激光—电子非线性康普顿散射特性研究
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摘要
自由电子激光诞生于上世纪七十年代,至诞生以来在理论和实验上都得到了迅速发展。研究自由电子激光产生的核心问题是自由电子与光场的相互作用问题。随着激光场和强激光技术的发展等极端条件的实现，电子在激光束上的非弹性散射开始显现，这个非弹性散射过程的能量交换的主要方式是非线性康普顿（Compton）散射的能量交换。即在电子与光场的相互作用的过程中吸收多个光子，发射一个新的光子的过程。对于这个散射过程的研究，不仅有利于进一步了解自由电子激光产生的原理，而且为产生短波长自由电子激光细致的研究和高性能自由电子激光和它的研制及应用都奠定了坚实的基础。
本文主要用两种模型对激光-电子非线性Compton散射特性进行研究。全文共包括五章。第一章简要地介绍了自由电子激光和非线性Compton散射的发展与现状。第二章用标准微扰论研究了非线性Compton散射的电子能量，散射光频率以及微分散射截面特性。在这一章首先研究了激光-电子非线性康普顿散射中散射光频率在不同散射方向随着入射角的变化，然后又研究了散射过程中电子能量变化特性，接着利用标准微扰理论推导出在电子静止参考系中激光-电子非线性Compton散射微分散射截面表达式并对其进行了讨论。最后通过洛仑兹变换得到实验室参考系中的激光-电子非线性Compton散射的微分散射截面并对其特性进行了研究。结果表明：散射光频率在散射角一定的情况下，电子能量变化，散射光频率除了与光子数成正比外在不同的方位角处随着入射角的变化趋势不同，同样在方位角一定时，不同散射角处的变化情况也不同。散射光的微分散射截面除了与光子数密度有关，并与它的（n-1）次方成正比外，还与散射角，方位角和初始条件有关。在进行上面研究中都利用了模拟计算进行细致研究。这就为以后工作中的实际操作提供了重要的参考价值。第三章介绍自由电子在外场中运动的量子电动力学理论，并且介绍了半经典方法，用这种方法可以处理电子在外场中发射光子问题。第四章用半经典方法对圆极化强平面电磁波场中的多光子非线性Compton散射过程中电子能量的变化，散射频率和微分散射截面特性进行了讨论。通过对低频极限下电子能量变化，散射光频率和微分散射截面与入射光强的关系进行研究得出：利用多光子非线性Compton散射产生短波光子从而得到实际所需要的散射光，此时需要在一定的散射方向和初始条件下选择适当的光场强度。对于电子能量和光场强度一定的非线性Compton散射，散射角一定时，不同的方位角所对应的散射过程都对应入射角都有一个临界值，该临界值前后就是光场的能量的增加或减小。第五章是对本论文的总结，总结本论文的主要结果，指出了多光子散射在短波光源和自由电子激光发展中的重要性。
The free electrons laser was born in1970’s , since its birth in theory and experiment sinceall have developed rapidly. The core problem of the free electrons laser is the free electronicand optical field interaction. With super laser field and strong laser technology development,and the realization of the extreme conditions, the electron on the laser beam of elasticscattering began to appear, the process of the main mechanism is the energy exchange ofnonlinear Compton (Compton) scattering energy exchange. That is in the electronic andoptical field interaction in the process of absorption more photons, launch a new photonprocess. To the scattering process, not only conducive to further understand the principle offree electrons laser produce, and to produce a short wave long free electronic laser and carefulstudies and high performance of the free electrons laser application development and laid asolid foundation.
This paper mainly uses two kinds of model of laser-electronic Compton scatteringcharacteristics of nonlinear. Full text includes five chapters. The first chapter brieflyintroduces the laser and nonlinear free electrons Compton scattering of development and thestatus quo. The second chapter using standard perturbation theory, study nonlinear Comptonscattering of electrical power, scattering the light frequency and differential scattering sectionfeatures. First studied n photon group nonlinear Compton scattering of light scatteringfrequency in different direction with the change of the incident Angle scattering, and thenstudy in the process of the scattering electronic energy variation characteristics, once again,we and use standard perturbation theory in electronic static reference is deduced the n photongroup Compton scattering nonlinear differential scattering section of the expression anddiscussion. Finally, we through the Lorentz transformation get in the frame of referencelaboratory nonlinear Compton scattering of photon differential scattering section features. Theresults show that: the scattering frequency in the scattering Angle certain electronic energychange, scattering light frequency is proportional to the number of photons except withdifferent place with external azimuth Angle change trend is different, also in the azimuth must,different Angle scattering in the changes of different also. Scattering light scattering section inaddition to and photonic differential number density (n-1) time is directly proportional tooutside, still and scattering Angle, azimuth and initial conditions about. In the above study ,use the simulation calculation for the detailed research. This further our future work in thepractical operation provides important reference value. Chapter 3 shows the freedom ofmovement in the field of electronic in quantum electrodynamics theory, and introduces the half classical method, using this method can deal with electronic field emission in the problem.The fourth chapter using a classical method, study the polarization of the plane wave longstrong nonlinear Compton scattering n photons in the process of the change of the electronicenergy, scattering frequency and differential scattering section features. Through to the lowfrequency limit of electronic energy change, scattering the light frequency and differentialcross section incident light scattering and the relationship between the strong research that:using nonlinear Compton scattering produces photons shortwave photon and get a real needthe scattering, here in certain scattering direction to initial conditions and choice of appropriatelight field strength. For the electronic energy and optical field intensity of Compton scatteringcertain nonlinear, scattering Angle must, different azimuth of the corresponding scatteringprocess corresponding incident Angle has a critical value, the critical value is light field ofenergy before and after the increase or decrease. The fifth chapter is summarized and outlook,this paper summarizes the main results, points out that the more photons in short wave lightsources and free scattering in the development of the electronic laser importance.
本文主要用两种模型对激光-电子非线性Compton散射特性进行研究。全文共包括五章。第一章简要地介绍了自由电子激光和非线性Compton散射的发展与现状。第二章用标准微扰论研究了非线性Compton散射的电子能量，散射光频率以及微分散射截面特性。在这一章首先研究了激光-电子非线性康普顿散射中散射光频率在不同散射方向随着入射角的变化，然后又研究了散射过程中电子能量变化特性，接着利用标准微扰理论推导出在电子静止参考系中激光-电子非线性Compton散射微分散射截面表达式并对其进行了讨论。最后通过洛仑兹变换得到实验室参考系中的激光-电子非线性Compton散射的微分散射截面并对其特性进行了研究。结果表明：散射光频率在散射角一定的情况下，电子能量变化，散射光频率除了与光子数成正比外在不同的方位角处随着入射角的变化趋势不同，同样在方位角一定时，不同散射角处的变化情况也不同。散射光的微分散射截面除了与光子数密度有关，并与它的（n-1）次方成正比外，还与散射角，方位角和初始条件有关。在进行上面研究中都利用了模拟计算进行细致研究。这就为以后工作中的实际操作提供了重要的参考价值。第三章介绍自由电子在外场中运动的量子电动力学理论，并且介绍了半经典方法，用这种方法可以处理电子在外场中发射光子问题。第四章用半经典方法对圆极化强平面电磁波场中的多光子非线性Compton散射过程中电子能量的变化，散射频率和微分散射截面特性进行了讨论。通过对低频极限下电子能量变化，散射光频率和微分散射截面与入射光强的关系进行研究得出：利用多光子非线性Compton散射产生短波光子从而得到实际所需要的散射光，此时需要在一定的散射方向和初始条件下选择适当的光场强度。对于电子能量和光场强度一定的非线性Compton散射，散射角一定时，不同的方位角所对应的散射过程都对应入射角都有一个临界值，该临界值前后就是光场的能量的增加或减小。第五章是对本论文的总结，总结本论文的主要结果，指出了多光子散射在短波光源和自由电子激光发展中的重要性。
The free electrons laser was born in1970’s , since its birth in theory and experiment sinceall have developed rapidly. The core problem of the free electrons laser is the free electronicand optical field interaction. With super laser field and strong laser technology development,and the realization of the extreme conditions, the electron on the laser beam of elasticscattering began to appear, the process of the main mechanism is the energy exchange ofnonlinear Compton (Compton) scattering energy exchange. That is in the electronic andoptical field interaction in the process of absorption more photons, launch a new photonprocess. To the scattering process, not only conducive to further understand the principle offree electrons laser produce, and to produce a short wave long free electronic laser and carefulstudies and high performance of the free electrons laser application development and laid asolid foundation.
This paper mainly uses two kinds of model of laser-electronic Compton scatteringcharacteristics of nonlinear. Full text includes five chapters. The first chapter brieflyintroduces the laser and nonlinear free electrons Compton scattering of development and thestatus quo. The second chapter using standard perturbation theory, study nonlinear Comptonscattering of electrical power, scattering the light frequency and differential scattering sectionfeatures. First studied n photon group nonlinear Compton scattering of light scatteringfrequency in different direction with the change of the incident Angle scattering, and thenstudy in the process of the scattering electronic energy variation characteristics, once again,we and use standard perturbation theory in electronic static reference is deduced the n photongroup Compton scattering nonlinear differential scattering section of the expression anddiscussion. Finally, we through the Lorentz transformation get in the frame of referencelaboratory nonlinear Compton scattering of photon differential scattering section features. Theresults show that: the scattering frequency in the scattering Angle certain electronic energychange, scattering light frequency is proportional to the number of photons except withdifferent place with external azimuth Angle change trend is different, also in the azimuth must,different Angle scattering in the changes of different also. Scattering light scattering section inaddition to and photonic differential number density (n-1) time is directly proportional tooutside, still and scattering Angle, azimuth and initial conditions about. In the above study ,use the simulation calculation for the detailed research. This further our future work in thepractical operation provides important reference value. Chapter 3 shows the freedom ofmovement in the field of electronic in quantum electrodynamics theory, and introduces the half classical method, using this method can deal with electronic field emission in the problem.The fourth chapter using a classical method, study the polarization of the plane wave longstrong nonlinear Compton scattering n photons in the process of the change of the electronicenergy, scattering frequency and differential scattering section features. Through to the lowfrequency limit of electronic energy change, scattering the light frequency and differentialcross section incident light scattering and the relationship between the strong research that:using nonlinear Compton scattering produces photons shortwave photon and get a real needthe scattering, here in certain scattering direction to initial conditions and choice of appropriatelight field strength. For the electronic energy and optical field intensity of Compton scatteringcertain nonlinear, scattering Angle must, different azimuth of the corresponding scatteringprocess corresponding incident Angle has a critical value, the critical value is light field ofenergy before and after the increase or decrease. The fifth chapter is summarized and outlook,this paper summarizes the main results, points out that the more photons in short wave lightsources and free scattering in the development of the electronic laser importance.
引文
[1] Jorunal of Fusion Energy,1991.10,No.2,127~156
[2]惠钟锡，杨振华.自由电子激光北京：国防工业出版社，1995
[3]刘盛纲.相对论电子学.北京：科学出版社，1987
[4]马歇尔著，尹元昭译.自由电子激光器北京：科学出版社，1993
[5] D.A.G. Deacon, L.R. Elias, J.M.J. Madey, G.J. Ramian, H.A. Schwettman andT.L. Smith. First Operation of a Free-Electron Laser. Phys. Rev. Lett.,1977, 38 (16) :892-894
[6]王明红.毫米波段自由电子激光特性的研究.电子科技大学博士学位论文，2003
[7]思源（译）.日本获得波长350nm，315nm的自由电子激光振荡器.强激光技术进展，1996, 6:22
[8]惠钟锡.曙光一号自由电子激光装置的设计研究.强激光与粒子束. 1990,2(3):257-272
[9] K Tiedtke, A Azima, N von Bargen, L Bittner, S Bonfigt et al. The soft x-rayfree-electron laser FLASH at DESY: beamlines, diagnostics and end-stations.New J. Phys. 2009,11(02):3029
[10] Williams, G. P. FAR-IR/THz radiation from the Jefferson Laboratory, energyrecovered linac, free electron laser. 2002 ,73(3):1461-1463
[11] B. G. Danly et al. IEEE J. Quan. Electron. 1987,23:1739.
[12]杨中海，卢波，彭良福.自由电子激光在生物医学与材料科学中的应用.科技大学出版社, 1991
[13]熊春乐,艾颖,张启仁,郭东升. Kapitza_Dirac效应的GAC理论及其应用.物理学进展, 2004, 24(1):106-126
[14] Dong-sheng Guo, Teijio berg and Bernd Crasemann Scattering theory ofmultiphoton ionization in Strong fields Phys. Rev. A 1989,40(9):4997-5005
[15] Bamber C, Boege S J, Koffas T, et al. Studies of nonlinear QED incollisions of 46.6 GeV electrons with intense laser pulses. Phys. Rev. D,1999, 60(09): 2004.
[16] C. Bula, K. T. McDonald, and E. J. Prebys, et al. Observation of NonlinearEffects in Compton Scattering. Phys. Rev. Lett. 1996,76(17): 3116–3119.
[17] Heinzl T, Seipt D , Kampfer B. Beam-shape effects in nonlinear Comptonand Thomson scattering. Phys. Rev. A, 2010, 81(02): 2125.
[18] Madalina Boca, Viorica Florescu. Nonlinear Compton scattering with a laserpulse. Phys. Rev. A, 2009, 80 (05): 3403.
[19]王平晓,霍裕昆,孔青,袁祥群,曹娜,邵磊.真空中激光加速电子的特性和机制.Strong Field Laser Physics--Proceedings of CCAST (World Laboratory)Workshop, 2000
[20] H. K. Avetissian and G. F. Mkrtchian. Nonlinear quantum regime of the x-rayCompton laser. Phys. Rev. E, 2002, 65(4):6505
[21]郝东山.多光子康普顿效应下的自由电子激光中电子与光子碰撞截面的特性.信阳师范学院学报(自然科学版), 1998, 11(3):242-244
[22]姜孟瑞,梁大光,孙和丽.相对论性电子的Compton散射.山东师范大学学报（自然科学版）, 2010, 25(3):37-39
[23] Singhal R. P. and Burns A. J. . Verification of Compton collision andKlein-Nishina formulas-an undergaruduate laboratory experiment. Am. J.Phys.,1978, 46(6):646-649
[24] H. Al Abawi, F. A. Hopf, and P. Meystre. Electron dynamics in a free electronlaser. Phys. Rev. A, 1977,16(2):666-671
[25] V. Yakimenko and I. V. Pogorelsky. Polarizedγsource based on Comptonbackscattering in a laser cavity. Phys. Rev. ST Accel. Beams, 2006,9(9):1001
[26] Chen J,Imasaki k,Fujita M,Yamanaka C,Asakawa M,Nakai S,Asakuma T 1994Nucl.Instr. and Meth. in Phys.Res.A 341 346.
[27] Yasunori Tanimoto, Tohru Honda, and Shogo Sakanaka. Experimentaldemonstration and visual observation of dust trapping in an electronstorage ring. Phys. Rev. ST Accel. Beams, 2009,12(11):0702
[28] J. X. Wang and Y. K. Ho. Energy-exchange characteristics in ordinary andnonlinear Compton scattering. Phys. Rev. A, 1999, 59(6):4522-4529
[29] Anthony Hartin. On the equivalence of semi-classical methods for QED inintense external fields. J. Phys.:Conf. Ser., 2009,198(1): 2004
[30] V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, in QuantumElectrodynamics, Course of Theoretical Physics, 2nd ed., translated fromRussian by T. B. Sykes and J. S. Bell Pergamon, New York, 1982, Vol. 4
[31] JOHN F. DAWSON, ZOLTAN FRIKD. Plane-Wave Packets and Their Limitation inNonlinear Compton Scattering. Phys. Rev. D, 1970, 1(12):3363-3370
[32] Milton D. Slaughter. Electron-laser pulse scattering. Phys. Rev. D, 1975,11(6):1639-1648
[33] Bergou J, Varro S. Nonlinear scattering processes in the presence of aquantised radiation field:II Relativistic treatment. J. Phys. A, 1981,81(09):2281.
[34] Gudrid Moortgat-Pick. The Furry Picture. J. Phys.:Conf. Ser.,2009,198(1):2002
[35] Dirac PAM The principles of quantum Mechanics. 4-th edn,Clarendon,London,1983
[36] J. Autschbach, W. H. E. Schwarz. Relativistic electron densities in thefour-component Dirac representation and in the two-component pictureHydrogen-like systems. Theor Chem Acc. 2000,104(1):82-88
[37] J. M. J. Madey. Relationship between Mean Radiated Energy, Mean SquareRadiated Energy and Spontaneous Power Spectrum in a Power Series Expansionof the Equation of Motion in a Free-Electron Laser. IL NUOVO CIMENTO, 1979,50(1):64-88
[38] S.Ya. Tochitsky, O.B. Williams, P. Musumeci, C. Sung, D. J. Haberberger,A.M. Cook, J. B. Rosenzweig, and C. Joshi. Efficient harmonic microbunchingin a 7th-order inverse-free-electron laser interaction. Phys.Rev.STAB.,2009,12(5):050703
[39] P. Sprangle, B. Hafizi, and J. R. Pe ano. Laser-pumped coherent x-rayfree-electron laser. Phys. Rev. STAB., 2009, 12(5):050702
[40] Richard Talman, Nikolay Malitsky, Frank Stulle. Emittance growth due tostatic and radiative space charge forces in an electron bunch compressor.Phys. Rev. STAB., 2009, 12(1):014201
[41] U.D. Jentschura1, and V.G. Serbo. Generation of High-Energy Photons withLarge Orbital Angular Momentum by Compton Scattering. Phys. Rev. Lett.,2011, 106(1):013001
[42] Erik L tstedt, and Ulrich D. Jentschura. Nonperturbative Treatment ofDouble Compton Backscattering in Intense Laser Fields. Phys. Rev. Lett.,2009, 103(11):110404
[43] Y. I. Salamin. Forward and backscattered ultrahigh-intensity Comptonspectra in a uniform magnetic field. Phys. Rev. A, 1999, 60(4):3276-3283
[44] F. Glotin, J.-M. Ortega, R. Prazeres, G. Devanz, and O. Marcouillé. TunableX-Ray Generation in a Free-Electron Laser by Intracavity ComptonBackscattering. Phys. Rev. Lett., 1996, 77(15):3130-3132
[45] W. Beall Fowler and D. L. Dexter. Relation between Absorption and EmissionProbabilities in Luminescent Center in Ionic Solids. Phys. Rev., 1962,128(5):2154-2165
[46]喀兴林.高等量子力学第二版[M].北京：高等教育出版社,2001
[47] Loudon R (Translated by Yu Liang). Quantum Theory of Optic. Beijing:HigherEducation Press, 1992, 225-226.
[48] V. L. Ginsburg. The Relativistic Theory of Excited Spin States of the Protonand the Neutron. Phys. Rev., 1943, 63(1):1-12
[49] E. Fermi and L. Marshall. On the Interaction Between Neutrons and Electrons.Phys. Rev. 1947, 72(12):1139-1146
[50] Mathan Rosen. Statistical Geometry and Fundamental Particles. Phys. Rev.,1947, 72(4):298-303
[51] A. I. Nikishov and V. I. Ritus. Pair Production by a Photon and PhotonEmission By an Electron in The Field of an Intense Electromagnetic Waveand In a Constant Field. Sov. Phys. JETP., 1967, 25(6):1135
[52]郭硕鸿.电动力学.第二版.北京：高等教育出版社，1997
[53]刘树杞等.量子电子学.天津：天津科学技术出版社，1990
[54] Joseph Kupersztych. Question of Unitarity of Foldy-WouthuysenTransformations and Volkov States in Two-Component Forms. Phys. Rev. Lett.,1979, 42(8):483-486
[55] S. Elhandi, S. Taj, and Y. Attaourti. Electron’s anomalousmagnetic-moment effects on electron-hydrogen elastic collisions in thepresence of a circularly polarized laser field. Phys. Rev. A, 2010,81(4):043422
[56] W. H. Furry. On Bound States and Scattering in Positron Theory. Phys. Rev.,1951, 81(1):115-124
[57] MATTHIAS HUBER and EDGARDO STOCKMEYER. Perturbative Implementation of theFurry Picture. Letters in Mathematical Physics, 2006, 79(1):99-108
[58] S. P. Gavrilov. The furry picture for the standard electroweak theory witha free non-Abelian external field. Elementary Particle Physics And FieldTheory, 1993, 35(10):969-973
[59] A. Vaidya, C. Farina and M. Hott. Furry’s picture in the path integralframework. IL Nuovo Cimento A, 1992, 105(7):925-934
[60] V. Ch. Zhukovsky, A. E. Lobanov, and E. M. Murchikova. Radiative effectsin the standard model extension. Phys. Rev. D, 2006, 73(6):065016
[61] R. A. Neville and F. Rohrlich. Quantum Electrodynamics on Null Planes andApplications to Lasers. Phys. Rev. D, 1971, 3(8):1692-1707
[62] Dorin Cezar Ionescu. Unitarity and electron-positron pairs created bystrong external fields. Phys. Rev. A, 1994, 49(5):3188-3195
[63] Chris Harvey and Thomas Heinzl. Signatures of high-intensity Comptonscattering. Phys. Rev. A, 2009, 79(6):063407
[64] H. PRAKASH, R. GOYAL and VACHASPATI. Effect of Coherence onIntensity-Dependent Frequency Shift in Compton Scattering. LETTERE ALNUOVO CIMENTO, 1971, 1(19):771-774
[65] F.V. Hartemann and A.K. Kerman. Classical Theory of Nonlinear ComptonScattering. Phys. Rev. Lett., 1996, 76(4):624-627[66] Frederic V. Hartemann, Félicie Albert, Craig W. Siders, and C. P. J. Barty.Low-Intehsity Nonlinear Spectral Effects in Compton Scattering. Phys. Rev.Lett., 2010, 105(13):130801
[2]惠钟锡，杨振华.自由电子激光北京：国防工业出版社，1995
[3]刘盛纲.相对论电子学.北京：科学出版社，1987
[4]马歇尔著，尹元昭译.自由电子激光器北京：科学出版社，1993
[5] D.A.G. Deacon, L.R. Elias, J.M.J. Madey, G.J. Ramian, H.A. Schwettman andT.L. Smith. First Operation of a Free-Electron Laser. Phys. Rev. Lett.,1977, 38 (16) :892-894
[6]王明红.毫米波段自由电子激光特性的研究.电子科技大学博士学位论文，2003
[7]思源（译）.日本获得波长350nm，315nm的自由电子激光振荡器.强激光技术进展，1996, 6:22
[8]惠钟锡.曙光一号自由电子激光装置的设计研究.强激光与粒子束. 1990,2(3):257-272
[9] K Tiedtke, A Azima, N von Bargen, L Bittner, S Bonfigt et al. The soft x-rayfree-electron laser FLASH at DESY: beamlines, diagnostics and end-stations.New J. Phys. 2009,11(02):3029
[10] Williams, G. P. FAR-IR/THz radiation from the Jefferson Laboratory, energyrecovered linac, free electron laser. 2002 ,73(3):1461-1463
[11] B. G. Danly et al. IEEE J. Quan. Electron. 1987,23:1739.
[12]杨中海，卢波，彭良福.自由电子激光在生物医学与材料科学中的应用.科技大学出版社, 1991
[13]熊春乐,艾颖,张启仁,郭东升. Kapitza_Dirac效应的GAC理论及其应用.物理学进展, 2004, 24(1):106-126
[14] Dong-sheng Guo, Teijio berg and Bernd Crasemann Scattering theory ofmultiphoton ionization in Strong fields Phys. Rev. A 1989,40(9):4997-5005
[15] Bamber C, Boege S J, Koffas T, et al. Studies of nonlinear QED incollisions of 46.6 GeV electrons with intense laser pulses. Phys. Rev. D,1999, 60(09): 2004.
[16] C. Bula, K. T. McDonald, and E. J. Prebys, et al. Observation of NonlinearEffects in Compton Scattering. Phys. Rev. Lett. 1996,76(17): 3116–3119.
[17] Heinzl T, Seipt D , Kampfer B. Beam-shape effects in nonlinear Comptonand Thomson scattering. Phys. Rev. A, 2010, 81(02): 2125.
[18] Madalina Boca, Viorica Florescu. Nonlinear Compton scattering with a laserpulse. Phys. Rev. A, 2009, 80 (05): 3403.
[19]王平晓,霍裕昆,孔青,袁祥群,曹娜,邵磊.真空中激光加速电子的特性和机制.Strong Field Laser Physics--Proceedings of CCAST (World Laboratory)Workshop, 2000
[20] H. K. Avetissian and G. F. Mkrtchian. Nonlinear quantum regime of the x-rayCompton laser. Phys. Rev. E, 2002, 65(4):6505
[21]郝东山.多光子康普顿效应下的自由电子激光中电子与光子碰撞截面的特性.信阳师范学院学报(自然科学版), 1998, 11(3):242-244
[22]姜孟瑞,梁大光,孙和丽.相对论性电子的Compton散射.山东师范大学学报（自然科学版）, 2010, 25(3):37-39
[23] Singhal R. P. and Burns A. J. . Verification of Compton collision andKlein-Nishina formulas-an undergaruduate laboratory experiment. Am. J.Phys.,1978, 46(6):646-649
[24] H. Al Abawi, F. A. Hopf, and P. Meystre. Electron dynamics in a free electronlaser. Phys. Rev. A, 1977,16(2):666-671
[25] V. Yakimenko and I. V. Pogorelsky. Polarizedγsource based on Comptonbackscattering in a laser cavity. Phys. Rev. ST Accel. Beams, 2006,9(9):1001
[26] Chen J,Imasaki k,Fujita M,Yamanaka C,Asakawa M,Nakai S,Asakuma T 1994Nucl.Instr. and Meth. in Phys.Res.A 341 346.
[27] Yasunori Tanimoto, Tohru Honda, and Shogo Sakanaka. Experimentaldemonstration and visual observation of dust trapping in an electronstorage ring. Phys. Rev. ST Accel. Beams, 2009,12(11):0702
[28] J. X. Wang and Y. K. Ho. Energy-exchange characteristics in ordinary andnonlinear Compton scattering. Phys. Rev. A, 1999, 59(6):4522-4529
[29] Anthony Hartin. On the equivalence of semi-classical methods for QED inintense external fields. J. Phys.:Conf. Ser., 2009,198(1): 2004
[30] V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, in QuantumElectrodynamics, Course of Theoretical Physics, 2nd ed., translated fromRussian by T. B. Sykes and J. S. Bell Pergamon, New York, 1982, Vol. 4
[31] JOHN F. DAWSON, ZOLTAN FRIKD. Plane-Wave Packets and Their Limitation inNonlinear Compton Scattering. Phys. Rev. D, 1970, 1(12):3363-3370
[32] Milton D. Slaughter. Electron-laser pulse scattering. Phys. Rev. D, 1975,11(6):1639-1648
[33] Bergou J, Varro S. Nonlinear scattering processes in the presence of aquantised radiation field:II Relativistic treatment. J. Phys. A, 1981,81(09):2281.
[34] Gudrid Moortgat-Pick. The Furry Picture. J. Phys.:Conf. Ser.,2009,198(1):2002
[35] Dirac PAM The principles of quantum Mechanics. 4-th edn,Clarendon,London,1983
[36] J. Autschbach, W. H. E. Schwarz. Relativistic electron densities in thefour-component Dirac representation and in the two-component pictureHydrogen-like systems. Theor Chem Acc. 2000,104(1):82-88
[37] J. M. J. Madey. Relationship between Mean Radiated Energy, Mean SquareRadiated Energy and Spontaneous Power Spectrum in a Power Series Expansionof the Equation of Motion in a Free-Electron Laser. IL NUOVO CIMENTO, 1979,50(1):64-88
[38] S.Ya. Tochitsky, O.B. Williams, P. Musumeci, C. Sung, D. J. Haberberger,A.M. Cook, J. B. Rosenzweig, and C. Joshi. Efficient harmonic microbunchingin a 7th-order inverse-free-electron laser interaction. Phys.Rev.STAB.,2009,12(5):050703
[39] P. Sprangle, B. Hafizi, and J. R. Pe ano. Laser-pumped coherent x-rayfree-electron laser. Phys. Rev. STAB., 2009, 12(5):050702
[40] Richard Talman, Nikolay Malitsky, Frank Stulle. Emittance growth due tostatic and radiative space charge forces in an electron bunch compressor.Phys. Rev. STAB., 2009, 12(1):014201
[41] U.D. Jentschura1, and V.G. Serbo. Generation of High-Energy Photons withLarge Orbital Angular Momentum by Compton Scattering. Phys. Rev. Lett.,2011, 106(1):013001
[42] Erik L tstedt, and Ulrich D. Jentschura. Nonperturbative Treatment ofDouble Compton Backscattering in Intense Laser Fields. Phys. Rev. Lett.,2009, 103(11):110404
[43] Y. I. Salamin. Forward and backscattered ultrahigh-intensity Comptonspectra in a uniform magnetic field. Phys. Rev. A, 1999, 60(4):3276-3283
[44] F. Glotin, J.-M. Ortega, R. Prazeres, G. Devanz, and O. Marcouillé. TunableX-Ray Generation in a Free-Electron Laser by Intracavity ComptonBackscattering. Phys. Rev. Lett., 1996, 77(15):3130-3132
[45] W. Beall Fowler and D. L. Dexter. Relation between Absorption and EmissionProbabilities in Luminescent Center in Ionic Solids. Phys. Rev., 1962,128(5):2154-2165
[46]喀兴林.高等量子力学第二版[M].北京：高等教育出版社,2001
[47] Loudon R (Translated by Yu Liang). Quantum Theory of Optic. Beijing:HigherEducation Press, 1992, 225-226.
[48] V. L. Ginsburg. The Relativistic Theory of Excited Spin States of the Protonand the Neutron. Phys. Rev., 1943, 63(1):1-12
[49] E. Fermi and L. Marshall. On the Interaction Between Neutrons and Electrons.Phys. Rev. 1947, 72(12):1139-1146
[50] Mathan Rosen. Statistical Geometry and Fundamental Particles. Phys. Rev.,1947, 72(4):298-303
[51] A. I. Nikishov and V. I. Ritus. Pair Production by a Photon and PhotonEmission By an Electron in The Field of an Intense Electromagnetic Waveand In a Constant Field. Sov. Phys. JETP., 1967, 25(6):1135
[52]郭硕鸿.电动力学.第二版.北京：高等教育出版社，1997
[53]刘树杞等.量子电子学.天津：天津科学技术出版社，1990
[54] Joseph Kupersztych. Question of Unitarity of Foldy-WouthuysenTransformations and Volkov States in Two-Component Forms. Phys. Rev. Lett.,1979, 42(8):483-486
[55] S. Elhandi, S. Taj, and Y. Attaourti. Electron’s anomalousmagnetic-moment effects on electron-hydrogen elastic collisions in thepresence of a circularly polarized laser field. Phys. Rev. A, 2010,81(4):043422
[56] W. H. Furry. On Bound States and Scattering in Positron Theory. Phys. Rev.,1951, 81(1):115-124
[57] MATTHIAS HUBER and EDGARDO STOCKMEYER. Perturbative Implementation of theFurry Picture. Letters in Mathematical Physics, 2006, 79(1):99-108
[58] S. P. Gavrilov. The furry picture for the standard electroweak theory witha free non-Abelian external field. Elementary Particle Physics And FieldTheory, 1993, 35(10):969-973
[59] A. Vaidya, C. Farina and M. Hott. Furry’s picture in the path integralframework. IL Nuovo Cimento A, 1992, 105(7):925-934
[60] V. Ch. Zhukovsky, A. E. Lobanov, and E. M. Murchikova. Radiative effectsin the standard model extension. Phys. Rev. D, 2006, 73(6):065016
[61] R. A. Neville and F. Rohrlich. Quantum Electrodynamics on Null Planes andApplications to Lasers. Phys. Rev. D, 1971, 3(8):1692-1707
[62] Dorin Cezar Ionescu. Unitarity and electron-positron pairs created bystrong external fields. Phys. Rev. A, 1994, 49(5):3188-3195
[63] Chris Harvey and Thomas Heinzl. Signatures of high-intensity Comptonscattering. Phys. Rev. A, 2009, 79(6):063407
[64] H. PRAKASH, R. GOYAL and VACHASPATI. Effect of Coherence onIntensity-Dependent Frequency Shift in Compton Scattering. LETTERE ALNUOVO CIMENTO, 1971, 1(19):771-774
[65] F.V. Hartemann and A.K. Kerman. Classical Theory of Nonlinear ComptonScattering. Phys. Rev. Lett., 1996, 76(4):624-627[66] Frederic V. Hartemann, Félicie Albert, Craig W. Siders, and C. P. J. Barty.Low-Intehsity Nonlinear Spectral Effects in Compton Scattering. Phys. Rev.Lett., 2010, 105(13):130801