The simplified cyclotron maser mode presented by Lau [1] is analyzed under small signal conditions with an exact analytical solution to the proper boundary condition taken across a thin, hollow rotating beam. Not only is

, but so are

and

. These discontinuities lead to the simultaneous presence of TE and TM modes, which leads to modifications in the dispersion relationship. The theory is applied to the drift space of klystron-type devices and to gyrotron-type devices operating in either TE or TM modes. Since radial displacements of the beam are taken into account, results presented also include space charge effects in peniotrons.