Abstract
In a free electron laser (FEL), the radiation field, wiggler field and electron beam resonantly couple and modify the refractive index in the vicinity of the electron beam, such that the radiation beam will tend to focus upon the electron beam. From the radiation envelope equation derived from the source dependent expansion (SDE) method of solving the 3-D wave equation in FELs, conditions and parameters necessary to achieve guided radiation beams (constant radius) in the Compton exponential gain regime are obtained for FELs driven by either induction linacs or rf linacs with various transverse profiles of the electron beam. From the efficiency of the guided radiation beam, the trapping potential of the ponderomotive potential prior to saturation and the required beam quality of the electron beam can be obtained. The wiggler field could be tapered to further increase the operating efficiency. The possibility of bending or steering radiation beams in FELs is discussed and a condition necessary for radiation guiding along a curved electron beam orbit is obtained.
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