Envelope model of beam radius variations in steady state beam-circuit interaction codes

The beam envelope equation [1] provides a simple model of the steady state dependence of the radius of an electron beam on axial location. Since the forces acting on a beam in any linear beam VE device depend on the beam radius, it is useful to have a model of the axial variation of the beam size in a beam-circuit interaction code. We describe an implementation of the envelope model in the CHRISTINE-CC large signal code for coupled-cavity TWTs [2], which ordinarily uses disks of fixed radius to represent the beam. Using this “add-in” envelope model, we illustrate some effects of beam expansion and contraction in a coupled-cavity TWT.