Some Investigations On Statistical Physics Analysis In Free Electron Laser Physics

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.