Sensitivity of a relativistic backward-wave oscillator to Budker's parameter

Using the self-consistent Vlasov approach, the sensitivity of the growth rate and frequency of the transverse magnetic modes of a relativistic backward-wave oscillator to Budker's parameter is calculated. A closed algebraic dispersion relation is derived, representing the linear stability properties of the free-streaming modes of a relativistic, thin, hollow, cylindrical electron beam moving down the axis of a disc-loaded waveguide in a strong axial magnetic guide field. The analysis is restricted to small ratios of Budker's parameter to the relativistic gamma factor of the beam.