Slice emittance, projected emittance and properties of the SASE FEL radiation

The existence of a characteristic coherence length in SASE FEL Physics determines the lasing of different portions, namely the slices, of the electron bunch. Each slice may be characterized by different phase space properties, namely by not necessarily equal emittances and Twiss coefficients. This fact opens new questions on the strategies of beam matching and how the various portions of the beam contribute to the performances of the output radiation, including those associated with the transverse coherence. s paper we discuss how the FEL intensity evolution and eventually the saturated power are affected either by the phase space distributions of the different slices and by the e-beam transport matching. The analysis we develop is based on a semi-analytical procedure having the advantages of providing reliable results, with an almost negligible computational effort. The drawback of the method is that of neglecting the field phase evolution and the slippage effects. The obtained results are compared with those obtained from other codes and with the recent data from the SPARC experiment.