摘要
本论文在相对论性电子辐射的自旋修正和介质效应两个课题上开展工作。作为论文工作的出发点,对电子辐射理论做了介绍,特别是对Jefimenko公式及其在介质状况下的推广形式,以及运动点电荷和偶极子电磁场的Heaviside-Feynman表达式作了综述。计入电子自旋,计算电子辐射的频谱角分布、频率分布、角分布和偏振。根据所得计算结果,考察储存环电子束流极化度与同步辐射光偏振度之间的关系,据此提出一种通过测量辐射光偏振度来得到电子束极化度的方法。从介质中的Maxwell方程组出发,考察介质中运动带电粒子的辐射机制,推导了其辐射频谱角分布的一般公式。对于在介质中超光速运动的带电粒子,分析指出稳定相位点在Cherenkov效应中所起的关键作用,并据此提出稳定相位法,和文献已有工作相比该方法解决本问题具有更大的通用性和应用性。由此计算了同步Cherenkov辐射在小角度以及临界角度处的频谱分布,指出了同步Cherenkov辐射在临界角处的频谱的不同特点。
This dissertation on radiation from a relativistic electron focuses on two topics, the spin modification and the medium effect. As the basis for the investigations, a comprehensive review on the classical radiation theory is made. The Jefimenko formulas and their generalization, as well as Heaviside-Feynman expression for fields generated by moving charge and dipole, are covered. A general expression for the spectral-angular distribution of the radiation energy from a relativistic electron with magnetic moment is obtained. Hence the spectral distribution of radiation in two polarizations from a relativistic synchronous electron is calculated including the modification of electron's magnetic moment. The relationship between the polarizations of the synchronous electrons and the radiation fields, which suggests getting information about spin polarization of electron beam from measuring the polarization of the synchrotron radiation, is provided. The general expression for spectral-angular distribution of the radiation emitted by a charged particle moving in exterior medium is derived from Maxwell equations in medium. On this expression which includes a Fourier type integral, the essential role of stationary phase points in Cherenkov effect is analyzed and stated definitely. Therefore for the calculation of synchrotron-Cherenkov radiation from charged particle moving in curved orbit the stationary phase method is proposed, which is more versatile and applicable compared with the exiting two kinds treatments in literatures. Consequently the spectral distribution of synchrotron-Cherenkov radiation is calculated by stationary phase method, and the result indicates the spectrum of synchrotron-Cherenkov radiation in directions near critical angle is quite different from that in the vicinity of the orbit plane.
引文
[I]Schott G A.1907. On the radiation from groups of electrons [J]. Ann. Phys. (Leipzig), 24:635-660.
[2]Schott G A.1912. Electromagnetic Radiation [M], Cambridge U. Press, London.
[3]Tzu H Y.1948. On the Radiation Emitted by a Fast Charged Particle in the Magnetic Field [J]. Proc. R. Soc. Lond. A 192:231-246.
[4]Schwinger J.1949. On the classical radiation of accelerated electrons [J]. Phys. Rev. 75:1912-1915.
[5]Schwinger J.1954. The Quantum Correction in the Radiation by Energetic Accelerated Electrons [J]. Proc. Nat. A. S.40:132-136.
[6]Khokonov M Kh, Nitta H.2002. Standard Radiation Spectrum of Relativistic Electrons Beyond the Synchrotron Approximation [J]. Phys. Rev. Lett.89:094801.
[7]Frolov I E, Zhukovsky V Ch.2007. Synchrotron radiation in the standard model extension [J]. J. Phys. A:Math. Theor.40:10625-10640
[8]谢家麟.2002.电子-光子相互作用的应用与自由电子激光的发展[J].中国科学院研究生院学报,19(1):7-17.
[9]Jackson J D.2001. Classical Electrodynamics (3rd Ed.) [M], New York:John Wiley & Sons,INC.
[10]尤峻汉.1998.天体物理中的辐射机制(第二版)[M],北京:科学出版社.
[11]Kim K J.1989. Characteristic of Synchrotron Radiation [J]. AIP Conf. Proc.184:565-632.
[12]Chunxi Wang.1993. Concise expression of a classical radiation spectrum[J]. Phys. Rev.,E 47: 4358-4363.
[13]Lindhard Jens.1991. Quantum-radiation spectra of relativistic particles derived by the correspondence principle [J]. Phys. Rev. A 43:6032-6037.
[14]Patterson B D.2011. A simplified approach to synchrotron radiation [J]. Am. J. Phys. 79:1046-1052.
[15]Kim K J.2009. Characteristics of Synchrotron Radiation, in X-ray Data Booklet, October 2009, PPⅡ.1-6.
[16]Nakamura K et al (Particle Data Group).2010. Review of Particle Physics [J]. J. Phys. G: Nucl. Part. Phys.37:075021.
[17]Klein J J.1968. Motion of a Charged Particle in a Uniform Magnetic Field [J]. Rev. Mod. Phys.40:523-530.
[18]Bordovitsyn V A, Ternov I M, Bagrov V G.1995. Spin light [J]. Phys. Usp.38:1037-1047.
[19]Bordovistyn V A, Gushchina V S, Ternov I M.1995. Structural composition of synchrotron radiation [J]. Nucl. Instr. Meth. A 359:34-57.
[20]Kulipanov G N, Bondar A E, Bordovitsyn V A, Gushchina V S.1998. Synchrotron radiation and spin light [J]. Nucl. Instr. Meth. A 405:191-194.
[21]Bordovitsyn V A, Telushkin V V.2008. Spin light identification in the presence of power synchrotron radiation [J]. Nucl. Instr. Meth. B 266:3708-3714.
[22]Miroslav Pardy.2009. The Bremsstrahlung Equation for the Spin Motion in Electromagnetic Field [J]. Int. J. Theor. Phys.48:3241-3248.
[23]Bordovistyn V A, Konstantinova O A.2012. Spin light of a neutron in classical and quantum theories [J]. J. Phys.:Conf. Ser.357:012007.
[24]Monaghan J J.1968. The Heaviside-Feynman expression for the fields of an accelerated dipole [J]. J. Phys. A:Gen. Phys.1:112-117.
[25]Heras Jose A.1994. Radiation fields of a dipole in arbitrary motion [J], Am. J. Phys. 62:1109-1115.
[26]Heras Jose A.1998. Explicit expressions for the electric and magnetic fields of a moving magnetic dipole [J]. Phys. Pev. E 58:5047-5056.
[27]Arzimovich L, Pomeranchuk I Ya.1945. The Radiation of Fast Electrons in the Magnetic Field [J]. J. Phys. USSR 9:267.
[28]Schwinger J.1946. Electron Radiation in High Energy Accelerators [J]. Phys. Rev. 70:798-799.
[29]Latal H G.1977. Quantum Modifications in Magnetic Bremsstrahlung [J]. Ann. Phys. 108:408-442.
[30]Kuznetsov A S.1993. Asymmetry of the Angular Distribution of the Il-Component of Synchrotron Radiation (SR), Caused by Electron Spin Polarization along the Acceleration Vector [J]. Europhys. Lett.21:545-549.
[31]Sokolov A A, Ternov I M.1964. On Polarization and Spin Effects in the Theory of Synchrotron Radiation [J]. Sov. Phys. Dokl.8:1203.
[32]Chao A.1981. Polarization of a stored electron beam. SLAC-PUB-2781.
[33]Chao A.2012. Lecture Notes on Special Topics in Accelerator Physics. SLAC-PUB-9574.
[34]Baler V N.1972. Radiative polarization of electrons in storage rings [J]. Sov. Phys. Usp. 14:695-714.
[35]Bagrov V G, Dolzhin M V.2007. Dependence of spectral-angular distribution of synchrotron radiation from spin orientation [J]. Nucl. Instr. Meth. A 575:231-233.
[36]Potylitsyn A P.2010. Coherent synchrotron radiation and radiative electron polarization [J]. J. Phys. G:Nucl. Part. Phys.37:115106.
[37]张剑锋.2009.电子储存环上束流自发极化的研究及应用[D]:[博士].合肥:中国科学技术大学,71-91.
[38]Ginzburg V L.1996. Radiation by uniformly moving sources (Vavilov-Cherenkov effect, transition radiation, and other phenomena) [J]. Phys. Usp.39:973-982.
[39]Bolotovskii B M.2009. Vavilov-Cherenkov radiation:its discovery and application [J]. Phys. Usp.52:1099-1110.
[40]Afanasiev G N.2005. Vavilov-Cherenkov and Synchrotron Radiation:Foundations and Applications [M], Kluwer Academic Publishers.
[41]Schwinger J, Tsai Wu-Yang, Erber T.1976. Classical and Quantum Theory of Synergic Synchrotron-Cerenkov Radiation [J]. Ann. Phys.96:303-332.
[42]Erber T, White D, Tsai Wu-Yang, Latal H G.1976. Experimental Aspects of Synchrotron-Cerenkov Radiation [J]. Ann. Phys.102:405-447.
[43]Rynne T M, Baumgartner G B, Erber T.1978. The angular distribution of synchrotron-Cerenkov radiation [J]. J. Appl. Phys.49:2233-2240.
[44]Rynne T M. Synchrotron-Cerenkov detectors for electrons [J]. J. Appl. Phys.50:5572-5578.
[45]Patro D N.1982. Microscopic Theory of Synchrotron-Cherenkov Radiation [J]. Phys. Rev. Lett.49:1083-1086.
[46]Bonin K D, McDonald K T, Russell D P, Flanz J B.1986. Observation of Interference between Cerenkov and Synchrotron Radiation [J]. Phys. Rev. Lett.57:2264-2267.
[47]Pratap R, Sasidharan K, Krishan V.1993. Characteristics of synchrotron Cerenkov radiation [J]. Phys. Rev. E 47:640-655.
[48]McDonald K T.2004. Synchrotron-Cerenkov Radiation [J]. Science 303:310.
[49]Konstantinovich A V, Konstantinovich I A.2008. Oscillations in radiation spectrum of electron moving in spiral in transparent medium and vacuum [J]. Astropart. Phys. 30:142-148.
[50]Saharian A A, Kotanjyan A S.2009. Synchrotron radiation from a charge moving along a helix around a dielectric cylinder [J]. J. Phys. A:Math. Theor.42:135402.
[51]Soln J.1999. Strong magnetic field helical Cerenkov effect with some astrophysical implications [J]. Astron. Nachr.320:141-146.
[52]Konstantinovich A V, Melnychuk S V, Konstantinovich I A.2006. Radiation spectrum of an electron moving in a spiral in magnetic field in transparent medium and in vacuum [J]. J. Mater. Sci:Mater Electron 17:315-320.
[53]Griffiths D J, Heald M A.1991. Time-dependent generalizations of the Biot-Savart and Coulomb laws [J]. Am. J. Phys.59:111-117.
[54]Bellotti U, Bornatici M.1996. Time-dependent, generalized Coulomb and Biot-Savart laws: A derivation based on Fourier transforms [J]. Am. J. Phys.64:568-570.
[55]Heras Jose A.1998. New approach to the classical radiation fields of moving dipoles [J]. Phys. Lett. A 237:343-348.
[56]Heras Jose A.1994. Jefimenko's formulas with magnetic monopoles and the Lienard-Wiechert fields of a dual-charged particle [J]. Am. J. Phys.62:525-531.
[57]Neuenschwander D E, Turner B N.1992. Generalization of the Biot-Savart law to Maxwell's equations using special relativity [J]. Am. J. Phys.60:35-38.
[58]Jefimenko Oleg D.1992. Solutions of Maxwell's equations for electric and magnetic fields in arbitrary media [J]. Am. J. Phys.60:899-902.
[59]Heras Jose A.1995. Time-dependent generalizations of the Biot-Savart and Coulomb laws:A formal derivation [J]. Am. J. Phys.63:928-932.
[60]McDonald K T.1997. The relation between expressions for time-dependent electromagnetic fields given by Jefimenko and by Panofsky and Phillips [J]. Am. J. Phys.65:1074-1076.
[61]Jefimenko Oleg D.2004. Presenting electromagnetic theory in accordance with the principle of causality [J]. Eur. J. Phys.25:287-296.
[62]Jefimenko Oleg D.1966. Electricity and Magnetism [M]. New York: Appleton-Century-Crofts.
[63]Ton Tran-Cong.1991. On the time-dependent, generalized Coulomb and Biot-Savart laws [J]. Am. J. Phys.59:520-528.
[64]拉夫连季耶夫M A,沙巴特Б B.2006.复变函数论方法(第6版)[M].北京:高等教育出版社.
[65]Feynman R P.1965. The Feynman Lectures on Physics [M], Reading, MA:Addison-Wesley.
[66]王竹溪,郭敦仁.2000.特殊函数概论[M].北京:北京大学出版社.
[67]Wiedemann H.2003. Particle Accelerator Physics (Ⅰ & Ⅱ, study edition) [M], Berlin: Springer Verlag.
[68]刘当波,尤峻汉.2008.切仑科夫线状辐射在类星体宽发射线起源探讨中的重要性(讲稿).上海交通大学物理系.
[69]You Jun-han, Cheng Fu-hua, Cheng Fu-zhen, Kiang T.1986. Cerenkov line radiation [J]. Phys. Rev. A 34:3015-3021.
[70]de Vries K D, van den Berg A M, Scholten O, Werner K.2011. Coherent Cherenkov Radiation from Cosmic-Ray-Induced Air Showers [J]. Phys. Rev. Lett.107:061101.
[71]Bender C M & Orszag S A.1999.Advanced Mathematical Methods for Scientists and Engineers[M], Berlin:Springer-Verlag.
[72]Griffiths D J.2005. Introduction to Electrodynamics (3rd Ed.) [M]. Prentice Hall.
[73]Watson G N.1995. A Treatise on the Theory of Bessel Functions (2nd Ed.) [M]. Cambridge University Press.
[74]Rutt H N.2003. On the evaluation of modified Bessel functions of the second kind and fractional order for synchrotron radiation calculations [J]. Nucl. Instrum. Methods Phys. Res. A 511:431-436.
[75]金玉明.2001.电子储存环物理(第2版)[M].合肥:中国科技大学出版社.
[76]李家春,周显初.2002.数学物理中的渐近方法[M].北京:科学出版社.
[77]Copson E T.1965. Asymptotic Expansions [M]. Cambridge University Press.