Transverse coherence of self-amplified spontaneous emission

Transverse coherence of Self-Amplified Spontaneous Emission (SASE) in high-gain FELs is investigated through a three-dimensional eigenmode analysis. It is the first time such an analysis could be carried out to account for the effects of emittance and betatron focusing. In addition to the variational solution (Xie, Nucl. Instr. and Meth. A 445 (2000) 59, these proceedings) found for the fundamental mode, E00, similar solutions are derived here for two higher order eigenmodes, E10 and E01. Based on the growth rates of these three modes, a universal criteria on transverse coherence of SASE is proposed.