Formation of an FEL field with uniform and constant phase due to the slippage effect

The sustained saturation in an free-electron laser (FEL) oscillator at perfect synchronism of an optical cavity (δL=0) was experimentally verified despite the well-known lethargy effect (Phys. Rev. Lett. 86 (2001) 5707). Formation of an FEL field with uniform and constant phase from an incoherent state is one of the key issues to understand the mechanism how the lasing occurs at δL=0. In this report, we show that phase of an FEL field becomes uniform and constant during passage through undulator periods due to the slippage effect in a model independent manner.