  Abstract -- We construct an analytical model for the dispersion of the hot
modes in a traveling wave tube (TWT) based on the Lagrangian field theory,
upgrading its constants to be frequency-dependent. The frequency dependence of
the parameters of the TWT slow wave structure (SWS) is recovered from full-wave
simulations by standard software (e.g., CST). We applied the model to study the
hot modes of a helical-based TWT and found an excellent agreement between the
results from our model and those from particle in cell (PIC) simulations. Our
additional studies show that the proposed approach can be applied to various
SWS geometries.
