The three-dimensional non-linear theory of the free electron laser in the amplifying configuration

This paper presents a self-consistent non-linear treatment of the finite transverse dimensional effects associated with (1) the wiggler field, (2) the electron beam and (3) the radiation beam of the free electron laser (FEL) in a steady state amplifying configuration. Our formulation incorporates various efficiency enhancement schemes. A linearly polarized magnetic wiggler is used for our formulation. The inherent gradient of the magnetic wigglers in the transverse direction introduces betatron oscillations, which cause an increase in the effective axial beam temperature. The radiation beam in the presence of the electron beam and the magnetic wiggler experience diffraction as well as refraction effects. We find that the 3-D effects can lead to substantial differences in the effects compared to the 1-D theory. Finally a 3-D numerical illustration of a 10.6 micron FEL is given.