自由电子激光中有关非线性效应的若干研究
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摘要
非线性是自由电子激光系统所具有的普遍特征,本论文研究自由电子激光系统的一些非线性相关问题。作为论文工作基本出发点,对自由电子激光的基本理论作了细致推导。在相对论性电子非理想入射的情况下,对波荡器中的自发辐射频谱进行了解析推导和数值计算,并与电子理想入射的相应结果进行了对比。对具有轴向引导场的螺旋型波荡器中的电子行为进行了分析,对于忽略自场影响的可积情况,考察电子轨道的周期和准周期情况的判据,以及满足稳定螺旋轨道的条件；进而分析强自场情况下电子运动的混沌特性,利用庞加莱截面方法对于电子的混沌行为进行定性分析和确认。通过对近可积系统的理论分析,和对电子轨道数值模拟结果的李雅普诺夫指数计算,分别得到系统达到完全混沌的临界条件。在波荡器高阶磁场和自场同时作用情况下,分析电子横向运动,考察电子受横向约束的条件。基于Colson-Bonifacio自由电子激光解析理论,建立了一维稳态自由电子激光的Mathematica数值模拟程序,对于高增益自由电子激光中自场的影响做了理论分析和模拟计算。对近年国外研究人员新提出的自由电子激光系统饱和状态分析的统计物理方法做了修正,使之能适用于包含自场的情况,由此考察和分析自场对自由电子激光饱和光强的影响。
Nonlinearity is universal for the free-electron lasers. This dissertation focuses on some problems related to the nonlinear behaviors in free-electron lasers. A detailed discussion of the basic FEL theory is provided, and this is the basis for our investigations. For a relativistic electron which is nonideally injected into an undulator, the spontaneous radiation spectrum is calculated theoretically and numerically, and a comparison with the corresponding results for ideally injected electron is made. The motion of electrons in a helical undulator with axial guiding field is analyzed. For the intergrable case when the self-field is neglected, the criterion of periodic or quasiperiodic electron orbit is investigated, as well as the initial condition for stable helical orbit. Further the chaotic properties of electrons motion for strong self-field regime are investigated. The chaotic nature is qualitative manifested and confirmed using Poincare maps method; under some theoretical analysis of nearly integrable system and the calculation of Lyapunov exponents for electron trajectories using numerical simulation, the threshold value of the self-field parameter for chaos is obtained respectively. The transverse motions of electron with both self-field and high-order wiggler field are analyzed, with an investigation on the confinement condition of electrons. Based on Colson-Bonifacio FEL theory, a numerical simulation code for 1-D steady state FEL is composed, hence the influence of self-field effect on output radiation field for high-gain FEL can be analyzed and numerical calculated. A novel statistical method for FEL saturation proposed by Julien Barre et. al. is modified in order to be adoptable to systems with self-field effect, via this method the influence of self-field on radiation intensity at saturation is investigated.
Nonlinearity is universal for the free-electron lasers. This dissertation focuses on some problems related to the nonlinear behaviors in free-electron lasers. A detailed discussion of the basic FEL theory is provided, and this is the basis for our investigations. For a relativistic electron which is nonideally injected into an undulator, the spontaneous radiation spectrum is calculated theoretically and numerically, and a comparison with the corresponding results for ideally injected electron is made. The motion of electrons in a helical undulator with axial guiding field is analyzed. For the intergrable case when the self-field is neglected, the criterion of periodic or quasiperiodic electron orbit is investigated, as well as the initial condition for stable helical orbit. Further the chaotic properties of electrons motion for strong self-field regime are investigated. The chaotic nature is qualitative manifested and confirmed using Poincare maps method; under some theoretical analysis of nearly integrable system and the calculation of Lyapunov exponents for electron trajectories using numerical simulation, the threshold value of the self-field parameter for chaos is obtained respectively. The transverse motions of electron with both self-field and high-order wiggler field are analyzed, with an investigation on the confinement condition of electrons. Based on Colson-Bonifacio FEL theory, a numerical simulation code for 1-D steady state FEL is composed, hence the influence of self-field effect on output radiation field for high-gain FEL can be analyzed and numerical calculated. A novel statistical method for FEL saturation proposed by Julien Barre et. al. is modified in order to be adoptable to systems with self-field effect, via this method the influence of self-field on radiation intensity at saturation is investigated.
引文
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[2]Wiedemann H.2003. Particle Accelerator Physics (Ⅰ & Ⅱ, study edition)[M], Springer Verlag.
[3]惠钟锡,杨震华.1995.自由电子激光[M].北京：国防工业出版社.
[4]Saldin E L, Schneidmiller E A, Yurkov M V.1995.The physics of free electron lasers. An introduction[J], Physics Reports,260:187-327
[5]Saldin E L, Schneidmiller E A, Yurkov M V.2000. The Physics of Free Electron Lasers (Advanced Texts in Physics)[M], Springer-Verlag, Berlin.
[6]Colson W B, Pegrini C, Renieri A,胡克松,钱民权等译.1993.激光手册(6)：自由电子激光[M].科学城.38-39
[7]Dattoli G, Renieri.1985. Experimental and theoretical aspects of free-electron laser, in M.L Stitch and M. Bass, Laser handbook(4)[M]. Amsterdam:North-Holland Pub. Co.
[8]Ciocci F, Dattoli G, Torre A & Renieri A.2000. Insertion Devices for Synchrotron Radiation and Free Electron Laser (Series on Synchrotron Radiation Techniques and Applications-Vol.6)[M]. World Scientific Publishing Co.
[9]Milton S et al.2001. Exponential Gain and Saturation of a Self-Amplified Spontaneous Emission Free-Electron Laser[J]. Science,292,2037.
[10]Prazeres R, Ortega J M, Bazin C et al.1988. Coherent harmonic generation in the vacuum ultraviolet spectral range on the storage ring ACO[J]. Nucl. Instrum. Meth. A,272:68-72.
[11]Yu L H, Babzien M, et al.2000. High-Gain Harmonic-Generation Free-Electron Laser[J]. Science,289:932-934.
[12]Plonjes E et al.2003.Taking free-electron lasers into the X-ray regime[J]. Phys. World, 16(7):33.
[13]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.
[14]谢家麟.1995.自由电子激光的研究及应用前景.中国科学院院士谈21世纪科学技术[M].上海：上海三联书店.
[15]O'Shea P G, Freund H P.2001. Free-electron lasers:status and applications[J]. Science,292: 1853-1858.
[16]Kapitza P L, Dirac PAM.1933. The reflection of electrons from standing light waves[J], Proc. Cambr. Phil. Soc.29:297.
[17]Motz H.1951. Applications of the Radiation form Fast Electron Beams[J], J. Appl. Phys,22: 527.
[18]Motz H, Thon H, Whitehurst R N.1953. Experiments on Radiation by Fast Electron Beams [J]. Appl. Phys,24:826.
[19]Phillips R M.1960. IRE Trans Electron Devices,7:231.
[20]Pantell R H, et al.1968. J. Quan. Elect,4:905.
[21]Bonifacio R, Pellegrini C, Narducci L M.1984. Exponential gain and self-bunching in a collective atomic recoil laser[J], Opt. Comm.50:373.
[22]Madey JMJ.1971. Stimulated Emission of Bremsstrahlung in a Periodic Magnetic Field[J]. J. Appl. Phys,42:1906.
[23]Deacon D A G, et al.1977. First Operation of a Free-Electron Laser[J]. Phys. Rev. Lett, 38:892.
[24]Marshall T C, et.al.1977. High-power millimeter radiation from an intense relativistic electron beam device[J], Appl. Phys. Lett,31:320.
[25]Vinokurov N A and Skrinsky A N.1979. On ultimate Power of the Optic Klystron Installed on the Electron storage Ring[J], Inst. of Nuclear Phys., Novosibirsk,
[26]褚成,卢载通,施瑞根等.1985.喇曼自由电子激光器的实验研究[J].中国激光,12(12)：767.
[27]谢家麟,庄杰佳,钟世材等.1989.北京自由电子激光装置的设计研究[J].强激光与粒子束,1(4)：289.
[28]谢家麟,庄杰佳,黄永章等.1994.北京自由电子激光最近进展—实现饱和振荡[J].高能物理与核物理,18(8)：763-768.
[29]惠钟锡.1990.曙光一号自由电子激光装置的设计研究[J].强激光与粒子束,2(3)：257.
[30]李传胪,刘永贵等.1991.圆波导契伦柯夫自由电子激光流体描述[J].强激光与粒子束,3(2)：136.
[31]李传胪,刘永贵等.1991.圆波导契伦柯夫自由电子激光的单粒子理论[J].强激光与粒子束,3(2)：147.
[32]Neil G R, Merminga L.2002. Technical approaches for high-average-power free-electron lasers[J]. Rev. Mod. Phys.74,685.
[33]刘静,舒挺,张军.2007.Research Development on Free Electron Laser in Europe[J],激光与光电子学进展,44(6)：43.
[34]陈森玉,何多慧.1999.SSRF深紫外自由电子激光实验装置的前期研究项目建议书.上海(内部资料).
[35]Billardon M.1990. Storage ring free-electron laser and chaos[J]. Phys. Rev. Lett,65:713.
[36]Wang W J, Wang G R, Chen S G.1995. Phenomenological description of the optical field chaos in storage ring free-electron lasers[J]. Phys. Rev. E,51:653.
[37]Ninno G D, Fanelli D.2004. Analytical theory and control of the longitudinal dynamics of a storage ring free-electron laser[J]. Phys. Rev. E,70:016503.
[38]Li Y L, Krinsky S, Lewellen J W.2003. Characterization of a chaotic optical field using a high-gain self-amplified Free-Electron Laser[J]. Phys.Rev.Lett,91:243602.
[39]Bielawski S, Bruni C, Orlandi G L, et al.2004. Suppression of the pulsed regimes appearing in free electron lasers using feedback control of an unstable stationary state[J]. Phys. Rev. E, 69:045502.
[40]Ninno G D, Fanelli D.2004.Controlled Hopf Bifurcation of a Storage-Ring Free-Electron Laser[J]. Phys.Rev.Lett,92:094801.
[41]霍裕平.1982.变参数自由电子激光器中电子的随机运动[J].物理学报,31(10)：1337.
[42]Chen C P,1988. Schmidt G. Comments Plasma Phys. Controlled Fusion.12,83.
[43]Riypoulos S, Tang C M.1988. The structure of the sideband spectrum in free electron lasers[J]. Phys. Fluids,31:1708.
[44]Chen C P, Davidson R C.1990. Self-field-induced chaoticity in the electron orbits in a helical wiggler free-electron laser with axial guide field [J]. Phys. Fluids. B,2:171.
[45]Michel L, Bourdier A and Buzzi J M.1991. Nucl. Instr.& Meth. A.304:465.
[46]Michel L, Bourdier A and Buzzi J M.1992. Nucl. Instr.& Meth. A.318:568.
[47]Michel L, Bourdier A and Buzzi J M.1993. Phys. Fluids. B,5:965.
[48]Bonifacio R, Casagrande F and Lugiato L A.1981. Opt. Commun.36:159.
[49]Bonifacio R, Casagrande F and Casati G.1982. Opt. Commun.40:219.
[50]张世昌,胡秀忠,王文耀.1990.常参数波荡器自由电子激光中电子相轨道从周期性到非周期性的演化[J].物理学报39：1745.
[51]Esmaeilzadeha M, Fallah M S.2007. Chaotic electron trajectories in a realizable helical wigglerwith axial magnetic field[J]. Physics of Plasmas,14:013103.
[52]Esmaeilzadeha M, Willett J E.2007. Self-fields effects on gain in a free-electron laser with helical wiggler and axial magnetic field [J]. Physics of Plasmas,14:033102.
[53]Schroeder C B, Pellegrini C, Chen P.2001. Quantum effects in high-gain free-electron lasers[J]. Phys. Rev. E,64,056502.
[54]Halbach K.1980. Nucl Instr and Meth,169:1～10.
[55]Halbach K.1981. Nucl Instr and Meth,187:109.
[56]Goldstein H.1980. Classical Mechanics[M], Addison-Wesley, MA.
[57]贾启卡,自由电子激光导论(内部讲义).
[58]Reiche.1999. Numerical studies for a single pass high gain Free-Electron Laser[D]. Hamberg, Hamberg University.
[59]Kim K J and Huang Z R.2003. Introduction to the Physics of FreeElectron Lasers(讲义); Kim K J and Huang Z R.2007.Review of x-ray free-electron laser theory [J]. Phys. Rev. ST Accel. Beams 10,034801
[60]Jackson J D.1999. Classical Electrodynamics, John Wiley & Sons,3rd edition.
[61]王竹溪,郭敦仁.2000.特殊函数概论[M].北京：北京大学出版社.
[62]刘秉正,彭建华.2004.非线性动力学[M].北京：高等教育出版社.
[63]Chen C P, Davidson R C.1991. Chaotic paticle dynamics in free-electron lasers [J]. Phys.Rev.A,43:5541.
[64]Bonnetin G, Galgani L et al.1978. Meccanica Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems[J], C R Academic Sci Puris A,206:431.
[65]Tran T M and Wurtele J S.1990. LRP 392/90, CRPP Report, Lausanne, Switzerland.
[66]Hammersley J M and Handscomb D C.1964. Monte Carlo Methods[M], Methuen, London.
[67]Barre J, Dauxois T, Ninno G,et al.2004. Statistical theory of high-gain free-electron laser saturation[J], Phys Rev E,69:045501.
[68]Antoniazzi A, Ruffo S.2006. An account of the statistical and dynamical properties of systems with long-range interactions[J], Nucl. Instrum. Meth. A,561:143.
[69]BarreJ.2003. Ph.D. thesis[D], ENS Lyon.
[70]Colson W B.1976. Theory of a Free Electron Laser[J]. Phys. Lett. A,59:187,
[71]Lynden-Bell.1967. Statistical mechanics of violent relaxation in stellar systems[J], Mon. Not. R. Astron. Soc,136,101.
[72]Curbis F, Antoniazzi A, Ninno G D, et al.2007. Maximum entropy principle and coherent harmonic generation using a single-pass free-electron laser[J], The European Phsyical Journal B,59:527.
[73]李明光.2008.高增益自由电子激光理论分析的一种新方法[D]:[硕士].合肥：中国科学技术大学,51-54.
[2]Wiedemann H.2003. Particle Accelerator Physics (Ⅰ & Ⅱ, study edition)[M], Springer Verlag.
[3]惠钟锡,杨震华.1995.自由电子激光[M].北京：国防工业出版社.
[4]Saldin E L, Schneidmiller E A, Yurkov M V.1995.The physics of free electron lasers. An introduction[J], Physics Reports,260:187-327
[5]Saldin E L, Schneidmiller E A, Yurkov M V.2000. The Physics of Free Electron Lasers (Advanced Texts in Physics)[M], Springer-Verlag, Berlin.
[6]Colson W B, Pegrini C, Renieri A,胡克松,钱民权等译.1993.激光手册(6)：自由电子激光[M].科学城.38-39
[7]Dattoli G, Renieri.1985. Experimental and theoretical aspects of free-electron laser, in M.L Stitch and M. Bass, Laser handbook(4)[M]. Amsterdam:North-Holland Pub. Co.
[8]Ciocci F, Dattoli G, Torre A & Renieri A.2000. Insertion Devices for Synchrotron Radiation and Free Electron Laser (Series on Synchrotron Radiation Techniques and Applications-Vol.6)[M]. World Scientific Publishing Co.
[9]Milton S et al.2001. Exponential Gain and Saturation of a Self-Amplified Spontaneous Emission Free-Electron Laser[J]. Science,292,2037.
[10]Prazeres R, Ortega J M, Bazin C et al.1988. Coherent harmonic generation in the vacuum ultraviolet spectral range on the storage ring ACO[J]. Nucl. Instrum. Meth. A,272:68-72.
[11]Yu L H, Babzien M, et al.2000. High-Gain Harmonic-Generation Free-Electron Laser[J]. Science,289:932-934.
[12]Plonjes E et al.2003.Taking free-electron lasers into the X-ray regime[J]. Phys. World, 16(7):33.
[13]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.
[14]谢家麟.1995.自由电子激光的研究及应用前景.中国科学院院士谈21世纪科学技术[M].上海：上海三联书店.
[15]O'Shea P G, Freund H P.2001. Free-electron lasers:status and applications[J]. Science,292: 1853-1858.
[16]Kapitza P L, Dirac PAM.1933. The reflection of electrons from standing light waves[J], Proc. Cambr. Phil. Soc.29:297.
[17]Motz H.1951. Applications of the Radiation form Fast Electron Beams[J], J. Appl. Phys,22: 527.
[18]Motz H, Thon H, Whitehurst R N.1953. Experiments on Radiation by Fast Electron Beams [J]. Appl. Phys,24:826.
[19]Phillips R M.1960. IRE Trans Electron Devices,7:231.
[20]Pantell R H, et al.1968. J. Quan. Elect,4:905.
[21]Bonifacio R, Pellegrini C, Narducci L M.1984. Exponential gain and self-bunching in a collective atomic recoil laser[J], Opt. Comm.50:373.
[22]Madey JMJ.1971. Stimulated Emission of Bremsstrahlung in a Periodic Magnetic Field[J]. J. Appl. Phys,42:1906.
[23]Deacon D A G, et al.1977. First Operation of a Free-Electron Laser[J]. Phys. Rev. Lett, 38:892.
[24]Marshall T C, et.al.1977. High-power millimeter radiation from an intense relativistic electron beam device[J], Appl. Phys. Lett,31:320.
[25]Vinokurov N A and Skrinsky A N.1979. On ultimate Power of the Optic Klystron Installed on the Electron storage Ring[J], Inst. of Nuclear Phys., Novosibirsk,
[26]褚成,卢载通,施瑞根等.1985.喇曼自由电子激光器的实验研究[J].中国激光,12(12)：767.
[27]谢家麟,庄杰佳,钟世材等.1989.北京自由电子激光装置的设计研究[J].强激光与粒子束,1(4)：289.
[28]谢家麟,庄杰佳,黄永章等.1994.北京自由电子激光最近进展—实现饱和振荡[J].高能物理与核物理,18(8)：763-768.
[29]惠钟锡.1990.曙光一号自由电子激光装置的设计研究[J].强激光与粒子束,2(3)：257.
[30]李传胪,刘永贵等.1991.圆波导契伦柯夫自由电子激光流体描述[J].强激光与粒子束,3(2)：136.
[31]李传胪,刘永贵等.1991.圆波导契伦柯夫自由电子激光的单粒子理论[J].强激光与粒子束,3(2)：147.
[32]Neil G R, Merminga L.2002. Technical approaches for high-average-power free-electron lasers[J]. Rev. Mod. Phys.74,685.
[33]刘静,舒挺,张军.2007.Research Development on Free Electron Laser in Europe[J],激光与光电子学进展,44(6)：43.
[34]陈森玉,何多慧.1999.SSRF深紫外自由电子激光实验装置的前期研究项目建议书.上海(内部资料).
[35]Billardon M.1990. Storage ring free-electron laser and chaos[J]. Phys. Rev. Lett,65:713.
[36]Wang W J, Wang G R, Chen S G.1995. Phenomenological description of the optical field chaos in storage ring free-electron lasers[J]. Phys. Rev. E,51:653.
[37]Ninno G D, Fanelli D.2004. Analytical theory and control of the longitudinal dynamics of a storage ring free-electron laser[J]. Phys. Rev. E,70:016503.
[38]Li Y L, Krinsky S, Lewellen J W.2003. Characterization of a chaotic optical field using a high-gain self-amplified Free-Electron Laser[J]. Phys.Rev.Lett,91:243602.
[39]Bielawski S, Bruni C, Orlandi G L, et al.2004. Suppression of the pulsed regimes appearing in free electron lasers using feedback control of an unstable stationary state[J]. Phys. Rev. E, 69:045502.
[40]Ninno G D, Fanelli D.2004.Controlled Hopf Bifurcation of a Storage-Ring Free-Electron Laser[J]. Phys.Rev.Lett,92:094801.
[41]霍裕平.1982.变参数自由电子激光器中电子的随机运动[J].物理学报,31(10)：1337.
[42]Chen C P,1988. Schmidt G. Comments Plasma Phys. Controlled Fusion.12,83.
[43]Riypoulos S, Tang C M.1988. The structure of the sideband spectrum in free electron lasers[J]. Phys. Fluids,31:1708.
[44]Chen C P, Davidson R C.1990. Self-field-induced chaoticity in the electron orbits in a helical wiggler free-electron laser with axial guide field [J]. Phys. Fluids. B,2:171.
[45]Michel L, Bourdier A and Buzzi J M.1991. Nucl. Instr.& Meth. A.304:465.
[46]Michel L, Bourdier A and Buzzi J M.1992. Nucl. Instr.& Meth. A.318:568.
[47]Michel L, Bourdier A and Buzzi J M.1993. Phys. Fluids. B,5:965.
[48]Bonifacio R, Casagrande F and Lugiato L A.1981. Opt. Commun.36:159.
[49]Bonifacio R, Casagrande F and Casati G.1982. Opt. Commun.40:219.
[50]张世昌,胡秀忠,王文耀.1990.常参数波荡器自由电子激光中电子相轨道从周期性到非周期性的演化[J].物理学报39：1745.
[51]Esmaeilzadeha M, Fallah M S.2007. Chaotic electron trajectories in a realizable helical wigglerwith axial magnetic field[J]. Physics of Plasmas,14:013103.
[52]Esmaeilzadeha M, Willett J E.2007. Self-fields effects on gain in a free-electron laser with helical wiggler and axial magnetic field [J]. Physics of Plasmas,14:033102.
[53]Schroeder C B, Pellegrini C, Chen P.2001. Quantum effects in high-gain free-electron lasers[J]. Phys. Rev. E,64,056502.
[54]Halbach K.1980. Nucl Instr and Meth,169:1～10.
[55]Halbach K.1981. Nucl Instr and Meth,187:109.
[56]Goldstein H.1980. Classical Mechanics[M], Addison-Wesley, MA.
[57]贾启卡,自由电子激光导论(内部讲义).
[58]Reiche.1999. Numerical studies for a single pass high gain Free-Electron Laser[D]. Hamberg, Hamberg University.
[59]Kim K J and Huang Z R.2003. Introduction to the Physics of FreeElectron Lasers(讲义); Kim K J and Huang Z R.2007.Review of x-ray free-electron laser theory [J]. Phys. Rev. ST Accel. Beams 10,034801
[60]Jackson J D.1999. Classical Electrodynamics, John Wiley & Sons,3rd edition.
[61]王竹溪,郭敦仁.2000.特殊函数概论[M].北京：北京大学出版社.
[62]刘秉正,彭建华.2004.非线性动力学[M].北京：高等教育出版社.
[63]Chen C P, Davidson R C.1991. Chaotic paticle dynamics in free-electron lasers [J]. Phys.Rev.A,43:5541.
[64]Bonnetin G, Galgani L et al.1978. Meccanica Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems[J], C R Academic Sci Puris A,206:431.
[65]Tran T M and Wurtele J S.1990. LRP 392/90, CRPP Report, Lausanne, Switzerland.
[66]Hammersley J M and Handscomb D C.1964. Monte Carlo Methods[M], Methuen, London.
[67]Barre J, Dauxois T, Ninno G,et al.2004. Statistical theory of high-gain free-electron laser saturation[J], Phys Rev E,69:045501.
[68]Antoniazzi A, Ruffo S.2006. An account of the statistical and dynamical properties of systems with long-range interactions[J], Nucl. Instrum. Meth. A,561:143.
[69]BarreJ.2003. Ph.D. thesis[D], ENS Lyon.
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