Diffraction effects in the self-amplified spontaneous emission FEL

In this paper we present a systematic approach for analytical description of SASE FEL (SASE: self-amplified spontaneous emission) in the linear mode. We calculate the average radiation power, radiation spectrum envelope, angular distribution of the radiation intensity in far zone, longitudinal and transverse correlation functions, degree of transverse coherence etc. Using the results of analytical calculations presented in reduced form, we analyze various features of the SASE FEL in the linear mode. The general result is applied to the special case of an electron beam having Gaussian profile and Gaussian energy distribution. These analytical results can serve as a primary standard for testing the codes. In this paper we present numerical study of the process of amplification in the SASE FEL using three-dimension time-dependent code FAST. Comparison with analytical results shows that in the high-gain linear limit there is good agreement between the numerical and analytical results. It has been found that even after finishing the transverse mode selection process the degree of transverse coherence of the radiation from SASE FEL visibly differs from unity. This is consequence of the interdependence of the longitudinal and transverse coherence. The SASE FEL has poor longitudinal coherence which develops slowly with the undulator length thus preventing a full transverse coherence.

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