Some Investigations Related To The Nonlinear Effects In Free Electron Lasers

Nonlinearity is universal for the free-electron lasers. This dissertation focuses on some problems related to the nonlinear behaviors in free-electron lasers. A detailed discussion of the basic FEL theory is provided, and this is the basis for our investigations. For a relativistic electron which is nonideally injected into an undulator, the spontaneous radiation spectrum is calculated theoretically and numerically, and a comparison with the corresponding results for ideally injected electron is made. The motion of electrons in a helical undulator with axial guiding field is analyzed. For the intergrable case when the self-field is neglected, the criterion of periodic or quasiperiodic electron orbit is investigated, as well as the initial condition for stable helical orbit. Further the chaotic properties of electrons motion for strong self-field regime are investigated. The chaotic nature is qualitative manifested and confirmed using Poincare maps method; under some theoretical analysis of nearly integrable system and the calculation of Lyapunov exponents for electron trajectories using numerical simulation, the threshold value of the self-field parameter for chaos is obtained respectively. The transverse motions of electron with both self-field and high-order wiggler field are analyzed, with an investigation on the confinement condition of electrons. Based on Colson-Bonifacio FEL theory, a numerical simulation code for 1-D steady state FEL is composed, hence the influence of self-field effect on output radiation field for high-gain FEL can be analyzed and numerical calculated. A novel statistical method for FEL saturation proposed by Julien Barre et. al. is modified in order to be adoptable to systems with self-field effect, via this method the influence of self-field on radiation intensity at saturation is investigated.