The dispersion relation of electromagnetic waves propagation through a plasma loaded helix traveling wave tube (TWT) is derived. The analysis is based on the self consistent and complete field theory for a configuration in which a magnetized pencil type beam propagates through cold plasma in the tape helix enclosed with a loss-free wall. A linear analysis of the interaction is considered subject to the boundary conditions imposed on different regions of the configuration. The resultant dispersion relation that is obtained implicitly includes azimuthal variations and all spatial harmonics of the tape helix. When the plasma medium is absent the dispersion relation reduces to the findings of Ref.
