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This paper presents a novel 3-D finite-element modeling technique for the arbitrary lossy slow-wave structure (SWS) of a traveling-wave tube (TWT). By using this technique, we can accurately and quickly calculate not only dielectric losses but also conductivity losses of the SWS. In this modeling technique, a new frequency-specified eigenmode analysis (FSEA) for SWSs is proposed and utilized. Unlike the traditional phase-advance-specified eigenmode analysis for SWSs, which has to solve a nonlinear generalized eigenvalue problem (GEP), the new FSEA approach only needs to solve a linear GEP and is capable of obtaining the attenuation constant more accurately and directly without any postprocessing when simulating the lossy SWSs. Moreover, to further significantly improve the efficiency of modeling lossy SWSs, three advanced techniques are introduced in the standard implicit restarted Arnoldi method (IRAM) and an improved inexact IRAM is proposed. By simulating many practical SWSs, the accuracy and highly efficient performance of this modeling technique have been validated. It is shown that this modeling technique would be very useful to design a low-loss SWS for high-efficiency TWTs.