09The thin beam model of an axis-encircling relativistic electron beam in a uniform, constant, external magnetic field in a cylindrical waveguide is used to develop a unified theory of the various interactions of such a beam with the electromagnetic field. The model includes the gyrotron interaction (longitudinal displacement of the beam) and the peniotron interaction (transverse displacement of the beam). Space-charge effects are included. The resulting selffields influence the boundary conditions of the perturbed electromagnetic field across the electron beam. For a beam with only azimuthal equilibrium flow and for propagation perpendicular to the equilibrium external magnetic field the well-known gyrotron instabilities are recovered. In addition, it is shown that the transverse beam modes (slow peniotron) are unstable for resonant interaction with the transverse electric (TE) waveguide mode. A general dispersion relation for propagation at any angle is derived for a beam with arbitrary energy and arbitrary pitch angle. This dispersion relation includes gyrotron, cyclotron autoresonance maser (CARM), peniotron, and harmonic autoresonant peniotron (HARP) interactions and the coupling between TE and transverse magnetic (TM) waveguide modes. For weak space charge, analytic expressions for the growth rates of the Doppler-shifted cyclotron resonance interaction of TE and TM modes with the gyrotron and slow peniotron modes are obtained.