Abstract: The dielectric tensor of the longitudinally magnetized relativistically gyrating and drifting electron beam is derived by means of the MHD equations. The coupling coefficients between various eigenmodes are then calculated by regarding the Gyro-TWA as a waveguide partially filled with an anisotropic medium. Analysis shows that only those modes with the same azimuthal index couple with each other. The results in this paper are of use for gyrotron devices operating in non-basic mode in estimating mode pureness.