Equilibrium and Confinement of Bunched Annular Beams

The azimuthally invariant cold-fluid equilibrium is obtained for a periodic, strongly bunched charged annular beam with an arbitrary radial density profile inside of a perfectly conducting cylinder and an externally applied uniform magnetic field. The selfelectric and self-magnetic fields, which are utilized in the equilibrium solution, are computed self-consistently using an electrostatic Green’s function technique and a Lorentz transformation to the longitudinal rest frame of the beam. An upper bound on the maximum value of an effective selffield parameter for the existence of a bunched annular beam equilibrium is obtained. As an application of the bunched annular beam equilibrium theory, it is shown that the Los Alamos National Laboratory relativistic klystron amplifier experiment is operating slightly above the effective selffield parameter limit, and a discussion of why this may be the cause for their observed beam loss and microwave pulse shortening is presented. The existence of bunched annular beam equilibria is also demonstrated for two other high-power microwave (HPM) experiments, the relativistic klystron oscillator experiment at Air Force Research Laboratory and the backward wave oscillator experiment at the University of New Mexico. In general, the results of the equilibrium analysis will be useful in the determination of the stability properties of strongly bunched annular beams in HPM devices.