A linear three-dimensional model for free electron laser amplifiers

This paper introduces a generalized, linear, three-dimensional model of the FEL amplifier. This 3-D model that is represented by a matrix gain-dispersion equation is valid in the various FEL gain regimes; the low and high gain regimes and the space-charge dominated regimes. It includes electron-beam longitudinal velocity spread effects that are caused by energy spread, transverse emittance and betatron motion. The model provides solutions for the EM-wave amplitude and phase profiles for any initial transverse profiles of the electron beam and of the EM wave, given at the entrance to the interaction region. The matrix gain-dispersion equation consists of angular spectrum components and therefore it is applicable for free-space FEL schemes and for rectangular waveguide schemes as well. Different linear three-dimensional effects, such as optical guiding, gain focusing, reduction of space-charge effects, bending of the radiation beam, off axis-gain, etc., are all inherently included in the presented model. Figurative results, derived according to the parameter sets of two representative high-gain FELs, are demonstrated.