An Improved Representation of AC Space-Charge Fields in Steady-State Simulation Codes for Linear-Beam Tubes

Accurate evaluation of the ac space-charge electric field is required in order to obtain accurate predictions for linear-beam-tube performance using steady-state simulation codes. The space-charge field is commonly calculated under the assumption that the beam current density and space-charge fields are all periodic in time and locally periodic in axial distance. In this brief, it is shown by example that there are cases in which it is important, in both the small and large signal regimes, to include departures from this "local spatial periodicity" assumption. We find in the cases that we have studied that it is sufficient to keep a single additional term, proportional to the spatial derivative of the bunched beam current density, in the expression for the space-charge electric field. The resulting expression is much faster to evaluate numerically than a full convolution integral over all axial wavelengths. The improved representation is suitable for use in both small- and large-signal linear-beam simulation codes. It has been implemented and tested in the CHRISTINE large-signal TWT simulation code