软X射线自由电子激光设计及相关物理研究
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摘要
自由电子激光,以其高功率、短波长、辐射相干和波长可调等特点,成为现代科学研究越来越重要的工具。世界上第一台硬x射线的自由电子激光装置LCLS已经顺利完成建设、安装及调试工作,投入到了用户使用阶段。LCLS的成功,向全世界证明了现代理论及模拟软件发展的成熟。与此同时,LCLS未来的发展方向成为大家关注的焦点。在这种背景下,我们开始了对A—Line软x射线自由电子激光的可行性研究工作。
本文首先对A—Line作为软x射线自由电子激光线的可行性进行了系统的研究。我们提出了新的束流加速方案,设计了新的A—Line束流传输系统,理论分析并模拟计算了电子束在通过束流传输系统时产生的物理效应(相干和非相干同步辐射效应等)对束流品质的影响,其结果论证了用A—Line作为软x射线自由电子激光线是可行的,为LCLS实现软、硬x射线自由电子激光的同时运行提供了理论依据。
软X射线波段自由电子激光的极化控制,是目前自由电子激光领域研究的热点之一。本文分别分析研究了采用交叉型波荡器和高频波荡器实现极化控制的两种方案。在已有的交叉波荡器结构的基础上,提出了效率更高的在两阶谐波上进行极化控制的新结构,并分析比较了交叉型波荡器在SASE和Seeded两种FEL工作模式下对基波和谐波的进行极化控制的效果,阐述了影响交叉型波荡器极化控制效率的因素。此外,我们从理论上全面分析了高频波荡器对功率源的需求。
受加工技术的限制,波荡器周期很难做到小于cm级,因此,有效利用平面型波荡器中的谐波场辐射,成为有效缩短辐射波长的方式。本文分析研究了一种可以有效增强谐波磁场场强的改进型波荡器结构,并对此结构的磁场及其对辐射谱的影响进行了理论分析及模拟计算。
FEL is becoming more and more important as a modern scientific research toolfor its unique characteristics, such as high power, short wavelength, coherent radiationand adjustable wavelength. As the first hard x-ray FEL facility in the world, LCLShas been successfully built, installed and commissioned, and now in user experimentphase. The unprecedented success of LCLS proved to the world the maturity of theoryand simulation tools, and it also drew people's attention to the future plan of LCLS.Under these circumstances, we started our work of studying the feasibility of usingA-Line as the soft x-ay FEL.
We first systematically studied the feasibility of using A-Line as the soft x-ray freeelectron laser beam line. We designed a new A-Line beam transport system, analyzedthe impact on the beam quality of different physical effects, such as the incoherent andcoherent synchrotron radiation. The results demonstrated that using A-Line as the softx-ray FEL beam line is viable and theoretically proved that LCLS could run hard andsoft x-ray simultaneously.
The polarization control of soft x-ray FELs is one of the most interesting topics inthe FEL field. We studied polarization control with the crossed undulator and RF undu-lator scheme, respectively. We analyzed the polarization control efficiency in SASE andSeeded FEL modes with the crossed undulator, and gave the explanation for the degra-dation of the polarization control efficiency. We proposed a new polarization scheme,which could provide a higher degree of circular polarization at second harmonic. Wealso comprehensively analyzed the power need for the radio frequency undulator.
Undulator period is very difficult to be fabricated to less than cm level confined bythe machining technique. Therefore, making good use of the harmonic radiation in aplanar undulator becomes an efficient method to reduce the radiation wavelength. Westudied and analyzed a modified undulator configuration. The magnetic field and itsimpacts on the radiation spectrum were also computed .
本文首先对A—Line作为软x射线自由电子激光线的可行性进行了系统的研究。我们提出了新的束流加速方案,设计了新的A—Line束流传输系统,理论分析并模拟计算了电子束在通过束流传输系统时产生的物理效应(相干和非相干同步辐射效应等)对束流品质的影响,其结果论证了用A—Line作为软x射线自由电子激光线是可行的,为LCLS实现软、硬x射线自由电子激光的同时运行提供了理论依据。
软X射线波段自由电子激光的极化控制,是目前自由电子激光领域研究的热点之一。本文分别分析研究了采用交叉型波荡器和高频波荡器实现极化控制的两种方案。在已有的交叉波荡器结构的基础上,提出了效率更高的在两阶谐波上进行极化控制的新结构,并分析比较了交叉型波荡器在SASE和Seeded两种FEL工作模式下对基波和谐波的进行极化控制的效果,阐述了影响交叉型波荡器极化控制效率的因素。此外,我们从理论上全面分析了高频波荡器对功率源的需求。
受加工技术的限制,波荡器周期很难做到小于cm级,因此,有效利用平面型波荡器中的谐波场辐射,成为有效缩短辐射波长的方式。本文分析研究了一种可以有效增强谐波磁场场强的改进型波荡器结构,并对此结构的磁场及其对辐射谱的影响进行了理论分析及模拟计算。
FEL is becoming more and more important as a modern scientific research toolfor its unique characteristics, such as high power, short wavelength, coherent radiationand adjustable wavelength. As the first hard x-ray FEL facility in the world, LCLShas been successfully built, installed and commissioned, and now in user experimentphase. The unprecedented success of LCLS proved to the world the maturity of theoryand simulation tools, and it also drew people's attention to the future plan of LCLS.Under these circumstances, we started our work of studying the feasibility of usingA-Line as the soft x-ay FEL.
We first systematically studied the feasibility of using A-Line as the soft x-ray freeelectron laser beam line. We designed a new A-Line beam transport system, analyzedthe impact on the beam quality of different physical effects, such as the incoherent andcoherent synchrotron radiation. The results demonstrated that using A-Line as the softx-ray FEL beam line is viable and theoretically proved that LCLS could run hard andsoft x-ray simultaneously.
The polarization control of soft x-ray FELs is one of the most interesting topics inthe FEL field. We studied polarization control with the crossed undulator and RF undu-lator scheme, respectively. We analyzed the polarization control efficiency in SASE andSeeded FEL modes with the crossed undulator, and gave the explanation for the degra-dation of the polarization control efficiency. We proposed a new polarization scheme,which could provide a higher degree of circular polarization at second harmonic. Wealso comprehensively analyzed the power need for the radio frequency undulator.
Undulator period is very difficult to be fabricated to less than cm level confined bythe machining technique. Therefore, making good use of the harmonic radiation in aplanar undulator becomes an efficient method to reduce the radiation wavelength. Westudied and analyzed a modified undulator configuration. The magnetic field and itsimpacts on the radiation spectrum were also computed .
引文
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[2] J. M. J. Madey, J. App. Phys. 42 (1971) 1906.
[3] R. Bonifacio, C.Pellegrini, L.M.Narduccci, Opt.Comm. 50 (1984) 373.
[4] L.R.Ellias et al. Phys. Rev. Lett. 37 (1976) 710.
[5] D.A.G Deacon, et al. Phys. Rev. Lett. 38 (1977) 892.
[6] The World Wide Web Virtual Library: FEL research and applications,http://sbfel3.ucsb.edu/www/vl fel.html
[7] Y. Ding, X-ray Science at the Femtosecond to Attosecond Frontier workshop,May 18-20, 2009, UCLA
[8] P. Emma, Z. Huang et al., Proc. of the 2005 IEEE Particle Accelerator Confer-ence,Knoxville, Tennessee, 2005.
[9] P. Emma et al., Phys. Rev. Lett. 92, 074801 (2004).
[10] A.A. Zholents, W. Fawley, Phys. Rev. Lett. 92, 224801 (2004).
[11]贾启卡,自由电子激光物理导论(内部讲义) .
[12] W. Colson,自由电子激光,激光手册,第六卷,胡克松等译,1993.
[13] K.J. Kim et al., Phys. Rev. Lett. 100, 244802 (2008).
[14] A.M. Kondratenko and E.L. Saldin, Part. Accel. 10, 207 (1980).
[15] Y. S. Debenev, A. M. Kondratenko, E. L. Saldin,Nucl. Instrum. Methods Phys. Res. A 193, 415 (1982).
[16] R. Bonifacio, C. Pellegrini and L. Narducci, Optics Comm. 50, 373 (1984).
[17] J. M. Wang and L. H. Yu, Nucl. Instrum. Methods Phys. Res. A 250, 484 (1986).
[18] K. J. Kim, Nucl. Instrum. Methods Phys. Res. A 250, 396 (1986).
[19] K. J. Kim, Phys. Rev. Lett. 57, 1871 (1986).
[20] The TESLA Test Facility FEL team, SASE FEL at the TESLA facility, phase 2 ,DESY report TESLA-FEL 2002-01, June 2002 .
[21] Linac Coherent Light Source Conceptual Design Report,SLAC-R-593, SLAC (2002).
[22] SPring-8 Compact SASE Source Conceptual Design Report,http://www-xfel.spring8.or.jp (2005).
[23] I. Ben-Zvi et al., Nucl. Instrum. Methods Phys. Res. A 304, 151 (1991).
[24] L. H. Yu, Phys. Rev. A. 44 5178 (1991).
[25] I. Ben-Zvi et al., Nucl. Instrum. Methods Phys. Res. A 318, 208 (1992).
[26] G. Stupakov, Phys. Rev. Lett., 102, 074801 (2009).
[27] D. Xiang and G. Stupakov, Phys. Rev. ST Accel. Beams 12, 030702 (2009).
[28] E.L. Saldin, E.A. Schneidmillera, M.V. Yurkov,Optics Communications 202 169–187 (2002) .
[29] J. Wu, L.H. Yu, Nucl. Instr. Meth. A 475 104 (2001).
[30] I. Ben-Zvi, K.M. Yang and L.-H. Yu,Nucl. Instrum. Methods A 318, 726 (1992).
[31] Fermi@Elettra conceptual design report , http://www.elettra.trieste.it/FERMI,Elettra (2007).
[32] R. Bonifacio, P. Pierini,C. Pellegrini et al., Nucl. Instr. and Meth. A 341 (1994)285.
[33] E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov, AIP Conference Proceedings,468 (1999) pp321.
[34] K. Honkavaara et al.,“Status of FLASH”, Proc. FEL 2008, Gyeongju, Korea,2008.
[35] P. Emma et. al., Proceedings of the 2009 IEEE Particle Accelerator Conference,Vancouver, BC, Canada, May, 2009.
[36] K.J. Kim, and Z. Huang, Introduction to the Physics of Free Electron Lasers,Lecture notes in USPAS 2008
[37] E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov, the Physics of Free ElectronLasers, Springer, 2000
[38] M. Xie, Proceedings of the 1995 IEEE Particle Accelerator Conference, Piscat-away, NJ, 1995.
[39] L.H. Yu, Science 289 932 (2000).
[40] S. Reiche, Nucl. Instr. and Meth. A 429 (1999) 243.
[41] W.M. Fawley, An Informal Manual for GINGER and its post-processor XPLOT-GIN, LBID-2141, CBP Tech Note-104, UC-414, 1995.
[42] H.P. Freund et. al. , Phys. Rev. E 52 (1995) 5401.
[43] R.J. Dejus, O. Shevchenko, N. Vinokurov, Nucl. Instr. and Meth. A 429 (1999)225.
[44] T.M. Tran, J.S. Wurtele, Computer Physics Communications 54 (1989) 263.
[45] S. Reiche, B. Faatz, Proceedings of the 1998 FEL Conference, II-37, Elsevier,Amsterdam, 1999.
[46] S.G. Biedron et. al. , Nucl. Instr. and Meth. A 445 (2000) 110.
[47] M. Dohlus, T. Limberg, and P. Emma. Bunch Compression for Linac-basedFELs, ICFA Beam Dynamics Newsletter, 50 38:15 (2005).
[48] M. Borland, elegant:A ?exible SDDS-Compilant Code for Accelerator Simula-tion, APS LS-287, September 2000.
[49] K. Flo¨ttmann, Astra User Manual,http://www.desy.de/ mpy/astra dokumentation.
[50] M. Dohlus and T. Limberg, CSRTrack: FASTER CALCULATION of 3-D CSREFFECTS, Proceedings of the 2004 FEL Conference, 18-21, 2004.
[51] M. Dohlus and T. Limberg, CSRtrack Version 1.2 Users Manual,http://www.desy.de/xfel-beam/csrtrack.
[52] The Stanford Two-Mile Accelerator, R.B. Neal, Editor (1968)
[53] R. Erickson et. al., Proceedings of 1992 Linear Accelerator Conference,Ottawa, Canada, August 24-28, 1992.
[54] http://mad.home.cern.ch/mad/mad8web/mad8.html
[55] Ya.S. Derbenev, et.al, DESY print,TESLA FEL 95– 05 (1995).
[56] Y. Ding et al., SLAC-PUB-13525, 2009
[57] S. Sasaki, Nucl. Instrum. Methods A 347, 83-86 (1994).
[58] K.-J. Kim, Nucl. Instrum. Methods A 445, 329 (2000).
[59] M. Born, E. Wolf, Principles of Optics (1999).
[60] A.E. Siegman, Lasers (1986).
[61] Y. Ding, Z. Huang, Phys. Rev. ST-AB 11, 030702 (2008).
[62] W.M. Fawley, Phys. Rev. ST Accel. Beams 5, 070701 (2002).
[63] E.L. Saldinet al., TESLA FEL-Report, 1997-02
[64] Z. Huang, S. Reiche, Proceedings of FEL04, p201-204
[65] Y. Li et. al., Proceedings of EPAC08, Genoa, Italy p2282
[66] Y. Li, W. Decking et al., Proceedings of the 2009 IEEE Particle AcceleratorConference (Vancouver, BC, Canada, May, 2009).
[67] J. Maraangos et. al., NLS Project: Science Case & Outline Facility Design,www.newlightsource.org, 2009
[68] N.R. Thompson et. al., Proceedings of FEL 2009, Liverpool, UK
[69] T. Shintake, K. Huke et. al., Jap. J. Appl. Phys. 22, pp. 844-851 (1983).
[70] V. Dolgashev, Microwave De?ectors: Normal Conducting Crab Cavity for APSand Discussion on Microwave Undulators, Talk at Argonne, 17 June 2005
[71] Sami G. Tantawi et al, Physical Review Special Topics-Accelerators and Beams8, 042002, April 2005.
[72] S. G. Tantawi , Z. Li et. al., Physical Review Special Topics-Accelerators andBeams, vol.5, no.3 (2002) .
[73] P. J. B. Clarricoats, and P. K. Saha, Electronics Letters, 5 No. 9, 1969
[74] D. Wagner et. al., International Journal of Infrared and Millimeter Waves, Vol.20, No. 4, 1999
[75] P. J. B. Clarricoats et. al., Proc. IEE, 118 No. 9, 1971
[76] P. Bellomo et. al., SPEAR 3 Design Report, SLAC-R-609, 2002
[77] A. Amir et. al., Physical Review A, 32 No. 5 , 1985
[78] T. M. Tran, B. G. Danly et. al., IEEE Journal of Quantum Electronics. Vol. QE-23, NO. 9, pp. 1578-1589, 1987
[79] K.Halbach,Nucl. Instr. and Meth. in Phys. Res. A 187 (1981) 109
[80] O’Shea et. al. , Nucl. Instr. and Meth. A 341(1994) 7.
[81] M. Asakawa et. al. , Nucl. Instr. and Meth. A 358 (1995) 399.
[82] J. Zeng, J. Zhuang, High Power Laser and Particle Beams Vol 9 No.1 , 1997
[83] Qika Jia, Undulator Harmonic field enhancement analysis, submitted toIPAC2010
[84] http://www.esrf.eu/Accelerators/Groups/InsertionDevices/Software/Radia
[85] http://www.esrf.eu/Accelerators/Groups/InsertionDevices/Software/B2e
[86] M. J. Schmitt and C.J. Elliott, IEEE J. Quantum Electron. QE-23 (1987) 1552
[87] Qika Jia,The effect of undulator harmonics field on Free-Electron Laser har-monic generation, submitted to FEL2010
[88] Q. Jia, IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 43, NO. 9,(2007) 833
[2] J. M. J. Madey, J. App. Phys. 42 (1971) 1906.
[3] R. Bonifacio, C.Pellegrini, L.M.Narduccci, Opt.Comm. 50 (1984) 373.
[4] L.R.Ellias et al. Phys. Rev. Lett. 37 (1976) 710.
[5] D.A.G Deacon, et al. Phys. Rev. Lett. 38 (1977) 892.
[6] The World Wide Web Virtual Library: FEL research and applications,http://sbfel3.ucsb.edu/www/vl fel.html
[7] Y. Ding, X-ray Science at the Femtosecond to Attosecond Frontier workshop,May 18-20, 2009, UCLA
[8] P. Emma, Z. Huang et al., Proc. of the 2005 IEEE Particle Accelerator Confer-ence,Knoxville, Tennessee, 2005.
[9] P. Emma et al., Phys. Rev. Lett. 92, 074801 (2004).
[10] A.A. Zholents, W. Fawley, Phys. Rev. Lett. 92, 224801 (2004).
[11]贾启卡,自由电子激光物理导论(内部讲义) .
[12] W. Colson,自由电子激光,激光手册,第六卷,胡克松等译,1993.
[13] K.J. Kim et al., Phys. Rev. Lett. 100, 244802 (2008).
[14] A.M. Kondratenko and E.L. Saldin, Part. Accel. 10, 207 (1980).
[15] Y. S. Debenev, A. M. Kondratenko, E. L. Saldin,Nucl. Instrum. Methods Phys. Res. A 193, 415 (1982).
[16] R. Bonifacio, C. Pellegrini and L. Narducci, Optics Comm. 50, 373 (1984).
[17] J. M. Wang and L. H. Yu, Nucl. Instrum. Methods Phys. Res. A 250, 484 (1986).
[18] K. J. Kim, Nucl. Instrum. Methods Phys. Res. A 250, 396 (1986).
[19] K. J. Kim, Phys. Rev. Lett. 57, 1871 (1986).
[20] The TESLA Test Facility FEL team, SASE FEL at the TESLA facility, phase 2 ,DESY report TESLA-FEL 2002-01, June 2002 .
[21] Linac Coherent Light Source Conceptual Design Report,SLAC-R-593, SLAC (2002).
[22] SPring-8 Compact SASE Source Conceptual Design Report,http://www-xfel.spring8.or.jp (2005).
[23] I. Ben-Zvi et al., Nucl. Instrum. Methods Phys. Res. A 304, 151 (1991).
[24] L. H. Yu, Phys. Rev. A. 44 5178 (1991).
[25] I. Ben-Zvi et al., Nucl. Instrum. Methods Phys. Res. A 318, 208 (1992).
[26] G. Stupakov, Phys. Rev. Lett., 102, 074801 (2009).
[27] D. Xiang and G. Stupakov, Phys. Rev. ST Accel. Beams 12, 030702 (2009).
[28] E.L. Saldin, E.A. Schneidmillera, M.V. Yurkov,Optics Communications 202 169–187 (2002) .
[29] J. Wu, L.H. Yu, Nucl. Instr. Meth. A 475 104 (2001).
[30] I. Ben-Zvi, K.M. Yang and L.-H. Yu,Nucl. Instrum. Methods A 318, 726 (1992).
[31] Fermi@Elettra conceptual design report , http://www.elettra.trieste.it/FERMI,Elettra (2007).
[32] R. Bonifacio, P. Pierini,C. Pellegrini et al., Nucl. Instr. and Meth. A 341 (1994)285.
[33] E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov, AIP Conference Proceedings,468 (1999) pp321.
[34] K. Honkavaara et al.,“Status of FLASH”, Proc. FEL 2008, Gyeongju, Korea,2008.
[35] P. Emma et. al., Proceedings of the 2009 IEEE Particle Accelerator Conference,Vancouver, BC, Canada, May, 2009.
[36] K.J. Kim, and Z. Huang, Introduction to the Physics of Free Electron Lasers,Lecture notes in USPAS 2008
[37] E. L. Saldin, E. A. Schneidmiller, M. V. Yurkov, the Physics of Free ElectronLasers, Springer, 2000
[38] M. Xie, Proceedings of the 1995 IEEE Particle Accelerator Conference, Piscat-away, NJ, 1995.
[39] L.H. Yu, Science 289 932 (2000).
[40] S. Reiche, Nucl. Instr. and Meth. A 429 (1999) 243.
[41] W.M. Fawley, An Informal Manual for GINGER and its post-processor XPLOT-GIN, LBID-2141, CBP Tech Note-104, UC-414, 1995.
[42] H.P. Freund et. al. , Phys. Rev. E 52 (1995) 5401.
[43] R.J. Dejus, O. Shevchenko, N. Vinokurov, Nucl. Instr. and Meth. A 429 (1999)225.
[44] T.M. Tran, J.S. Wurtele, Computer Physics Communications 54 (1989) 263.
[45] S. Reiche, B. Faatz, Proceedings of the 1998 FEL Conference, II-37, Elsevier,Amsterdam, 1999.
[46] S.G. Biedron et. al. , Nucl. Instr. and Meth. A 445 (2000) 110.
[47] M. Dohlus, T. Limberg, and P. Emma. Bunch Compression for Linac-basedFELs, ICFA Beam Dynamics Newsletter, 50 38:15 (2005).
[48] M. Borland, elegant:A ?exible SDDS-Compilant Code for Accelerator Simula-tion, APS LS-287, September 2000.
[49] K. Flo¨ttmann, Astra User Manual,http://www.desy.de/ mpy/astra dokumentation.
[50] M. Dohlus and T. Limberg, CSRTrack: FASTER CALCULATION of 3-D CSREFFECTS, Proceedings of the 2004 FEL Conference, 18-21, 2004.
[51] M. Dohlus and T. Limberg, CSRtrack Version 1.2 Users Manual,http://www.desy.de/xfel-beam/csrtrack.
[52] The Stanford Two-Mile Accelerator, R.B. Neal, Editor (1968)
[53] R. Erickson et. al., Proceedings of 1992 Linear Accelerator Conference,Ottawa, Canada, August 24-28, 1992.
[54] http://mad.home.cern.ch/mad/mad8web/mad8.html
[55] Ya.S. Derbenev, et.al, DESY print,TESLA FEL 95– 05 (1995).
[56] Y. Ding et al., SLAC-PUB-13525, 2009
[57] S. Sasaki, Nucl. Instrum. Methods A 347, 83-86 (1994).
[58] K.-J. Kim, Nucl. Instrum. Methods A 445, 329 (2000).
[59] M. Born, E. Wolf, Principles of Optics (1999).
[60] A.E. Siegman, Lasers (1986).
[61] Y. Ding, Z. Huang, Phys. Rev. ST-AB 11, 030702 (2008).
[62] W.M. Fawley, Phys. Rev. ST Accel. Beams 5, 070701 (2002).
[63] E.L. Saldinet al., TESLA FEL-Report, 1997-02
[64] Z. Huang, S. Reiche, Proceedings of FEL04, p201-204
[65] Y. Li et. al., Proceedings of EPAC08, Genoa, Italy p2282
[66] Y. Li, W. Decking et al., Proceedings of the 2009 IEEE Particle AcceleratorConference (Vancouver, BC, Canada, May, 2009).
[67] J. Maraangos et. al., NLS Project: Science Case & Outline Facility Design,www.newlightsource.org, 2009
[68] N.R. Thompson et. al., Proceedings of FEL 2009, Liverpool, UK
[69] T. Shintake, K. Huke et. al., Jap. J. Appl. Phys. 22, pp. 844-851 (1983).
[70] V. Dolgashev, Microwave De?ectors: Normal Conducting Crab Cavity for APSand Discussion on Microwave Undulators, Talk at Argonne, 17 June 2005
[71] Sami G. Tantawi et al, Physical Review Special Topics-Accelerators and Beams8, 042002, April 2005.
[72] S. G. Tantawi , Z. Li et. al., Physical Review Special Topics-Accelerators andBeams, vol.5, no.3 (2002) .
[73] P. J. B. Clarricoats, and P. K. Saha, Electronics Letters, 5 No. 9, 1969
[74] D. Wagner et. al., International Journal of Infrared and Millimeter Waves, Vol.20, No. 4, 1999
[75] P. J. B. Clarricoats et. al., Proc. IEE, 118 No. 9, 1971
[76] P. Bellomo et. al., SPEAR 3 Design Report, SLAC-R-609, 2002
[77] A. Amir et. al., Physical Review A, 32 No. 5 , 1985
[78] T. M. Tran, B. G. Danly et. al., IEEE Journal of Quantum Electronics. Vol. QE-23, NO. 9, pp. 1578-1589, 1987
[79] K.Halbach,Nucl. Instr. and Meth. in Phys. Res. A 187 (1981) 109
[80] O’Shea et. al. , Nucl. Instr. and Meth. A 341(1994) 7.
[81] M. Asakawa et. al. , Nucl. Instr. and Meth. A 358 (1995) 399.
[82] J. Zeng, J. Zhuang, High Power Laser and Particle Beams Vol 9 No.1 , 1997
[83] Qika Jia, Undulator Harmonic field enhancement analysis, submitted toIPAC2010
[84] http://www.esrf.eu/Accelerators/Groups/InsertionDevices/Software/Radia
[85] http://www.esrf.eu/Accelerators/Groups/InsertionDevices/Software/B2e
[86] M. J. Schmitt and C.J. Elliott, IEEE J. Quantum Electron. QE-23 (1987) 1552
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