Theoretical Research And Computer Realization Of N-photon Scattering In Compton Free Electron Laser

Free electron laser, since born in 1977, has been developed so rapidly in aspects of both theory and experiment. The interaction of optical field with free electron is the core issue of producing free electron laser. With the development of intense laser technology, some extreme cases, such as super-intense filed, have been obtained, in which nonlinear phenomena become obvious. The scattering of multi-photon with a free electron is a nonlinear phenomenon,in which multi-photon is absorbed and a new photon is emitted.Two modes are used in this paper: one is n-photon group mode, in which the intensity of optical field is ignored, n photons are all absorbed, and the standard perturbation theory is used; the other is nonlinear interaction in a strong external field, in which the intensity of field is considered, partial photons are absorbed and semi-classical method is used.Based on the above two modes, the properties of differential scattered cross-section and energy-exchange in the process of N-photon scattering are investigated, and Matlab is used to program and do the numerical analysis. This paper consists of five chapters.In Chapter 1, we introduce the development, current issue and applied prospect of free electron laser. The development and current research state of multi-photon phenomenon is summarized. Finally, the issue of N-photon scattering in Compton free electron laser is led out.In Chapter 2, we research the characteristics of scattered photon frequency, electron energy change and differential scattered cross-section of n-photon scattering by n-photon group mode. Differential scattered cross-section of n-photon group scattering in the electron rest frame is deduced from standard perturbation theory, and the relation between differential cross-section and scattered angle is derived exactly in the case of double-photon group. Based on this relation and relativistic conversion, we investigate the related character in the laboratory frame, and analyze the differential cross-section and the averaged energy change of free electron in the process of double-photon group scattering. It is concluded that, in general, the value of the scattered photon frequency, the differential cross-section and electron energy change are all related to azimuthal angle, and the differential cross-section derived from the standard perturbation theory is proportional to the (n-1)th power of number density of the incident photons. In the case of double-photon group, when given the electron energy, there exists an optimum value of the initial angle between the propagation direction of incident photon and the direction motion of the electron before scattering. If initial angle equals to this value, the scattered photon with the maximum peak intensity, can be detected in the range of small taper angle near the direction of electron motion before scattering. There also exists a critical value of initial angle. If initial angle is larger than the critical value, the electron's energy is converted into the new photon's. If initial angle is smaller than the critical value, the energy of photons is converted into electron's.In Chapter 3, we introduce the quantum electrodynamics theory of motion of an electron and the semi-classical method of emitting a photon in an external field.In Chapter 4, we use the semi-classical method to analyze the character of the differential cross-section and the electron energy change in the process of n-photon nonlinear Compton scattering in an intense plane electromagnetic wave field with circle polarization. The angle distribution about the differential cross-section is considered, and the intensity and energy dependence is also investigated numerically. The spectrum of backscattering (the head-on collision) is discussed numerically. It is concluded that the suitable value of the field intensity is needed in order to produce short wave light by n-photon nonlinear Compton scattering. When given the electron energy and field intensity before scattering, there exists a critical value of initial angle in the case of n-photon. If initial angle is larger than the critical value, the electron's energy is converted into the new photon's. If initial angle is smaller than the critical value, the energy of photons is converted into electron's. To the double-photon nonlinear Compton scattering, when the normalized field intensity is much smaller than the Lorentz factor of electron energy before scattering, the critical value is equal to the one in double-photon group Compton scattering for the same electron energy. The critical value is seldom affected by the field intensity, while mainly depends on the electron energy before scattering.In Chapter 5, we summarize the main results from this paper, and illustrate the important role of N-photon scattering on the development of free electron laser and short wave light.