Simulation of cyclotron wave growth in a helical slow wave structure

Growth of large amplitude coherent cyclotron waves on unneutralized relativistic electron beams has been studied analytically and numerically. The mechanism for growth is the unstable coupling of helical waveguide modes with relativistic electron beam cyclotron waves. Approximate analytic growth rates are found to be in good agreement with the exact numerical solution of the linearized plasma equations on a self-consistent cylindrical beam equilibrium. Particle simulations performed in cylindrical geometry quantitatively confirm the theory. The calculations were conducted in both an infinite medium and realistically terminated configuration. In the latter, matched impedances on the helix were required to reduce transients and unwanted reflections to tolerable levels. Saturation in both cases is due either to convection or, in sufficiently long waveguides, growth of the wave until it physically intersected the helix.