The Non-Linear Theory of the Free Electron Laser with Transverse Dimensional Effects
This paper treats finite transverse dimensional effects associated with i) the wiggler field, ii) electron beam and iii) radiation beam in a steady state free electron laser (FEL) in an amplifying configuration. Our formulation incorporates various efficiency enhancement schemes such as spatially contouring the wiggler field as well as accelerating the electron beam. Three dimensional effects associated with the wiggler field introduce an axial velocity shear which is equivalent to a beam temperature. For a given amplitude input signal, the transverse gradients in the wiggler places a restriction on the electron beam radius. The restriction on the radius insures that a substantial fraction of beam electrons will be trapped in the ponderomotive brackets. We also find that the radiation field experiences diffraction and refraction effects in such a way that the superposition of the input radiation field and excited radiation field do not destructively interfere. Finally, a 3-D numerical illustration of a 10.6 μm FEL with enhanced efficiency is given.
KeywordsElectron Beam Radiation Field Free Electron Laser Input Field Refraction Effect
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