The time-domain studies of the modal fields in a lossy waveguide are executed. The waveguide has a perfectly conducting surface. Its cross section domain is bounded by a singly-connected contour of rather arbitrary but enough smooth form. Possible waveguide losses are modeled by a conductive medium which fills the waveguide volume. Standard formulation of the boundary-value problem for the system of Maxwell's equations with time derivative is given and rearranged to the transverse-longitudinal decompositions. Hilbert space of the real-valued functions of coordinates and time is chosen as a space of solutions. Complete set of the TE-time-domain modal waves is established and studied in detail. A continuity equation for the conserved energetic quantities for the time-domain modal waves propagating in the lossy waveguide is established. Instant velocity of transportation of the modal flux energy is found out as a function of time for any waveguide cross section. Fundamental solution to the problem is obtained in accordance with the causality principle. Exact explicit solutions are obtained and illustrated by graphical examples.
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