Linear stability of a high-current, relativistic, charged particle beam drifting in a resonant cavity

Summary form only given. The effect that beam space-charge has on the stability of a relativistic, charged particle beam drifting in a cylindrical cavity resonator was investigated. This configuration is often referred to as a transit time oscillator (TTO). In the case of TTOs, existing linear theories are generally devoid of a self-consistent treatment of the oscillating cavity fields and the nonlinear beam equilibrium. This deficiency is removed by employing the Maxwell-fluid equations, in conjunction with a self-consistent model of the beam equilibrium, to derive a dispersion relation for symmetric, transverse-magnetic modes supported by the configuration composed of a relativistic, charged particle beam drifting in a cylindrical cavity resonator and confined by a large, external, axial magnetic field. For the case of a proton beam TTO, the dispersion relation is solved using different beam-equilibria to determine the effect that space-charge has on stability