Electromagnetic Wiggler Free Electron Laser Frequency Nonlinear Theories

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.