A three-dimensional multifrequency large signal model for helix traveling wave tubes

A three-dimensional (3D) multifrequency large signal model of the beam wave interaction in a helix TWT is described. The beam is divided into a set of discrete rays, or "beamlets", instead of the disks or rings used in one-dimensional (1-D) or two-dimensional (2-D) models. The RF fields supported by the helix are represented by a tape helix model that uses a modal expansion including the full (Bessel function) radial dependence of the fields; both forward and backward synchronous space harmonics are included in the model. RF space charge fields are obtained from solutions of the Helmholtz equations for the RF electric and RF magnetic fields, using the beam current and charge densities as sources. The dc space charge electric field is similarly obtained from a solution of Poisson's equation. This model has been implemented in a code called CHRISTINE 3D, a generalization of the one dimensional CHRISTINE code. The full three dimensional treatment permits the accurate computation of large signal gain and efficiency, taking into account the self-consistent variation of beam radius along the interaction space. The code also computes helix interception current and transverse beam distributions at the entrance to the collector-important design data that are unavailable from a 1D model. Results from the CHRISTINE 3D code are shown to compare very favorably with measurements of output power, efficiency, and interception current vs. drive power. Its predictions for spent beam distributions also compare very well with measurements. Run times for the code are problem dependent, but for a single case of interest are typically 1 to 5 min on a 450 MHz PC, orders of magnitude shorter than that required for a comparable 3D particle-in-cell simulation.