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.

The interaction impedance is computed directly by calculating the magnitude of the space harmonic component of the longitudinal electric field with which the electron beam is synchronous, and the total RF power flow. Because the interaction impedance cannot be measured directly, the experimental approach involves measuring resonant frequencies in a perturbed resonant circuit and deriving an expression relating the change in resonant frequencies between the perturbed and unperturbed circuits to the interaction impedance. This derivation necessitates several approximations, rendering the experimental procedure less accurate than direct computation with MAFIA.

The computation of RF losses involves consideration of the effects of finite conductivity of the helix and barrel, and of the loss tangent of the dielectric (taken to be 0.0006 for BeO). In the study, the effect of surface roughness in increasing the effective resistivity of the tape was also taken into account. The total RF loss was calculated as a sum of surface resistivity and dielectric losses and summarized in terms of attenuation per turn of the helix as a function of frequency.

Figure 2. Three Parameters of Major Interest for characterizing the performance of the slow-wave structure depicted in Figure 1 were computed by MAFIA and measured.

Figure 2 shows principal electromagnetic parameters of the slow-wave structure, both as computed by MAFIA and as determined experimentally. The excellent agreement between computational and experimental results demonstrates the utility of numerical simulation as a substitute for building and testing TWTs to analyze numerous alternative TWT designs. In comparison with experimentation, numerical simulation costs less and takes less time, and thereby also affords additional freedom to analyze both novel designs and small variations on previous designs.

This work was done by Carol L. Kory of Analex Corp. for Lewis Research Center. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com under the Electronic Components and Circuits category, or circle no. 176 on the TSP Order Card in this issue to receive a copy by mail ($5 charge).

Inquiries concerning rights for the commercial use of this invention should be addressed to

NASA Lewis Research Center
Commercial Technology Office
Attn: Tech Brief Patent Status
Mail Stop 7-3
21000 Brookpark Road
Ohio 44135.

Refer to LEW-16571.

NASA Tech Briefs Magazine

This article first appeared in the April, 1998 issue of NASA Tech Briefs Magazine.

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