A computational study has been performed to show that one can accurately compute the cold-test electromagnetic characteristics of the helical slow-wave circuit of a traveling-wave tube (TWT).

Previous efforts to apply computer-aided design techniques to helical TWT circuits had involved computer codes based partly on simplifying approximations of TWT geometries as they relate to electromagnetic characteristics; helices have been approximated as sheaths, helix tapes have been approximated as having zero thicknesses, and dielectric rods that support the helices have been approximated by combinations of homogeneously and inhomogeneously loaded volumes with effective permittivities. However, to simulate electromagnetic characteristics accurately, one must use a computer code that represents the geometry of the TWT in its three-dimensional complexity. This can be done by use of the computer program MAFIA (Solution of Maxwell's Equations by the Finite-Integration-Algorithm) - a powerful, modular electromagnetic-simulation code written in FORTRAN 77 for use in the computer-aided design and analysis of two- and three-dimensional electromagnetic devices, including magnets, radio-frequency cavities, waveguides, and antennas.

Figure 1. Three Turns of the Helical TWT Slow-Wave Circuit are depicted here by a plot from MAFIA, wherein the helix is generated in a cylindrical coordinate system by varying axial and azimuthal coordinates consistently with the formula for a circular helix. For clarity, the barrel surrounding the dielectric rods is omitted from this view.

In MAFIA, the geometric accuracy is limited only by the resolution of the computational grid used to represent the geometry of the modeled device. The finite integration technique (FIT) algorithm implemented in MAFIA yields a matrix of finite-difference equations for the electric and magnetic fields in the device under study. Solutions can be obtained in the time or the frequency domain, or in the static domain where applicable.

In the study, MAFIA was applied to a TWT slow-wave structure that included a copper-plated rectangular tape wound into a helix, which was supported by rectangular BeO dielectric rods inside a conductive barrel (see Figure 1). The electrical resistivities of the helix and barrel; the width, thickness, and helical pitch of the tape; and the dielectric properties and dimensions of the rods were all incorporated into the MAFIA model.

The TWT cold-test characteristics of primary interest are the slow-wave dispersion (normalized phase velocity vs. frequency), the on-axis electron-beam/slow-wave interaction impedance, and radio-frequency (RF) losses. The computational approach to determining the dispersion characteristics involved the use of boundary conditions analogous to those used in the experimental approach: In the experimental approach, one determines the dispersion characteristics from measurement of resonant frequencies of a section of the slow-wave circuit shorted at both longitudinal ends. In the computational approach, a MAFIA helix model is truncated with either electric or magnetic walls at two end points to simulate standing waves with an integral number of half wavelengths in the circuit section thus isolated.