MODE DECOMPOSITION OF A TAPERED FREE ELECTRON LASER

SUMMARY Thetaperundulatorschemewiththreekindsoftransverseelectric beam distributions is investigated for a TW FEL.The transverse coherence property is discussed by mode de-composition. An approach of nding the mode contents ofa complex electric eld generated from GENESIS simulationis proposed and proven to be reliable. It is discovered thatin the post saturation region, over 90% of the total powerbelongs to the fundamental mode. For the three dierenttransverse distributions, the percentage of the fundamentalmode power is higher in the attop and parabolic cases thanin the Gaussian case. The high percentage of the funda-mental mode guarantees a high transverse coherence. Withthe knowledge of the mode contents, the source location isalso calculated, which provides information for downstreamx-ray beam line design. ACKNOWLEDGEMENT The authors would like to thank Professor S.-Y. Lee ofIndiana University for many stimulated discussions. K.F.would like to express his gratitude to Prof. Lee for manyadvices. The work was supported by the US Department ofEnergy(DOE)undercontractDE-AC02-76SF00515andtheUS DOE Oce of Science Early Career Research Programgrant FWP-2013-SLAC-100164. The work of K.F. was alsosupported by the US DOE grant DE-FG02-12ER41800 andNational Science Foundation grant NSFPHY-1205431.