自由电子激光物理中统计物理分析方法的若干研究
|
摘要
本文致力于近年来国际上提出的高增益自由电子激光饱和状态分析的统计物理方法的改进和推广。作为本文工作的基础,对相关自由电子激光基础理论做了综述,特别考察了波荡器低阶磁场近似下非理想入射电子的三维运动,及其对自发辐射的影响。在自由电子激光一维Colson-Bonifacio模型的基础上建立了一种能描述电子横向运动的三维归一化简化模型。在国外同行和小组已有工作基础上,针对这种模型重新以Matlab语言编写了直接数值模拟的完整程序,进而分析包含电子横向振荡的三维模型对一维模型的修正。对这种新的三维模型,引入守恒量,通过系统达到饱和状态的熵极大条件,发展求解饱和态参数的理论和算法,并编写了相应的Matlab程序。对于螺旋型波荡器中Compton型自放大自发辐射(SASE)自由电子激光由起振增益到饱和状态的过程,通过直接动力学模拟分析了在一定横向发射度情况下失谐量为零不同能散电子束和冷电子束、暖电子束入射情况下系统的光强、聚束因子、以及相空间分布三者的对应关系,并将三维模拟同一维模拟作了比较,考察了三维模拟中不同的初始横向发射度的影响。在与以上初始情况相同的条件下,采用一维和三维统计方法计算了饱和态的光场强度和聚束因子,并讨论了上述两种方法下三维理论对一维理论的相对修正。
This thesis is dedicated to the improvement and generalization of the methods of the methods statistical physics in the analysis of high-gain free-electron laser at saturation. As the basis of this thesis we first review the relevant basic theory of the free electron laser, and especially the motion and radiation of a non-ideally injected election in three-dimensional low order magnetic is analyzed. Start from the one dimensional (1D) theory of Colson-Bonifacio FEL model we construct a three dimensional (3D) normalized simplified model which includes the transverse movement of the electrons. With the help of the foreign colleagues and from the former work of our team a direct numerical simulation code was rewritten for this new model using Matlab program; consequently the amendment of the3D mode included electronic transverse oscillation and the1D mode is investigated. With the Maximum Entropy condition at saturation and by introducing new conserved quantity the3D statistical theory is developed in order to calculate the saturation state parameters. In addition the relevant calculating algorithm is developed and the code in Matlab is composed. As an application of the3D direct numerical simulation codes we discuss the saturation process of the self-amplified spontaneous emission Compton FEL in helical undulator. In certain transverse emittance case the relations of intensity bunching and electrons distributions are investigated for zero detuning with different energy dispersive electron beam "cold electron beam" and "warm electron beam". With a comparison between the results from3D and1D model respectively. The effects of different initial transverse emittance are also discussed by3D simulations. As main work of this thesis the intensity and bunching factor are calculated via1D and3D statistical methods in the same initial condition with the simulation methods. The relative correction between1D and3D model in both methods are also covered.
This thesis is dedicated to the improvement and generalization of the methods of the methods statistical physics in the analysis of high-gain free-electron laser at saturation. As the basis of this thesis we first review the relevant basic theory of the free electron laser, and especially the motion and radiation of a non-ideally injected election in three-dimensional low order magnetic is analyzed. Start from the one dimensional (1D) theory of Colson-Bonifacio FEL model we construct a three dimensional (3D) normalized simplified model which includes the transverse movement of the electrons. With the help of the foreign colleagues and from the former work of our team a direct numerical simulation code was rewritten for this new model using Matlab program; consequently the amendment of the3D mode included electronic transverse oscillation and the1D mode is investigated. With the Maximum Entropy condition at saturation and by introducing new conserved quantity the3D statistical theory is developed in order to calculate the saturation state parameters. In addition the relevant calculating algorithm is developed and the code in Matlab is composed. As an application of the3D direct numerical simulation codes we discuss the saturation process of the self-amplified spontaneous emission Compton FEL in helical undulator. In certain transverse emittance case the relations of intensity bunching and electrons distributions are investigated for zero detuning with different energy dispersive electron beam "cold electron beam" and "warm electron beam". With a comparison between the results from3D and1D model respectively. The effects of different initial transverse emittance are also discussed by3D simulations. As main work of this thesis the intensity and bunching factor are calculated via1D and3D statistical methods in the same initial condition with the simulation methods. The relative correction between1D and3D model in both methods are also covered.
引文
[1]Murphy J, Pellegrini C. Introduction to the physics of the free electron laser[J]. Frontiers of Particle Beams,1988:163-219.
[2]谢家麟.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,2002,19(1)：7-17.
[3]Winick H, Bienenstock A. Synchrotron radiation research[J]. Annual Review of Nuclear and Particle Science,1978,28(1):33-113.
[4]Louisell WH, Lam JF, Copeland DA, et al. Exact Classical Electron Dynamic Approach for a Free-Electron Laser-Amplifier[J]. Physical Review A,1979,19(1):288-300.
[5]Saldin EL, Schneidmiller EA, Yurkov MV. The Physics of Free-Electron Lasers-an Introduction[J]. Physics Reports-Review Section of Physics Letters,1995,260(4-5):187-327.
[6]E.L.Saldin, E.A.Schneidmiller, M.V.Yurkov. The Physics of Free Electron Lasers[M]. Springer,2000.
[7]惠钟锡,杨振华.自由电子激光[M].北京：国防工业出版社,1995.
[8]W.B.Colson,C.Pellegrini,A.Renieri.自由电子激光[M].科学城.1993.
[9]Yu LH. High-Gain Harmonic-Generation Free-Electron Laser[J]. Science,2000,289(5481): 932-934.
[10]Saldin E, Schneidmiller E, Yurkov M. Properties of the third harmonic of the radiation from self-amplified spontaneous emission free electron laser[J]. Physical Review Special Topics-Accelerators and Beams,2006,9(3).
[11]Kim K-J, Shvyd'ko Y, Reiche S. A Proposal for an X-Ray Free-Electron Laser Oscillator with an Energy-Recovery Linac[J]. Physical Review Letters,2008,100(24).
[12]Kapitza P, Dirac P. The reflection of electrons from standing light waves:proceedings of the Mathematical Proceedings of the Cambridge Philosophical Society,1933[C]. Cambridge Univ Press.
[13]Motz H. Applications of the radiation from fast electron beams[J]. Journal of Applied Physics, 1951,22(5):527-535.
[14]Motz H, Thon W, Whitehurst R. Experiments on radiation by fast electron beams[J]. Journal of Applied Physics,1953,24(7):826-833.
[15]Phillips R. The ubitron, a high-power traveling-wave tube based on a periodic beam interaction in unloaded waveguide[J]. Electron Devices, IRE Transactions on,1960,7(4): 231-241.
[16]Madey JMJ. Stimulated emission of bremsstrahlung in a periodic magnetic field[J]. Journal of Applied Physics,1971,42(5):1906-1913.
[17]Arthur J, Anfinrud P, Linac Coherent Light Source (LCLS) Conceptual Design Report,2002.
[18]Group EF, XFEL/SPring8 beamline technical design report,2010.
[19]Group DXP, Team EXP, Elektronen-Synchrotron D, et al. The European X-Ray Free-Electron Laser Technical design report [M].2007.
[20]Stupakov G. Using the Beam-Echo Effect for Generation of Short-Wavelength Radiation[J]. Physical Review Letters,2009,102(7).
[21]Zhao Z, Wang D, Chen J, et al. First lasing of an echo-enabled harmonic generation free-electron laser[J]. Nature Photonics,2012.
[22]Colson W. Theory of a free electron laser[J]. Physics Letters A,1976,59(3):187-190.
[23]Lynden-Bell D. STATISTICAL MECHANICS OF VIOLENT RELAXATION IN STELLAR SYSTEMS[J]. Journal Name:Mon Notic Roy Astron Soc,136:101-21(1967); Other Information:Orig Receipt Date:31-DEC-68; Bib Info Source:UK (United Kingdom (sent to DOE from)),1967:Medium:X.
[24]Mynick HE, Kaufman AN. Soluble Theory of Nonlinear Beam-Plasma Interaction[J]. Physics of Fluids,1978,21(4):653-663.
[25]Barr6 J, Dauxois T, De Ninno G, et al. Statistical theory of high-gain free-electron laser saturation[J]. Physical Review E,2004,69(4).
[26]Barrg J, Bouchet F, Dauxois T, et al. Large Deviation Techniques Applied to Systems with Long-Range Interactions[J]. Journal of Statistical Physics,2005,119(3-4):677-713.
[27]Antoniazzi A, Ninno GD, Fanelli D, et al. Wave-particle interaction:from plasma physics to the free-electron laser[J]. Journal of Physics:Conference Series,2005,7:143-153.
[28]Antoniazzi A, Elskens Y, Fanelli D, et al. Statistical mechanics and Vlasov equation allow for a simplified Hamiltonian description of Single-Pass Free Electron Laser saturated dynamics[J]. The European Physical Journal B,2006,50(4):603-611.
[29]Antoniazzi A, Ruffo S. An account of the statistical and dynamical properties of systems with long-range interactions[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment,2006,561(2):143-150.
[30]Bouchet F, Barre J. Statistical mechanics of systems with long range interactions[J]. Third 21coe Symposium:Astrophysics as Interdisciplinary Science,2006,31:18-26.
[31]Barr6 J, Bouchet F, Dauxois T, et al. The Vlasov equation and the Hamiltonian mean-field model[J]. PhysicaA:Statistical Mechanics and its Applications,2006,365(1):177-183.
[32]Firpo MC, Leyvraz F, Attuel G. Equilibrium statistical mechanics for single waves and wave spectra in Langmuir wave-particle interaction[J]. Physics of Plasmas,2006,13(12):122302.
[33]Antoniazzi A, Fanelli D, Barre J, et al. Maximum entropy principle explains quasistationary states in systems with long-range interactions:The example of the Hamiltonian mean-field model[J]. Physical Review E,2007,75(1).
[34]Curbis F, Antoniazzi A, De Ninno G, et al. Maximum entropy principle and coherent harmonic generation using a single-pass free-electron laser[J]. The European Physical Journal B,2007,59(4):527-533.
[35]李政道.李政道讲义：统计力学[M].上海科学技术出版社,2006.
[36]Sprangle P, Tang C, x, et al. Three dimensional nonlinear theory of the free electron laser [J]. Applied Physics Letters,1981,39(9):677-679.
[37]Papadichev VA. Betatron Oscillations, Undulator Acceptance and Beam Conditioning (Beta-Parallel-to(R)=Const) Taking Space-Charge Effects into Account[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,1995,358(1-3):418-421.
[38]Mishra G, Gupta V, Rajput NP, et al. Damping of betatron oscillations in undulator magnets with the aid of an axial magnetic field[J]. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment, 2004,527(3):233-239.
[39]Gupta V, Mishra G. Harmonic undulator free electron laser and betatron oscillations[J]. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment,2006,556(1):350-356.
[40]Jackson JD. Classical Electrodynamics[M]. Wiley,1998.
[41]Colson W. The nonlinear wave equation for higher harmonics in free-electron lasers[J]. Quantum Electronics, IEEE Journal of,1981,17(8):1417-1427.
[42]Tran TM, Danly BG, Wurtele JS. Free-Electron Lasers with Electromagnetic Standing Wave Wigglers[J]. Ieee Journal of Quantum Electronics,1987,23(9):1578-1589.
[43]Dattoli G, Giannessi L, Mezi L, et al. Linear undulator brightness:Inclusion of sextupolar magnetic-field contributions and of higher-order energy corrections[J]. Phys Rev A, 1992,45(6):4023-4035.
[44]Dattoli G, Voykov GK, Carpanese M. Betatron Motion and Linear Undulator Brightness-Inhomogeneous Broadening Effects Due to Electron-Beam Emittance and Twiss Parameters[J]. Physical Review E,1995,52(6):6809-6817.
[45]Chhotray SK, Mishra G, Dutta AK. Inclusion of electron betatron motion on longitudinal wiggler-undulator radiation[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,1998,408(2-3):543-552.
[46]Dattoli G, Bucci L. Free electron lasers operating with variably polarization undulators[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,2000,450(2-3):479-490.
[47]Chouhan SS, Mishra G. Effects of inhomogeneous broadening on two-frequency longitudinal wiggler brightness[J]. Physics Letters A,2002,299(4):392-400.
[48]Krinsky S, Yu LH. Output power in guided modes for amplified spontaneous emission in a single-pass free-electron laser[J]. Physical Review A,1987,35(8):3406-3423.
[49]Dattoli G, Cesarano C, Sacchetti D. Pseudo-Bessel Functions and Applications[J]. Georgian Mathematical Journal,2002,9(3):473-480.
[50]Korsch HJ, Klumpp A, Witthaut D. On two-dimensional Bessel functions[J]. Journal of Physics A:Mathematical and General,2006,39(48):14947-14964.
[51]Dattoli G, Torre A. theory and applications of generalized bessel functions[M]. Frascati, Roma, Italia:ENEA Dipartimento Innovazione,1996.
[52]Klein J. Motion of a Charged Particle in a Uniform Magnetic Field[J]. Reviews of Modern Physics,1968,40(3):523-530.
[53]Oneil TM, Winfrey JH, Malmberg JH. Nonlinear Interaction of a Small Cold Beam and a Plasma[J]. Physics of Fluids,1971,14(6):1204-&.
[54]Taguchi T, Mima K, Mochizuki T. Saturation Mechanism and Improvement of Conversion Efficiency of the Free-Electron Laser[J]. Physical Review Letters,1981,46(13):824-827.
[55]Freund H, Ganguly A. Three-dimensional theory of the free-electron laser in the collective regime[J]. Physical Review A,1983,28(6):3438-3449.
[56]Ciocci F, Dattoli G, Torre A. The Effect of Emittance Inhomogeneous Broadening on the Brightness of a Magnetic Undulator[J]. Ieee Journal of Quantum Electronics,1994,30(3): 793-799.
[57]Litvinenko VN.3d Free-Electron Laser Gain for an Electron-Beam with Finite Emittance and Energy Spread[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,1995,359(1-2):50-56.
[58]Geloni G, Kocharyan V, Saldin E. The effects of betatron motion on the preservation of FEL microbunching[J]. Arxiv preprint arXiv:11053878,2011.
[59]Smith TI, Madey JMJ. Realizable Free-Electron Lasers[J]. Applied Physics B-Photophysics and Laser Chemistry,1982,27(4):195-199.
[60]Edwards DA, Syphers MJ. An introduction to the physics of high energy accelerators [M]. Wiley-VCH,2008.
[61]Kim K-J. Three-Dimensional Analysis of Coherent Amplification and Self-Amplified Spontaneous Emission in Free-Electron Lasers[J]. Physical Review Letters,1986,57(15): 1871-1874.
[62]Saldin EL, Schneidmiller EA, Yurkov MV. On a Linear-Theory of an Fel Amplifier with an Axisymmetrical Electron-Beam[J]. Optics Communications,1993,97(3-4):272-290.
[63]Rossbach J, Saldin EL, Schneidmiller EA, et al. Interdependence of parameters of an X-ray FEL[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,1996,374(3):401-407.
[64]Chin Y, Kim K-J, Xie M. Three-dimensional theory of the small-signal high-gain free-electron laser including betatron oscillations[J]. Physical Review A,1992,46(10): 6662-6683.
[65]Huang Z, Kim KJ. Three-dimensional analysis of harmonic generation in high-gain free-electron lasers[J]. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, 2000,62(5 Pt B):7295-7308.
[66]Huang Z, Kim K-J. Review of x-ray free-electron laser theory[J]. Physical Review Special Topics-Accelerators and Beams,2007,10(3).
[67]T.M.Tran, J.S.Wurtele. Review of Free-electron-laser (FEL) Simulation Techniques[M]. Computer Physics Reports,1990:32.
[68]Tran TM, Wurtele JS. TDA-A three-dimensional axisymmetric code for free-electron-laser (FEL) simulation[J]. Computer Physics Communications,1989,54(2-3):263-272.
[69]Saldin EL, Schneidmiller EA, Yurkov MV. FAST:a three-dimensional time-dependent FEL simulation code[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,1999,429(1-3):233-237.
[70]Reiche S. Numerical studies for a single pass high gain free-electron laser[D]:Deutsches Elektronen-Synchrotron,2000.
[71]Davidson RC, Mcmullin WA. Stochastic Particle Instability for Electron Motion in Combined Helical Wiggler, Radiation, and Longitudinal-Wave Fields[J]. Physical Review A,1982,26(1): 410-422.
[72]Hui ZX. High-Gain Fel with Variable Parameter Wigglers[J]. International Journal of Infrared and Millimeter Waves,1989,10(6):651-660.
[73]Halbach K. Design of Permanent Multipole Magnets with Oriented Rare-Earth Cobalt Material[J]. Nuclear Instruments & Methods,1980,169(1):1-10.
[74]Kimura S, Kamada M, Hama H, et al. Design of a helical undulator for UVSOR[J]. Journal of Electron Spectroscopy and Related Phenomena,1996,80:437-440.
[75]张鹏飞,庞宗柱,阮图南,et al.非理想注入电子在平面型波荡器中的运动与辐射[J].中国科学技术大学学报,2009,(009)：917-921.
[76]张鹏飞,李明光,邹冰,et al.非理想注入电子在螺旋型波荡器中的运动与辐射[J].中国科学技术大学学报,2010,40(003)：221-225.
[77]Scharlemann ET. Wiggle plane focusing in linear wigglers[J]. Journal of Applied Physics, 1985,58(6):2154-2161.
[78]Bonifacio R, Piovella N, Robb G, et al. Quantum regime of free electron lasers starting from noise[J]. Physical Review Special Topics-Accelerators and Beams,2006,9(9).
[79]Erber T, Latal HG. Unified radiation formulae for classical and quantum electrodynamics[J]. European journal of physics,2002,24(1):67.
[80]Antoni M, Elskens Y, Escande DF. Explicit reduction of N-body dynamics to self-consistent particle--wave interaction[J]. Physics of Plasmas,1998,5(4):841-852.
[81]Firpo MC, Elskens Y. Kinetic limit of N-body description of wave-particle self-consistent interaction[J]. Journal of Statistical Physics,1998,93(1-2):193-209.
[82]Firpo MC, Elskens Y. Phase transition in the collisionless damping regime for wave-particle interaction[J]. Phys Rev Lett,2000,84(15):3318-3321.
[83]Piovella N, Cola M, Volpe L, et al. Three-Dimensional Wigner-Function Description of the Quantum Free-Electron Laser[J]. Physical Review Letters,2008,100(4).
[84]邓海啸.Three-dimensional numerical investigations of the laser-beam interactions in an undulator[J].中国物理C：英文版,2011,35(3).
[85]Bonifacio R, Casagrande F, Cerchioni G, et al. Physics of the High-Gain Fel and Superradiance[J]. Rivista Del Nuovo Cimento,1990,13(9):1-69.
[86]Farina D, Casagrande F, Colombo U, et al. Hamiltonian analysis of the transition to the high-gain regime in a Compton free-electron-laser amplifier[J]. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics,1994,49(2):1603-1609.
[87]Firpo MC, Doveil F, Elskens Y, et al. Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model[J]. Physical Review E,2001,64(2).
[88]Morita H, Kaneko K. Collective Oscillation in a Hamiltonian System[J]. Physical Review Letters,2006,96(5).
[89]Smith GR, Pereira NR. Phase-Locked Particle Motion in a Large-Amplitude Plasma-Wave[J]. Physics of Fluids,1978,21(12):2253-2262.
[90]Bachelard R, Chandre C, Fanelli D, et al. Stabilizing the intensity for a Hamiltonian model of the FEL[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,2008,593(1-2):94-97.
[91]Bachelard R, Chandre C, Vittot M. Hamiltonian description of a self-consistent interaction between charged particles and electromagnetic waves[J]. Physical Review E,2008,78(3).
[92]Gluckstern RL, Krinsky S, Okamoto H. Analysis of the saturation of a high-gain free-electron laser[J]. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics,1993,47(6): 4412-4429.
[93]Vinokurov NA, Huang Z, Shevchenko OA, et al. Quasilinear theory of high-gain FEL saturation[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,2001,475(1-3):74-78.
[94]Sprangle P, Tang C-M, Manheimer WM. Nonlinear theory of free-electron lasers and efficiency enhancement[J]. Physical Review A,1980,21(1):302-318.
[95]Adam JC, Laval G, Mendonca I. Time-dependent nonlinear Langmuir waves[J]. Physics of Fluids,1981,24(2):260-267.
[96]束小建,窦玉焕.SASE自由电子激光起振问题及统计特性的数值模拟[J].强激光与粒子束,2002,14(6)：857-861.
[97]Bonifacio R, Piovella N, Cola MM, et al. Experimental requirements for X-ray compact free electron lasers with a laser wiggler[J]. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment,2007,577(3): 745-750.
[98]Cola MM, Volpe L, Piovella N, et al.3D Wigner model for a quantum free electron laser with a laser wiggler[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment,2008,593(1-2):75-79.
[99]Bonifacio R, Pellegrini C, Narducci L. Collective instabilities and high-gain regime in a free electron laser[J]. Optics Communications,1984,50(6):373-378.
[100]Venturini M, Zholents A. Modeling microbunching from shot noise using Vlasov solvers[J]. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment,2008,593(1-2):53-56.
[101]沈惠川Vlasov方程的精确解[J].数学物理学报：A辑,1996,16(1)：40-47.
[102]黄文会,王光伟.Vlasov方程的数值求解[J].高能物理与核物理,1999,23(012)：1216-1222.
[103]Pfaffelmoser K. Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data[J]. J Differential Equations,1992,95(2):281-303.
[104]Mangeney A, Califano F, Cavazzoni C, et al. A numerical scheme for the integration of the Vlasov-Maxwell system of equations[J]. Journal of Computational Physics,2002,179(2): 495-538.
[105]Yamaguchi YY, Barre J, Bouchet F, et al. Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model[J]. Physica A:Statistical Mechanics and its Applications,2004,337(1-2):36-66.
[106]Chavanis PH, Sommeria J, Robert R. Statistical mechanics of two-dimensional vortices and collisionless stellar systems[J]. Astrophysical Journal,1996,471(1):385-399.
[107]Krinsky S, Gluckstern R. Analysis of statistical correlations and intensity spiking in the self-amplified spontaneous-emission free-electron laser[J]. Physical Review Special Topics-Accelerators and Beams,2003,6(5).
[108]Barre J, Dauxois T. Lyapunov exponents as a dynamical indicator of a phase transition[J]. Europhysics Letters,2001,55(2):164-170.
[109]Barre J, Mukamel D, Ruffo S. Inequivalence of ensembles in a system with long-range Interactions[J]. Physical Review Letters,2001,87(3).
[110]Curbis F, Antoniazzi A, Ninno GD, et al. THE SATURATED REGIME OF A SEEDED SINGLE-PASS FREE ELECTRON LASER:A THEORETICAL INVESTIGATION THROUGH THE STATISTICAL MECHANICS OF THE VLASOV EQUATION:proceedings of the Proceedings of FEL, Berlin, Germany, [C].2006.
[111]Shevchenko OA, Vinokurov NA. STATISTICAL THEORY OF THE SASE FEL BASED ON THE TWO-PARTICLE CORRELATION FUNCTION EQUATION:proceedings of the Proceedings of FEL, Liverpool, UK, [C].2009.
[112]邹冰,李明光,张鹏飞,et al.高增益自由电子激光饱和状态分析的一种统计物理方法[J].中国科学技术大学学报,2010,40(006)：612-617.
[113]李明光.高增益自由电子激光理论分析的一种新方法[D]：中国科学技术大学,2008.
[114]Antoniazzi A, Johal RS, Fanelli D, et al. On the origin of quasi-stationary states in models of wave-particle interaction[J]. Communications in Nonlinear Science and Numerical Simulation,2008,13(1):2-10.
[115]Antoni M, Ruffo S. Clustering and relaxation in Hamiltonian long-range dynamics[J]. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics,1995,52(3):2361-2374.
[116]Bouchet F, Barre J, Venaille A. Equilibrium and out of equilibrium phase transitions in systems with long range interactions and in systems with long range interactions and in 2D flow[J].2008.
[117]Ruffo S. Equilibrium and nonequilibrium properties of systems with long-range interactions[J]. The European Physical Journal B,2008,64(3-4):355-363.
[118]Bachelard R, Antoniazzi A, Chandre C, et al. Stabilizing the intensity of a wave amplified by a beam of particles[J]. The European Physical Journal D,2006,42(1):125-132.
[119]Bachelard R, Chandre C, Leoncini X, et al. Contr oler l'interaction onde-particules[J]. 2006.
[120]Bachelard R, Chandre C, Leoncini X, et al. Controle d'une interaction onde-particule par une onde-test[J].2007.
[121]Bachelard R, Fanelli D. Short-time dynamics in the presence of wave-particles interactions:A perturbative approach[J]. Communications in Nonlinear Science and Numerical Simulation,2010,15(1):40-47.
[122]Ettoumi W, Firpo MC. Stochastic treatment of finite-N effects in mean-field systems and its application to the lifetimes of coherent structures[J]. Physical Review E,2011,84(3).
[123]张善才,何多慧.上海深紫外自由电子激光装置从头至尾模拟计算研究[J].中国科学技术大学学报,2007,37(4)：461-465.
[124]Bachelard R, Chandre C, Leoncini X, et al. Control of the intensity of a wave interacting with charged particles:proceedings of the Proceedings of FEL, Berlin, Germany, [C].2006.
[125]Bachelard R, Antoniazzi A, Chandre C, et al. Enhancement of particle trapping in the wave-particle interaction[J]. Communications in Nonlinear Science and Numerical Simulation,2008,13(3):660-665.
[126]袁勤良.王友智.加速器束流发射度测量[J].原子能科学技术,1988,4：015.
[127]陈银宝.FEL中的束流发射度分析[J].核科学与工程,1992,2：011.
[128]杨震华,武玉璞.曙光一号自由电子激光器(FEL)电子束发射度的分析[J].计算物理,1994,11(3)：262-268.
[129]LIU WB, WANG SH, YE Q, et al. Emittance Measurement at BEPCⅡ Linac[J]. Chinese Physics C,2008,32(S1):86-88.
[130]Lapostolle PM. Possible emittance increase through filamentation due to space charge in continuous beams[J]. Nuclear Science, IEEE Transactions on,1971,18(3):1101-1104.
[131]顾强,戴建枰,戴志敏,et al.100MeV电子直线加速器的物理设计[J].强激光与粒子束,2008.
[132]王相綦,郝浩,冯光耀.合肥光源储存环中等发射度模式理论计算研究[J].中国科学技术大学学报,2009,(6)：599-602.
[133]Shintake T, Status report on Japanese XFEL construction project at SPring-8,2010.
[2]谢家麟.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,2002,19(1)：7-17.
[3]Winick H, Bienenstock A. Synchrotron radiation research[J]. Annual Review of Nuclear and Particle Science,1978,28(1):33-113.
[4]Louisell WH, Lam JF, Copeland DA, et al. Exact Classical Electron Dynamic Approach for a Free-Electron Laser-Amplifier[J]. Physical Review A,1979,19(1):288-300.
[5]Saldin EL, Schneidmiller EA, Yurkov MV. The Physics of Free-Electron Lasers-an Introduction[J]. Physics Reports-Review Section of Physics Letters,1995,260(4-5):187-327.
[6]E.L.Saldin, E.A.Schneidmiller, M.V.Yurkov. The Physics of Free Electron Lasers[M]. Springer,2000.
[7]惠钟锡,杨振华.自由电子激光[M].北京：国防工业出版社,1995.
[8]W.B.Colson,C.Pellegrini,A.Renieri.自由电子激光[M].科学城.1993.
[9]Yu LH. High-Gain Harmonic-Generation Free-Electron Laser[J]. Science,2000,289(5481): 932-934.
[10]Saldin E, Schneidmiller E, Yurkov M. Properties of the third harmonic of the radiation from self-amplified spontaneous emission free electron laser[J]. Physical Review Special Topics-Accelerators and Beams,2006,9(3).
[11]Kim K-J, Shvyd'ko Y, Reiche S. A Proposal for an X-Ray Free-Electron Laser Oscillator with an Energy-Recovery Linac[J]. Physical Review Letters,2008,100(24).
[12]Kapitza P, Dirac P. The reflection of electrons from standing light waves:proceedings of the Mathematical Proceedings of the Cambridge Philosophical Society,1933[C]. Cambridge Univ Press.
[13]Motz H. Applications of the radiation from fast electron beams[J]. Journal of Applied Physics, 1951,22(5):527-535.
[14]Motz H, Thon W, Whitehurst R. Experiments on radiation by fast electron beams[J]. Journal of Applied Physics,1953,24(7):826-833.
[15]Phillips R. The ubitron, a high-power traveling-wave tube based on a periodic beam interaction in unloaded waveguide[J]. Electron Devices, IRE Transactions on,1960,7(4): 231-241.
[16]Madey JMJ. Stimulated emission of bremsstrahlung in a periodic magnetic field[J]. Journal of Applied Physics,1971,42(5):1906-1913.
[17]Arthur J, Anfinrud P, Linac Coherent Light Source (LCLS) Conceptual Design Report,2002.
[18]Group EF, XFEL/SPring8 beamline technical design report,2010.
[19]Group DXP, Team EXP, Elektronen-Synchrotron D, et al. The European X-Ray Free-Electron Laser Technical design report [M].2007.
[20]Stupakov G. Using the Beam-Echo Effect for Generation of Short-Wavelength Radiation[J]. Physical Review Letters,2009,102(7).
[21]Zhao Z, Wang D, Chen J, et al. First lasing of an echo-enabled harmonic generation free-electron laser[J]. Nature Photonics,2012.
[22]Colson W. Theory of a free electron laser[J]. Physics Letters A,1976,59(3):187-190.
[23]Lynden-Bell D. STATISTICAL MECHANICS OF VIOLENT RELAXATION IN STELLAR SYSTEMS[J]. Journal Name:Mon Notic Roy Astron Soc,136:101-21(1967); Other Information:Orig Receipt Date:31-DEC-68; Bib Info Source:UK (United Kingdom (sent to DOE from)),1967:Medium:X.
[24]Mynick HE, Kaufman AN. Soluble Theory of Nonlinear Beam-Plasma Interaction[J]. Physics of Fluids,1978,21(4):653-663.
[25]Barr6 J, Dauxois T, De Ninno G, et al. Statistical theory of high-gain free-electron laser saturation[J]. Physical Review E,2004,69(4).
[26]Barrg J, Bouchet F, Dauxois T, et al. Large Deviation Techniques Applied to Systems with Long-Range Interactions[J]. Journal of Statistical Physics,2005,119(3-4):677-713.
[27]Antoniazzi A, Ninno GD, Fanelli D, et al. Wave-particle interaction:from plasma physics to the free-electron laser[J]. Journal of Physics:Conference Series,2005,7:143-153.
[28]Antoniazzi A, Elskens Y, Fanelli D, et al. Statistical mechanics and Vlasov equation allow for a simplified Hamiltonian description of Single-Pass Free Electron Laser saturated dynamics[J]. The European Physical Journal B,2006,50(4):603-611.
[29]Antoniazzi A, Ruffo S. An account of the statistical and dynamical properties of systems with long-range interactions[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment,2006,561(2):143-150.
[30]Bouchet F, Barre J. Statistical mechanics of systems with long range interactions[J]. Third 21coe Symposium:Astrophysics as Interdisciplinary Science,2006,31:18-26.
[31]Barr6 J, Bouchet F, Dauxois T, et al. The Vlasov equation and the Hamiltonian mean-field model[J]. PhysicaA:Statistical Mechanics and its Applications,2006,365(1):177-183.
[32]Firpo MC, Leyvraz F, Attuel G. Equilibrium statistical mechanics for single waves and wave spectra in Langmuir wave-particle interaction[J]. Physics of Plasmas,2006,13(12):122302.
[33]Antoniazzi A, Fanelli D, Barre J, et al. Maximum entropy principle explains quasistationary states in systems with long-range interactions:The example of the Hamiltonian mean-field model[J]. Physical Review E,2007,75(1).
[34]Curbis F, Antoniazzi A, De Ninno G, et al. Maximum entropy principle and coherent harmonic generation using a single-pass free-electron laser[J]. The European Physical Journal B,2007,59(4):527-533.
[35]李政道.李政道讲义：统计力学[M].上海科学技术出版社,2006.
[36]Sprangle P, Tang C, x, et al. Three dimensional nonlinear theory of the free electron laser [J]. Applied Physics Letters,1981,39(9):677-679.
[37]Papadichev VA. Betatron Oscillations, Undulator Acceptance and Beam Conditioning (Beta-Parallel-to(R)=Const) Taking Space-Charge Effects into Account[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,1995,358(1-3):418-421.
[38]Mishra G, Gupta V, Rajput NP, et al. Damping of betatron oscillations in undulator magnets with the aid of an axial magnetic field[J]. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment, 2004,527(3):233-239.
[39]Gupta V, Mishra G. Harmonic undulator free electron laser and betatron oscillations[J]. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment,2006,556(1):350-356.
[40]Jackson JD. Classical Electrodynamics[M]. Wiley,1998.
[41]Colson W. The nonlinear wave equation for higher harmonics in free-electron lasers[J]. Quantum Electronics, IEEE Journal of,1981,17(8):1417-1427.
[42]Tran TM, Danly BG, Wurtele JS. Free-Electron Lasers with Electromagnetic Standing Wave Wigglers[J]. Ieee Journal of Quantum Electronics,1987,23(9):1578-1589.
[43]Dattoli G, Giannessi L, Mezi L, et al. Linear undulator brightness:Inclusion of sextupolar magnetic-field contributions and of higher-order energy corrections[J]. Phys Rev A, 1992,45(6):4023-4035.
[44]Dattoli G, Voykov GK, Carpanese M. Betatron Motion and Linear Undulator Brightness-Inhomogeneous Broadening Effects Due to Electron-Beam Emittance and Twiss Parameters[J]. Physical Review E,1995,52(6):6809-6817.
[45]Chhotray SK, Mishra G, Dutta AK. Inclusion of electron betatron motion on longitudinal wiggler-undulator radiation[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,1998,408(2-3):543-552.
[46]Dattoli G, Bucci L. Free electron lasers operating with variably polarization undulators[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,2000,450(2-3):479-490.
[47]Chouhan SS, Mishra G. Effects of inhomogeneous broadening on two-frequency longitudinal wiggler brightness[J]. Physics Letters A,2002,299(4):392-400.
[48]Krinsky S, Yu LH. Output power in guided modes for amplified spontaneous emission in a single-pass free-electron laser[J]. Physical Review A,1987,35(8):3406-3423.
[49]Dattoli G, Cesarano C, Sacchetti D. Pseudo-Bessel Functions and Applications[J]. Georgian Mathematical Journal,2002,9(3):473-480.
[50]Korsch HJ, Klumpp A, Witthaut D. On two-dimensional Bessel functions[J]. Journal of Physics A:Mathematical and General,2006,39(48):14947-14964.
[51]Dattoli G, Torre A. theory and applications of generalized bessel functions[M]. Frascati, Roma, Italia:ENEA Dipartimento Innovazione,1996.
[52]Klein J. Motion of a Charged Particle in a Uniform Magnetic Field[J]. Reviews of Modern Physics,1968,40(3):523-530.
[53]Oneil TM, Winfrey JH, Malmberg JH. Nonlinear Interaction of a Small Cold Beam and a Plasma[J]. Physics of Fluids,1971,14(6):1204-&.
[54]Taguchi T, Mima K, Mochizuki T. Saturation Mechanism and Improvement of Conversion Efficiency of the Free-Electron Laser[J]. Physical Review Letters,1981,46(13):824-827.
[55]Freund H, Ganguly A. Three-dimensional theory of the free-electron laser in the collective regime[J]. Physical Review A,1983,28(6):3438-3449.
[56]Ciocci F, Dattoli G, Torre A. The Effect of Emittance Inhomogeneous Broadening on the Brightness of a Magnetic Undulator[J]. Ieee Journal of Quantum Electronics,1994,30(3): 793-799.
[57]Litvinenko VN.3d Free-Electron Laser Gain for an Electron-Beam with Finite Emittance and Energy Spread[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,1995,359(1-2):50-56.
[58]Geloni G, Kocharyan V, Saldin E. The effects of betatron motion on the preservation of FEL microbunching[J]. Arxiv preprint arXiv:11053878,2011.
[59]Smith TI, Madey JMJ. Realizable Free-Electron Lasers[J]. Applied Physics B-Photophysics and Laser Chemistry,1982,27(4):195-199.
[60]Edwards DA, Syphers MJ. An introduction to the physics of high energy accelerators [M]. Wiley-VCH,2008.
[61]Kim K-J. Three-Dimensional Analysis of Coherent Amplification and Self-Amplified Spontaneous Emission in Free-Electron Lasers[J]. Physical Review Letters,1986,57(15): 1871-1874.
[62]Saldin EL, Schneidmiller EA, Yurkov MV. On a Linear-Theory of an Fel Amplifier with an Axisymmetrical Electron-Beam[J]. Optics Communications,1993,97(3-4):272-290.
[63]Rossbach J, Saldin EL, Schneidmiller EA, et al. Interdependence of parameters of an X-ray FEL[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,1996,374(3):401-407.
[64]Chin Y, Kim K-J, Xie M. Three-dimensional theory of the small-signal high-gain free-electron laser including betatron oscillations[J]. Physical Review A,1992,46(10): 6662-6683.
[65]Huang Z, Kim KJ. Three-dimensional analysis of harmonic generation in high-gain free-electron lasers[J]. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, 2000,62(5 Pt B):7295-7308.
[66]Huang Z, Kim K-J. Review of x-ray free-electron laser theory[J]. Physical Review Special Topics-Accelerators and Beams,2007,10(3).
[67]T.M.Tran, J.S.Wurtele. Review of Free-electron-laser (FEL) Simulation Techniques[M]. Computer Physics Reports,1990:32.
[68]Tran TM, Wurtele JS. TDA-A three-dimensional axisymmetric code for free-electron-laser (FEL) simulation[J]. Computer Physics Communications,1989,54(2-3):263-272.
[69]Saldin EL, Schneidmiller EA, Yurkov MV. FAST:a three-dimensional time-dependent FEL simulation code[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,1999,429(1-3):233-237.
[70]Reiche S. Numerical studies for a single pass high gain free-electron laser[D]:Deutsches Elektronen-Synchrotron,2000.
[71]Davidson RC, Mcmullin WA. Stochastic Particle Instability for Electron Motion in Combined Helical Wiggler, Radiation, and Longitudinal-Wave Fields[J]. Physical Review A,1982,26(1): 410-422.
[72]Hui ZX. High-Gain Fel with Variable Parameter Wigglers[J]. International Journal of Infrared and Millimeter Waves,1989,10(6):651-660.
[73]Halbach K. Design of Permanent Multipole Magnets with Oriented Rare-Earth Cobalt Material[J]. Nuclear Instruments & Methods,1980,169(1):1-10.
[74]Kimura S, Kamada M, Hama H, et al. Design of a helical undulator for UVSOR[J]. Journal of Electron Spectroscopy and Related Phenomena,1996,80:437-440.
[75]张鹏飞,庞宗柱,阮图南,et al.非理想注入电子在平面型波荡器中的运动与辐射[J].中国科学技术大学学报,2009,(009)：917-921.
[76]张鹏飞,李明光,邹冰,et al.非理想注入电子在螺旋型波荡器中的运动与辐射[J].中国科学技术大学学报,2010,40(003)：221-225.
[77]Scharlemann ET. Wiggle plane focusing in linear wigglers[J]. Journal of Applied Physics, 1985,58(6):2154-2161.
[78]Bonifacio R, Piovella N, Robb G, et al. Quantum regime of free electron lasers starting from noise[J]. Physical Review Special Topics-Accelerators and Beams,2006,9(9).
[79]Erber T, Latal HG. Unified radiation formulae for classical and quantum electrodynamics[J]. European journal of physics,2002,24(1):67.
[80]Antoni M, Elskens Y, Escande DF. Explicit reduction of N-body dynamics to self-consistent particle--wave interaction[J]. Physics of Plasmas,1998,5(4):841-852.
[81]Firpo MC, Elskens Y. Kinetic limit of N-body description of wave-particle self-consistent interaction[J]. Journal of Statistical Physics,1998,93(1-2):193-209.
[82]Firpo MC, Elskens Y. Phase transition in the collisionless damping regime for wave-particle interaction[J]. Phys Rev Lett,2000,84(15):3318-3321.
[83]Piovella N, Cola M, Volpe L, et al. Three-Dimensional Wigner-Function Description of the Quantum Free-Electron Laser[J]. Physical Review Letters,2008,100(4).
[84]邓海啸.Three-dimensional numerical investigations of the laser-beam interactions in an undulator[J].中国物理C：英文版,2011,35(3).
[85]Bonifacio R, Casagrande F, Cerchioni G, et al. Physics of the High-Gain Fel and Superradiance[J]. Rivista Del Nuovo Cimento,1990,13(9):1-69.
[86]Farina D, Casagrande F, Colombo U, et al. Hamiltonian analysis of the transition to the high-gain regime in a Compton free-electron-laser amplifier[J]. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics,1994,49(2):1603-1609.
[87]Firpo MC, Doveil F, Elskens Y, et al. Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model[J]. Physical Review E,2001,64(2).
[88]Morita H, Kaneko K. Collective Oscillation in a Hamiltonian System[J]. Physical Review Letters,2006,96(5).
[89]Smith GR, Pereira NR. Phase-Locked Particle Motion in a Large-Amplitude Plasma-Wave[J]. Physics of Fluids,1978,21(12):2253-2262.
[90]Bachelard R, Chandre C, Fanelli D, et al. Stabilizing the intensity for a Hamiltonian model of the FEL[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,2008,593(1-2):94-97.
[91]Bachelard R, Chandre C, Vittot M. Hamiltonian description of a self-consistent interaction between charged particles and electromagnetic waves[J]. Physical Review E,2008,78(3).
[92]Gluckstern RL, Krinsky S, Okamoto H. Analysis of the saturation of a high-gain free-electron laser[J]. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics,1993,47(6): 4412-4429.
[93]Vinokurov NA, Huang Z, Shevchenko OA, et al. Quasilinear theory of high-gain FEL saturation[J]. Nuclear Instruments & Methods in Physics Research Section a-Accelerators Spectrometers Detectors and Associated Equipment,2001,475(1-3):74-78.
[94]Sprangle P, Tang C-M, Manheimer WM. Nonlinear theory of free-electron lasers and efficiency enhancement[J]. Physical Review A,1980,21(1):302-318.
[95]Adam JC, Laval G, Mendonca I. Time-dependent nonlinear Langmuir waves[J]. Physics of Fluids,1981,24(2):260-267.
[96]束小建,窦玉焕.SASE自由电子激光起振问题及统计特性的数值模拟[J].强激光与粒子束,2002,14(6)：857-861.
[97]Bonifacio R, Piovella N, Cola MM, et al. Experimental requirements for X-ray compact free electron lasers with a laser wiggler[J]. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment,2007,577(3): 745-750.
[98]Cola MM, Volpe L, Piovella N, et al.3D Wigner model for a quantum free electron laser with a laser wiggler[J]. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment,2008,593(1-2):75-79.
[99]Bonifacio R, Pellegrini C, Narducci L. Collective instabilities and high-gain regime in a free electron laser[J]. Optics Communications,1984,50(6):373-378.
[100]Venturini M, Zholents A. Modeling microbunching from shot noise using Vlasov solvers[J]. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment,2008,593(1-2):53-56.
[101]沈惠川Vlasov方程的精确解[J].数学物理学报：A辑,1996,16(1)：40-47.
[102]黄文会,王光伟.Vlasov方程的数值求解[J].高能物理与核物理,1999,23(012)：1216-1222.
[103]Pfaffelmoser K. Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data[J]. J Differential Equations,1992,95(2):281-303.
[104]Mangeney A, Califano F, Cavazzoni C, et al. A numerical scheme for the integration of the Vlasov-Maxwell system of equations[J]. Journal of Computational Physics,2002,179(2): 495-538.
[105]Yamaguchi YY, Barre J, Bouchet F, et al. Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model[J]. Physica A:Statistical Mechanics and its Applications,2004,337(1-2):36-66.
[106]Chavanis PH, Sommeria J, Robert R. Statistical mechanics of two-dimensional vortices and collisionless stellar systems[J]. Astrophysical Journal,1996,471(1):385-399.
[107]Krinsky S, Gluckstern R. Analysis of statistical correlations and intensity spiking in the self-amplified spontaneous-emission free-electron laser[J]. Physical Review Special Topics-Accelerators and Beams,2003,6(5).
[108]Barre J, Dauxois T. Lyapunov exponents as a dynamical indicator of a phase transition[J]. Europhysics Letters,2001,55(2):164-170.
[109]Barre J, Mukamel D, Ruffo S. Inequivalence of ensembles in a system with long-range Interactions[J]. Physical Review Letters,2001,87(3).
[110]Curbis F, Antoniazzi A, Ninno GD, et al. THE SATURATED REGIME OF A SEEDED SINGLE-PASS FREE ELECTRON LASER:A THEORETICAL INVESTIGATION THROUGH THE STATISTICAL MECHANICS OF THE VLASOV EQUATION:proceedings of the Proceedings of FEL, Berlin, Germany, [C].2006.
[111]Shevchenko OA, Vinokurov NA. STATISTICAL THEORY OF THE SASE FEL BASED ON THE TWO-PARTICLE CORRELATION FUNCTION EQUATION:proceedings of the Proceedings of FEL, Liverpool, UK, [C].2009.
[112]邹冰,李明光,张鹏飞,et al.高增益自由电子激光饱和状态分析的一种统计物理方法[J].中国科学技术大学学报,2010,40(006)：612-617.
[113]李明光.高增益自由电子激光理论分析的一种新方法[D]：中国科学技术大学,2008.
[114]Antoniazzi A, Johal RS, Fanelli D, et al. On the origin of quasi-stationary states in models of wave-particle interaction[J]. Communications in Nonlinear Science and Numerical Simulation,2008,13(1):2-10.
[115]Antoni M, Ruffo S. Clustering and relaxation in Hamiltonian long-range dynamics[J]. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics,1995,52(3):2361-2374.
[116]Bouchet F, Barre J, Venaille A. Equilibrium and out of equilibrium phase transitions in systems with long range interactions and in systems with long range interactions and in 2D flow[J].2008.
[117]Ruffo S. Equilibrium and nonequilibrium properties of systems with long-range interactions[J]. The European Physical Journal B,2008,64(3-4):355-363.
[118]Bachelard R, Antoniazzi A, Chandre C, et al. Stabilizing the intensity of a wave amplified by a beam of particles[J]. The European Physical Journal D,2006,42(1):125-132.
[119]Bachelard R, Chandre C, Leoncini X, et al. Contr oler l'interaction onde-particules[J]. 2006.
[120]Bachelard R, Chandre C, Leoncini X, et al. Controle d'une interaction onde-particule par une onde-test[J].2007.
[121]Bachelard R, Fanelli D. Short-time dynamics in the presence of wave-particles interactions:A perturbative approach[J]. Communications in Nonlinear Science and Numerical Simulation,2010,15(1):40-47.
[122]Ettoumi W, Firpo MC. Stochastic treatment of finite-N effects in mean-field systems and its application to the lifetimes of coherent structures[J]. Physical Review E,2011,84(3).
[123]张善才,何多慧.上海深紫外自由电子激光装置从头至尾模拟计算研究[J].中国科学技术大学学报,2007,37(4)：461-465.
[124]Bachelard R, Chandre C, Leoncini X, et al. Control of the intensity of a wave interacting with charged particles:proceedings of the Proceedings of FEL, Berlin, Germany, [C].2006.
[125]Bachelard R, Antoniazzi A, Chandre C, et al. Enhancement of particle trapping in the wave-particle interaction[J]. Communications in Nonlinear Science and Numerical Simulation,2008,13(3):660-665.
[126]袁勤良.王友智.加速器束流发射度测量[J].原子能科学技术,1988,4：015.
[127]陈银宝.FEL中的束流发射度分析[J].核科学与工程,1992,2：011.
[128]杨震华,武玉璞.曙光一号自由电子激光器(FEL)电子束发射度的分析[J].计算物理,1994,11(3)：262-268.
[129]LIU WB, WANG SH, YE Q, et al. Emittance Measurement at BEPCⅡ Linac[J]. Chinese Physics C,2008,32(S1):86-88.
[130]Lapostolle PM. Possible emittance increase through filamentation due to space charge in continuous beams[J]. Nuclear Science, IEEE Transactions on,1971,18(3):1101-1104.
[131]顾强,戴建枰,戴志敏,et al.100MeV电子直线加速器的物理设计[J].强激光与粒子束,2008.
[132]王相綦,郝浩,冯光耀.合肥光源储存环中等发射度模式理论计算研究[J].中国科学技术大学学报,2009,(6)：599-602.
[133]Shintake T, Status report on Japanese XFEL construction project at SPring-8,2010.