Tape helix perturbation including 3-D dielectrics for TWTs

Abstract

A perturbation technique described in a previous paper has been applied to the tape helix model of a traveling wave tube (TWT). The perturbation technique employs two solutions; the unperturbed solution is that for a helix in a conducting sleeve, suspended in vacuum, and the perturbed solution is with the above configuration, but with the introduction of dielectric support rods. Usually the perturbed solution is not known and is approximated by the homogeneous dielectric solution. Then in three-dimensional (3-D) fashion, the perturbation technique weights the dielectric with an energy-like term that is only evaluated within the discrete dielectric. Therefore, the model accounts for the distribution of dielectric material. Extending the perturbation to the tape helix, the current density is accurately portrayed in space. In all cases, the perturbed tape helix solution has a lower least square error in normalized phase velocity than the unperturbed tape helix solution. It had a lower error than the perturbed sheath helix solution of the previous paper, which in turn had a lower least square error than the Naval Research Laboratory's (NRL's) Small Signal Gain (SSG) Program. An initial discussion of the tape helix is presented and the calculated dispersion relation given. This solution incorporates a conducting backwall or shield with a homogeneous dielectric between it and the helix, using n=-6 to n=+6 space harmonics. Then the perturbation theory is applied, first for uniform support rods, and then to include notched rods. The resultant simulations produce phase velocity and coupling impedance data. Deviation from theory to experiment is reported by comparing the square root of the average sum of the squares difference, divided by an average phase velocity, between calculated phase velocities and a second order least squares fit of the measured data. Experimental data on the dispersion properties of four helices came from Northrop. The average error in phase velocity for four cases was 0.95%. For uniform rods the perturbation theory lowers the phase velocity, but doesn't significantly alter the dispersion. However, for notched rods, the perturbation theory raises the phase velocity and flattens the dispersion, in agreement with experiment. Computations can be performed in 1/2 min for a ten-frequency-step problem on a Pentium II processor.