The compact and the short wavelenghth FEL was the study highlight in this field,The wiggler with the short wiggler period and the strong electromagnetic field is a effective way to solve these problems.In this paper,We analyse the mechanism of plasma-wave-field wiggler,The angular spectrum of spontaneous emission from relativistic electrons is derived.Furthermore,resorting to the Madey theorem and the theory about phased antenna array,we enhance the formula of stimulated emission and the small singal gain of FEL is calculated in this kind of wiggler.