In this paper, the problem of free electron laser excitation by a rela
tivistic electron beam passing through background plasma with ion acou
stic wave as wiggler is studied. Under the case of Compton and Raman r
egime, both the linear dispersion relation and the growth, are present
ed. The analysis makes no assumption on the relative relation of the b
eam density and the background plasma electron density, and the result
is also lit to bath ion ripple laser case and the large amplitude ion
acoustic wave case.