berkovits, I. Fishman. and et al. Proceedings of LINAC2012,Tel-Aviv, Israel.1038-1040.
[14] L. Weissman, D. Berkovits, I. Eliyahu and et al. Proceedings of LinearAccelerator Conference LINAC2010, Tsukuba, Japan.679-683.
[15] B. Mustapha, P.N. Ostroumov and Z.A. Conway. Proceedings of IPAC2012,New Orleans, Louisiana, USA.2289-2291.
[16] S. D. Holmes, M. Kaducak, R. Kephart and et al. Proceedings of PAC2013,Pasadena, CA USA.315-317.
[17] Robert Kephart. Proceedings of HB2012, Beijing, China.541-545.
[18] Z.A. Conway, R.L. Fischer, M.J. Kedzie and et al. Proceedings of IPAC2012,New Orleans, Louisiana, USA.3865-3867.
[19] Robin FERDINAND, Patrick BERTRAND. Proceedings of Linear AcceleratorConference LINAC2010, Tsukuba, Japan.16-20.
[20] G. Olry, D. Longuevergne, H. Saugnac and et al. Proceedings of SRF2009,Berlin, Germany.495-501.
[21] H. Saugnac, C. Commeaux, C. Joly and et al. Proceedings of LINAC08, Victoria,BC, Canada.792-794.
[22] G. Olry, J-L. Biarrotte, S. Blivet and et al. Proceedings of the12th InternationalWorkshop on RF Superconductivity, Cornell University, Ithaca, New York, USA.323-327.
[23] E. Petit. Proceedings of IPAC2011, San Sebastián, Spain.1912-1916.
[24] J.L. Biarrotte, A.C. Mueller. Proceedings of Linear Accelerator ConferenceLINAC2010, Tsukuba, Japan.440-442.
[25] H. Podlech, M. Amberg, H. Klein and et al. Proceedings of IPAC2011, SanSebastián, Spain.2574-2576.
[26] D. Vandeplassche. Proceedings of IPAC2011, San Sebastián, Spain.2718-2720.
[27] WANG Zhi-Jun, HE Yuan, LIU Yong and et al. The design simulation of thesuperconducting section in the ADS injectorII. Chinese physics C201236(3):256-260
[28] WANG Zhi-Jun, HE Yuan, WANG Wang-Sheng and et al. End-to-end simulationof the C-ADS Injector Ⅱ with a3-D field map.201337(4):047003
[29] Y. He, Z.J. Wang, B. Zhang and et al. Progress of One of10MeVSuperconducting Proton Linear Injectors for C-ADS. Proceedings of LINAC2012,Tel-Aviv, Israel.909-911
[30] Y. He, Z.J. Wang, Y. Liu and et al. The Conceptual Design of Injector II of ADSin China. Proceedings of IPAC2011, San Sebastián, Spain.2613-2615
[31] J. R. Delayen, C. L. Bohn and C. T. Roche. IEEE Trans.Magn.1991,27:1924.
[32] A. Mosnier. Proceedings of LINAC2012, Tel-Aviv, Israel.407-411.
[33] M. Pekeler, S. Bauer, K. Dunkel. Proceedings of the12th International Workshopon RF Superconductivity, Cornell University, Ithaca, New York, USA.331-333.
[34] R. Stassen, W. Br utigam, R. Eichhorn. and et al. Proceedings of the11thWorkshop on RF Superconductivity, Lübeck/Travemünder, Germany.52-56.
[35] P.N. Ostroumov, B. Mustapha, Z.A. Conway and et al. Proceedings of IPAC2012,New Orleans, Louisiana, USA.2295-2297.
[36] P. N. Ostroumov and K.W. Shepard. Phys. Rev. ST Accel. Beams4,2001,110101.
[37] A.Palczewski, H.Tian,and R.L.Geng，Optimizing Centrifugal Barrel Polishingfor Mirror Finish SRFCavity and Rf Tests at Jefferson Lab, IPAC2012, p2435.
[38] K. Watanabe, H. Hayano，Cavity Inspection and Repair Techniques, SRF2011，p598-590.
[39] E. Zaplatin, P. Bosland, Ph. Bredy and et al. Proceedings of PAC09, Vancouver,BC, Canada.981-983
[40] A. Perry, D. Berkovits, I. Gertz. Proceedings of SRF2009, Berlin, Germany.263-267.
[41] E. Zaplatin, R. Eichhorn, F.M.Esser and et al. Proceedings of the11th Workshopon RF Superconductivity, Lübeck/Travemünder, Germany.437-441.
[42]李永明博士论文.射频超导加速腔性能相关物理与技术问题研究.北京：北京大学，2013.
[43]K. Schulze, Proceedings of the International Symposium, edited by H. Stuart, SanFrancsico, The Metallurgical Society of AIME, p163(981).
[44]G. Ciovati， HIGH FIELD Q-SLOPE AND THE BAKING EFFECT，SRF2009，Berlin, Germany，p88-94.
[45]J. Knobloch, R. L. Geng, M. Liepe and et al. Proceedings of SRF1999, Santa Fe,New Mexico, USA.77-91.
[46] J. Wilks. The Properties of Liquid and Solid Helium. Oxford: ClarendonPress.1967.
[47] D. Berkovits, L. Weissman, A. Arenshtam and et al. Operational Experience andFuture Goals of the SARAF Proton/Deuteron Linac. Proceedings of LINAC2012,Tel-Aviv, Israel.100-104.
[48] P.N. Ostroumov, Z.A. Conway, M.P. Kelly and et al. SARAF Phase II P/D40MeV Linac Design Studies. Proceedings of LINAC2012, Tel-Aviv, Israel.1064-1068.
[49] Axel Neumann. Compensating Microphonics in SRF Cavities to Ensure BeamStability for Future Free-Electron-Lasers. PH.D thesis. Humboldt-Universit t zuBerlin.2008.
[50] http://www.bnl.gov/magnets/Staff/Gupta/cryogenic-data-handbook/Section9.pdf
[51] Chao A W.Physics of collective beam instabilities in high energy accelerators,John Wiley&Sons Inc.,1993
[52] Padamsee H.,Knobloch J.,Hays T. RF Superconductivity for Accelerators.Ithaca,New York: John Wiley&Sons, Inc.,1998.
[53]刘乃泉，加速器理论，清华大学出版社.2004年第3版.
[54] David M.Pozar. Microwave Engineering Third Edition. New York: John Wiley&Sons,2006.259-260.
[55]模态分析理论与应用.上海交通大学出版社，2000年.
[56]弹性和塑形力学中的有限单元法.机械工业出版社.1981年.
[57]电磁场有限元方法.西安电子科技大学出版社.1998年.
[58]王勖成编著.有限单元法.清华大学出版社.2003年第一版.
[59]梁醒培，王辉编著.应用有限元分析.清华大学出版社.2010年第1版.
[60]梁醒培，王辉编著.基于有限元法的结构优化设计.清华大学出版社.2010年第1版.
[61]杨柳博士论文，用于高平均流强质子加速的超导QWR腔研究.北京：北京大学，2013.
[62] Weiming Yue, Yuan He, S.H.Zhang et al. Proc. of the26th LINAC. Tel-Aviv,Israel2012,600
[63] ANSYS, Inc., Canonsburg, Pennsylvania, USA. Www. ansys.com
[64] Yuan HE. Limits for peak fields and gradient in low-beta cavities for highintensity projects. TTC Meeting report. DESY Hamburg. March24-27,2014
[65]张生虎，HWR水平测试总结，近代物理所直线加速器室内部报告.
[66]高郑，HWR颤噪效应测试报告，近代物理所直线加速器室内部报告.
[67] Sam Posen and Matthias Liepe. PHYSICAL REVIEW SPECIAL TOPICS-ACCELERATORS AND BEAMS15,022002(2012)
[68]苟文选主编，材料力学I.科学出版社.2010年第二版.
[69] Y. HE, W.M. YUE,ect. SRF CAVITIES FOR ADS PROJECT IN CHINA,Proceedings of SRF2013, Paris, France
[70]岳伟明，Taper HWR EM design.近代物理所直线加速器室内部报告.
[71]许哲，CSR实验环高频系统的研制.中科院近物所博士学位论文.2008
[72]清华大学通信教研组编.高频电路（上）（下）.北京：人民邮电出版社，1979.
[73] M. Aberg, M.L. Ainalem, R. Ainsworth and et al. ESS Technical Design Report.2012. release1.
[74] Yuriy Pischalnikov. Overview of Slow and Fast Tuners for SuperconductingCavities.LLRF2011International Workshop, DESY, Germany, October17-20,2011
[75] S. Simrock. Review of Slow and Fast Tuners.12th International Workshop onSRF Superconductivity, Cornell University, Ithaca, New York,2005
[76] D. Longuevergne, S. Blivet, G. Martinet and et al. Proceedings of LINAC2008,Victoria, BC, Canada.789-791.