The Cerenkov maser at millimeter wavelengths

The dispersion relation for the transverse magnetic modes, TM(on) of a partially filled, dielectric-lined, cylindrical waveguide driven by a cold relativistic electron beam is derived. The effect of a gap between the electron beam and the dielectric liner is included. The dispersion relation is then used to calculate the growth rate for the Cerenkov instability in the collective tenuous beam limit. Expressions are developed for the minimum current necessary for oscillation threshold and for the power output of the Cerenkov maser in the collective regime.