How Accurate Is Pierce's Theory of Traveling Wave Tube?

This paper provides a rigorous test of the accuracy of Pierce's classical theory of traveling wave tubes (TWTs). The EXACT dispersion relation for a dielectric TWT is derived, from which the spatial amplification rate, ki, is calculated. This ki is compared with that obtained from Pierce's widely used 3-wave theory and his more general 4-wave theory (which includes the reverse propagating circuit mode [1]). We have used various procedures to extract Pierce's gain parameter C and space charge parameter Q from the exact dispersion relation. We find that, in general, the 3-wave theory is a poor representation to the exact dispersion relation if C \textgreater 0.05. However, the 4-wave theory gives excellent agreement even for C as high as 0.12 and over more than 20 percent bandwidth, if the quantity (k$^2$ $\times$ C$^3$) is evaluated accurately as a function of frequency, and if Q is expanded to first order in the wavenumber k [2], where Q is the difference between the exact dispersion relation and its 4-wave representation in which Q is set to zero [3]. Similar tests will be performed on the disk-on-rod slow wave TWT, for which the hot tube dispersion relation including all space harmonics has been obtained. \\[4pt] [1] J.R. Pierce, Traveling Wave Tubes, p. 113 (1950).\\[0pt] [2] D. Dialetis, et al, IEEE Trans. ED 54, 888 (2007).\\[0pt] [3] Y. Y. Lau and D. Chernin, Phys. Fl. B4, 3473 (1992).