The free-electron laser (FEL) based on the self-amplified spontaneous emission (SASE) is an effective candidate of the coherent optical sources at wavelengths in ultraviolet and x-rays. It requires a relativistic electron beam with extremely high quality and extremely stable transmission. In this paper we analyze the dynamic behavior of the relativistic electron in that device by calculating the entropy-like quantity. Results show that if there is no adiabatic field of the wiggler, the electron beam may have great fluctuation in velocity space and diverge in configuration space.