Limitations of the transverse coherence in the self-amplified spontaneous emission FEL

In this paper we analyze the process of the formation of transverse coherence of radiation from a self-amplified spontaneous emission (SASE) FEL. It is shown that in the high-gain linear regime the degree of transverse coherence approaches unity asymptotically as z−1, but not exponentially, as one would expect from a simple physical assumption that the transverse coherence is established due to the transverse mode selection. 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 a 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.