Using kinetic coupling mode theory of three waves, the effect of longi
tudinal momentum spread in ion-ripple laser (IRL), which is an advance
d new scheme to generate tunable-coherent radiation with frequency ran
ging from microwaves to x-rays, is investigated. For a Gaussian distri
bution in beam longitudinal momentum, the results show that the growth
rate of IRL falls of rapidly with increasing momentum spread, and the
momentum spread causes linear damping of beam space-charge wave, weak
ening the beam-radiation mode coupling and lowering the output radiati
on frequency apart from broadening the radiation spectrum. The dispers
ion relation and phase matching conditions are also obtained.