A general linear growth rate formula for large orbit, annular electron beams

Microwave radiation can be produced at cyclotron harmonics as a result of the synchronous interaction between a rotating E layer and an em wave. The derivation of a general growth rate expression is presented here for systems involving large orbit, thin, annular, relativistic electron beams. This growth rate formula is written in terms of parameters which contain the required information about the waveguide wall structure. This method extends previous results to systems that have empty waveguide modes which are hybrids. As an example of this latter case, growth rates for coaxial systems with dielectric liners are calculated via this formalism.