A state variable electromagnetic (EM) analysis technique called rigorous wave coupled theory (RCWT) (used for the EM and optical analysis of planar diffraction gratings) is applied to determine the radiation and scattering that arises from phi-periodic circular cylindrical dielectric systems which have arbitrary radial and azimuthal, inhomogeneous, permittivity variation. The RCWT state matrix equations and the associated boundary matrix equations (derived from a multi-layer cylindrical ladder analysis) are presented and solved for the cases: (1) when a plane wave (TM polarization, electric field parallel to the cylinder axis) is incident on the phi-periodic dielectric cylinder and (2) when an electric line current source excites EM radiation inside the phi-periodic dielectric cylinder. Numerical examples of plane wave scattering and line source radiation from phi-periodic dielectric cylinder systems are presented. Comparisons for the first time of scattering and radiation from inhomogeneous step profile dielectric cylinder systems are made with scattering and radiation from uniform dielectric cylinder systems (assuming that both systems have an equal bulk or average dielectric permittivity value).