电磁波摇摆器短波长自由电子激光非线性理论研究
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摘要
相对论性自由电子与强激光场作用时，表现出一些非线性现象，不同于常规的康普顿散射，使得短波长自由电子激光的研究进入一个全新的领域。提出了获得短波长自由电子激光的一种新方案，即通过研究相对论性电子与强场的对撞，可以在背散射方向获得短波长的散射光。此外，为扩展在背散射方向各谐波光谱的范围，本论文首次采用圆极化强电磁场和强磁场共同充当摇摆器，这对于完善背散射方向获得短波长自由电子激光具有十分重要的意义。
本论文主要从两种理论模型来研究相对论性电子与强激光场散射的作用机制：一是基于强场QED半经典理论，研究方法是将光场看做外场，作用过程吸收多个光子，发射一个新光子；二是采用经典理论，从哈密顿—雅可比方程出发，研究相对论性电子与强激光场的散射过程。主要探讨了强场条件下的一些非线性现象、重点讨论了对撞情形下散射频率及光子发射几率表达式、在背散射方向产生谐波光谱、并对微分散射截面进行了推导和数值分析。全文内容共分六章：
第一章绪论，介绍自由电子激光的发展与应用，概述电磁波摇摆器短波长FEL非线性理论发展及研究现状，提出获得短波长自由电子激光的一种新方案。
第二章介绍相对论性自由电子在强场摇摆器中运动的量子电动力学理论，并介绍处理电子在外场中发射光子问题的半经典方法。
第三章采用强场QED半经典理论，使相对论性电子与强激光发生对撞，在背散射方向可获得最短波长的的散射光子。探讨强场条件下的一些非线性现象、重点讨论了相对论性电子和圆极化强平面电磁波场对撞情形下的散射频率及光子发射几率表达式，并通过解析和数值分析。结果表明，强度效应对散射频率的非线性影响主要表现在两方面：一是电子可以吸收更多的光子，非线性首先表现在作用的光子数目上；二是激光强度因子出现在散射频率表达式的分母上。当相对论性电子在强场中运动，其质量转移与场强度有定量关系。为得到短波长自由电子激光,我们需要“蓝移逆Compton”散射，此时电子能量转化为光场能量。因此可以通过调节激光场的强度(?)使得光谱处于“蓝移逆Compton”区域。强场条件下，随吸收光子数n的增加，光子发射微分几率呈下降趋势，n = 1的基频谐波对应的光子发射几率处于主导地位，光子发射几率的贡献主要来自基频谐波。在背散射和向前散射方向只有基频谐波有贡献,对于高次谐波，在背散射方向有一个“死锥角区”。
第四章采用经典理论研究了相对论电子在横向圆极化平面电磁波的时空位置、动量、能量的普遍表达式。并通过洛伦兹变换将电子坐标系中n次谐波单位立体角平均辐射功率表达式转换为实验室坐标下的n次谐波单位立体角平均辐射功率表达式。重点讨论了相对论电子与强激光场对撞，在背散射方向产生谐波光谱，并对微分散射截面进行了推导和数值分析。结果表明：微分散射截面与初始条件、散射光子的出射方向有关。考虑圆极化强场的背散射情形,只有n =1的基频谐波,微分散射截面不为零，因此利用对撞情形的散射可以在高能电子运动方向上获得最大频率的相干光子。提高电子能量有利于产生高频光，而无限度地提高光强将不利于产生高频光。所以要利用非线性背散射来做短波光源，入射光场的强度要选择适当，不能过高也不能过低,过高则会提高对电子能量的要求,过低则非线性效应不明显。
第五章采用圆极化强电磁场和强磁场共同充当摇摆器，主要讨论了电子的动力学方程、散射频率以及功率微分散射截面。从δ函数可以看到背散射谱是由n次谐波构成，对于探索背散射方向短波长自由电子激光提出了一大胆的尝试。
第六章总结，概括本论文的主要结论，指出利用强场充当摇摆器，不断完善短波长自由电子激光的非线性理论。
When relativistic free-electrons interact with intense laser field in vacuum, somenonlinear penomena begins to appear, which is quite different from the ordinaryCompton scattering, leading the study of short-wavelength FEL to a completely newfield. A new scenario is proposed that a high-power intense laser is brought intohead-on collision with an electron beam, which can produce a new short-wavelengthphoton in the backscattered direction. Furthermore, to expand the backscatteredharmonics spectra, a intense laser field and a strong uniform magnetic field act aswiggler, which has very import significance in perfecting the theory ofshort-wavelength free electron laser in the backscattered direction.
Two modes are used to study free-electron–photon interaction mechanisms inthis paper: one is strong-field QED semi-classical method, in which the intensity offield is considered, multi-photon are absorbed and a new photon is emitted; the otheris classical method, in which a systematic derivation of the electron position andvelocity vectors is given starting from the Hamilton-Jacobi equation of the system andharmonic generation by the scattering of very-high-intensity laser light fromrelativistic free electrons is investigated theoretically. In this paper, the nonlinearpenomena is mainly discussed, by both analytical and numerical methods, we explorethe properties of differential scattered cross-section and the differential rate of photonemission in the process of free-electron–photon interaction. The expression of thescattered-photon frequency is deduced in the intense laser field. This paper consists ofsix chapters.
In Chapter 1, we give a brief introduction of the development and applications ofthe free electron laser. The development and current research state of electromagneticwave wiggler and short-wavelength FEL is summarized. Finally, we introduce a newscenario of producing short-wavelength FEL.
In Chapter 2, we introduce the quantum electrodynamics theory of motion ofrelativistic free-electrons interacting with intense laser fields and the semi-classicalmethod of emitting a photon in an external field.
In Chapter 3, based on QED semi-classical method, a high-powermonochromatic circularly polarized intense laser field is brought into head-oncollision with an electron beam, which can produce a new short-wavelength photon inthe backscattered direction. The nonlinear phenomenon in the interaction of freeelectrons with intense laser fields is researched. We research the characteristics ofscattered photon frequency and the differential rate of photon emission in the processof free-electron–photon interaction by both analytical and numerical methods. It isconcluded that, the two nonlinear effects on the scattered frequency are the number ofphotons involved in the interaction and its dependence on the field intensity. At highintensities one expects to see intensity-dependent mass shift of the electrons withinthe laser beam. In order to produce short-wavelength free electron laser, blue-shift“inverse Compton”is needed, in which the photon gains energy from the electrons.Thus by tuning the intensity, we effectively change the frame of reference, goingcontinuously from ordinary to inverse Compton scattering. The spectrum ofbackscattering (the head-on collision) is discussed numerically. It is concluded thatthe differential rate of photon emission decreases with the the number of photonsabsorbed by electrons and the largest signal is due to the fundamental harmonic, n=1.Thus, in particular, real backscattering at only occurs for n=1, while for the higherharmonics one has“dead cones”with an opening angle of about 0.1 rad, slightlyincreasing with harmonic number n.
In Chapter 4, we use the classical method to analyze the character of theharmonic generation by the scattering of very-high-intensity laser light fromrelativistic free electrons. A general solution for the trajectory of an electron, movinginitially with anopposite direction to the monochromatic circularly polarized intense laser is deduced.Based on Lorentz transformation, we present a general derivation expression for theaverage power per unit solid angle radiated into the nth harmonic. From thatexpression,the total average power per unit solid angle radiated into all the harmonicsas well as formulas for the corresponding differential scattering cross sections arederived. Then,we present and discuss the results of numerical calculations, under different initial conditions, of the harmonic cross sections. It is concluded that, ingeneral, the value of the scattered photon frequency, the differential cross-section areall related to initial conditions and direction of the scattered photon. Consideredingmonochromatic circularly polarized intense laser field, none of the harmonics of orderhigher than n=1 are scattered in the forward and backward directions. Improving theenergy of the initial electron is helpful to produce higher-frequency scatteredphoton,while unlimitedly improving the value of the field intensity is not helpful toproduce higher-frequency scattered photon.Therefore, the suitable value of the fieldintensity is needed. If the value of the field intensity is too large, the electron’s energyis also required high; if the value of the field intensity is too small, the nonlinearpenomena is not obvious.
In Chapter 5, by the use of a intense laser field and a strong uniform magneticfield acting as wiggler, richer backscattered spectra may arise.We present exacttrajectory solutions for a relativistic electron in the presence of a superintensecircularly polarized laser pulse and a uniform magnetic field. In this paper, the resultsof analytic investigations of the backscattered spectra is presented, which consist ofmany lines whose frequencies depend upon the laser-field intensity, the magnetic-fieldstrength,and the initial electron speed. Finaly we the backscattered differentialcross-section is deduced in the presence of a intense laser field and a strong uniformmagnetic field.
In Chapter 6, we summarize the main results from this paper, and illustrate theimportance role of intense fields wiggler in the development of short-wavelength freeelectron laser.
本论文主要从两种理论模型来研究相对论性电子与强激光场散射的作用机制：一是基于强场QED半经典理论，研究方法是将光场看做外场，作用过程吸收多个光子，发射一个新光子；二是采用经典理论，从哈密顿—雅可比方程出发，研究相对论性电子与强激光场的散射过程。主要探讨了强场条件下的一些非线性现象、重点讨论了对撞情形下散射频率及光子发射几率表达式、在背散射方向产生谐波光谱、并对微分散射截面进行了推导和数值分析。全文内容共分六章：
第一章绪论，介绍自由电子激光的发展与应用，概述电磁波摇摆器短波长FEL非线性理论发展及研究现状，提出获得短波长自由电子激光的一种新方案。
第二章介绍相对论性自由电子在强场摇摆器中运动的量子电动力学理论，并介绍处理电子在外场中发射光子问题的半经典方法。
第三章采用强场QED半经典理论，使相对论性电子与强激光发生对撞，在背散射方向可获得最短波长的的散射光子。探讨强场条件下的一些非线性现象、重点讨论了相对论性电子和圆极化强平面电磁波场对撞情形下的散射频率及光子发射几率表达式，并通过解析和数值分析。结果表明，强度效应对散射频率的非线性影响主要表现在两方面：一是电子可以吸收更多的光子，非线性首先表现在作用的光子数目上；二是激光强度因子出现在散射频率表达式的分母上。当相对论性电子在强场中运动，其质量转移与场强度有定量关系。为得到短波长自由电子激光,我们需要“蓝移逆Compton”散射，此时电子能量转化为光场能量。因此可以通过调节激光场的强度(?)使得光谱处于“蓝移逆Compton”区域。强场条件下，随吸收光子数n的增加，光子发射微分几率呈下降趋势，n = 1的基频谐波对应的光子发射几率处于主导地位，光子发射几率的贡献主要来自基频谐波。在背散射和向前散射方向只有基频谐波有贡献,对于高次谐波，在背散射方向有一个“死锥角区”。
第四章采用经典理论研究了相对论电子在横向圆极化平面电磁波的时空位置、动量、能量的普遍表达式。并通过洛伦兹变换将电子坐标系中n次谐波单位立体角平均辐射功率表达式转换为实验室坐标下的n次谐波单位立体角平均辐射功率表达式。重点讨论了相对论电子与强激光场对撞，在背散射方向产生谐波光谱，并对微分散射截面进行了推导和数值分析。结果表明：微分散射截面与初始条件、散射光子的出射方向有关。考虑圆极化强场的背散射情形,只有n =1的基频谐波,微分散射截面不为零，因此利用对撞情形的散射可以在高能电子运动方向上获得最大频率的相干光子。提高电子能量有利于产生高频光，而无限度地提高光强将不利于产生高频光。所以要利用非线性背散射来做短波光源，入射光场的强度要选择适当，不能过高也不能过低,过高则会提高对电子能量的要求,过低则非线性效应不明显。
第五章采用圆极化强电磁场和强磁场共同充当摇摆器，主要讨论了电子的动力学方程、散射频率以及功率微分散射截面。从δ函数可以看到背散射谱是由n次谐波构成，对于探索背散射方向短波长自由电子激光提出了一大胆的尝试。
第六章总结，概括本论文的主要结论，指出利用强场充当摇摆器，不断完善短波长自由电子激光的非线性理论。
When relativistic free-electrons interact with intense laser field in vacuum, somenonlinear penomena begins to appear, which is quite different from the ordinaryCompton scattering, leading the study of short-wavelength FEL to a completely newfield. A new scenario is proposed that a high-power intense laser is brought intohead-on collision with an electron beam, which can produce a new short-wavelengthphoton in the backscattered direction. Furthermore, to expand the backscatteredharmonics spectra, a intense laser field and a strong uniform magnetic field act aswiggler, which has very import significance in perfecting the theory ofshort-wavelength free electron laser in the backscattered direction.
Two modes are used to study free-electron–photon interaction mechanisms inthis paper: one is strong-field QED semi-classical method, in which the intensity offield is considered, multi-photon are absorbed and a new photon is emitted; the otheris classical method, in which a systematic derivation of the electron position andvelocity vectors is given starting from the Hamilton-Jacobi equation of the system andharmonic generation by the scattering of very-high-intensity laser light fromrelativistic free electrons is investigated theoretically. In this paper, the nonlinearpenomena is mainly discussed, by both analytical and numerical methods, we explorethe properties of differential scattered cross-section and the differential rate of photonemission in the process of free-electron–photon interaction. The expression of thescattered-photon frequency is deduced in the intense laser field. This paper consists ofsix chapters.
In Chapter 1, we give a brief introduction of the development and applications ofthe free electron laser. The development and current research state of electromagneticwave wiggler and short-wavelength FEL is summarized. Finally, we introduce a newscenario of producing short-wavelength FEL.
In Chapter 2, we introduce the quantum electrodynamics theory of motion ofrelativistic free-electrons interacting with intense laser fields and the semi-classicalmethod of emitting a photon in an external field.
In Chapter 3, based on QED semi-classical method, a high-powermonochromatic circularly polarized intense laser field is brought into head-oncollision with an electron beam, which can produce a new short-wavelength photon inthe backscattered direction. The nonlinear phenomenon in the interaction of freeelectrons with intense laser fields is researched. We research the characteristics ofscattered photon frequency and the differential rate of photon emission in the processof free-electron–photon interaction by both analytical and numerical methods. It isconcluded that, the two nonlinear effects on the scattered frequency are the number ofphotons involved in the interaction and its dependence on the field intensity. At highintensities one expects to see intensity-dependent mass shift of the electrons withinthe laser beam. In order to produce short-wavelength free electron laser, blue-shift“inverse Compton”is needed, in which the photon gains energy from the electrons.Thus by tuning the intensity, we effectively change the frame of reference, goingcontinuously from ordinary to inverse Compton scattering. The spectrum ofbackscattering (the head-on collision) is discussed numerically. It is concluded thatthe differential rate of photon emission decreases with the the number of photonsabsorbed by electrons and the largest signal is due to the fundamental harmonic, n=1.Thus, in particular, real backscattering at only occurs for n=1, while for the higherharmonics one has“dead cones”with an opening angle of about 0.1 rad, slightlyincreasing with harmonic number n.
In Chapter 4, we use the classical method to analyze the character of theharmonic generation by the scattering of very-high-intensity laser light fromrelativistic free electrons. A general solution for the trajectory of an electron, movinginitially with anopposite direction to the monochromatic circularly polarized intense laser is deduced.Based on Lorentz transformation, we present a general derivation expression for theaverage power per unit solid angle radiated into the nth harmonic. From thatexpression,the total average power per unit solid angle radiated into all the harmonicsas well as formulas for the corresponding differential scattering cross sections arederived. Then,we present and discuss the results of numerical calculations, under different initial conditions, of the harmonic cross sections. It is concluded that, ingeneral, the value of the scattered photon frequency, the differential cross-section areall related to initial conditions and direction of the scattered photon. Consideredingmonochromatic circularly polarized intense laser field, none of the harmonics of orderhigher than n=1 are scattered in the forward and backward directions. Improving theenergy of the initial electron is helpful to produce higher-frequency scatteredphoton,while unlimitedly improving the value of the field intensity is not helpful toproduce higher-frequency scattered photon.Therefore, the suitable value of the fieldintensity is needed. If the value of the field intensity is too large, the electron’s energyis also required high; if the value of the field intensity is too small, the nonlinearpenomena is not obvious.
In Chapter 5, by the use of a intense laser field and a strong uniform magneticfield acting as wiggler, richer backscattered spectra may arise.We present exacttrajectory solutions for a relativistic electron in the presence of a superintensecircularly polarized laser pulse and a uniform magnetic field. In this paper, the resultsof analytic investigations of the backscattered spectra is presented, which consist ofmany lines whose frequencies depend upon the laser-field intensity, the magnetic-fieldstrength,and the initial electron speed. Finaly we the backscattered differentialcross-section is deduced in the presence of a intense laser field and a strong uniformmagnetic field.
In Chapter 6, we summarize the main results from this paper, and illustrate theimportance role of intense fields wiggler in the development of short-wavelength freeelectron laser.
引文
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