An Exact Treatment of Helix Traveling Wave Tubes with Cold Tube Loss

Recent work on an exact treatment of a thin tape helix traveling wave tube (TWT) indicates that Pierce's classical linear theory requires revision at high beam currents to include space charge effects on the circuit mode [1]. These circuit mode space charge effects are characterized by a new parameter q, which acts in an analogous manner to the familiar space charge parameter Q that affects the beam mode. However, this approach has the crucial assumption that there are no ohmic losses in the tube, setting Pierce's cold tube loss parameter d $=$ 0. Here, we include these lossy effects by introducing an imaginary component of permittivity into the dielectric support structure and propose a modified dispersion relation that takes the effects of both q and d into account. We demonstrate the validity of our model by comparing our results to the classical theory in test cases with both uniform and non-uniform attenuation over the length of the tube. [1] P. Wong, D. Chernin, and Y. Y. Lau, IEEE Electron Device Lett. 39, 1238 (2018).