The three-dimensional perturbation effect of relativistic electron beam in ion-channel is analyzed by use of the charge fluid linear perturbation theory without extra magnetic field.The equivalent dielectric tensor of the system is derived.Particular research and numerical calculation for propagating axial electromagnetic wave are presented.The dispersion relation of the system is obtained.It is clearly shown that the electromagnetic slow-wave characteristics exist in the system.The electromagnetic radiation may result from the coupling of microwave mode to electronic Betatron motion.Finally

the research result gives a circumstantial evidence that the electromagnetic radiation

which brought from the electromagnetic instability in the system

might be Cherenkov radiation under a certain condition.