Stability properties of coherently gyrating electron beams

Summary form only given, as follows. Vlasov-Maxwell theory is used to analyze stability properties of a relativistic electron beam, traveling along and gyrating about the field lines of a uniform magnetic field. Perturbations of the right- and left-handed radiation fields together with the longitudinal electric field are considered. The equilibrium distribution is of the general form f/sub 0/(p/sub /spl perp//, p/sub z/,/spl phi/-/spl Omega//sub c///spl gamma/t) where /spl phi/ is the momentum phase of an electron and /spl Omega//sub c/ is the nonrelativistic cyclotron frequency. For the case of zero energy spread, an exact dispersion relation is obtained. The temporal periodicity of the equilibrium distribution is dependent on the single particle energy. Consequently, for the case of a finite energy energy spread, the dispersion relation is governed by a set of coupled integral equations. Work is in progress to analyze the effect of the energy spread on the stability properties of the system.