A kinetic theory for the electron cyclotron maser interaction in a lossy cylindrical waveguide: Mode coupling among all supported waveguide modes

A general dispersion relation is derived assuming all supported empty waveguide modes are included in the electron cyclotron maser interaction within a good conducting cylindrical waveguide. Four energy transfer mechanisms exist of which three are directly related to the beam–wave interaction. The beam modes are shown to be coupled as a consequence of azimuthal asymmetry in the fields. New contributions to the instability terms result. Assuming single mode operation, new contributions to both the instability and the stability terms are obtained. Growth rates are examined. It is explicitly shown that all instability, stability, and coupling contributions due to a particular transverse magnetic mode vanish if a beam dispersion curve just grazes the empty waveguide dispersion curve of that mode. By adjusting the radius of a radially thin beam, the dominant azimuthally symmetric mode of operation can be adjusted.