Analysis of an FEL oscillator at zero detuning length of an optical cavity

The field of an FEL oscillator at zero detuning length of an optical cavity (δL=0) is characteristic of self-amplified spontaneous emission (SASE) FEL. For both cases, the field is composed of the precedent incoherent and subsequent coherent states. The evolution and saturation of the coherent field are studied analytically. The field during evolution is found to scale with FEL parameter ρ and the round-trip number, and that at saturation with ρ and an optical cavity loss. The field at δL=0 is similar to that of the leading edge of SASE FEL with high electron beam density.