Dispersion characteristics of electromagnetic waves with radial and azimuthal polarization in a rotating relativistic electron beam guided by an ion channel are investigated. Ion-channel electrostatic field and self-fields of relativistic electron beam were included in the formalism. It is shown that the wave with radial polarization is unstable in two regions due to coupling with fast space charge wave. The behaviors of the instability magnitude and spread are analyzed as a function of equilibrium parameters. The introduced instability can be used for amplification and production of high-intensity laser pulse with radial polarization
