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Generalized lightning traveling-current-source return-stroke model (GTCSM) has been used to calculate the conductivity of the channel corona sheath and to examine the radiated lightning electromagnetic pulse (LEMP) during the return stroke. By using a two-layer cylindrical model of the lightning channel, the connection between the channel sheath conductivity and the channel discharge function is derived. The conductivities of the corona sheath for different channel line charge density distributions are calculated and compared with the predictions of transmission-line type of models. It is concluded that the GTCSM and the transmission line model (TLM) predict similar values of the corona sheath conductivity during the return-stroke process along the bottom portion of the channel on the order of 10 muS/m. However, the time for achieving more or less constant value of the corona sheath conductivity is about 200 ns for the GTCSM, about two orders of magnitude smaller than that for the TLM. Different line charge distributions along the bottom portion of the channel are analyzed, and corresponding waveforms of the radiated LEMP are calculated. The GTCSM eliminates completely all shortcomings of the ldquoengineeringrdquo traveling-current-source type of return-stroke models concerning the current discontinuities and the discontinuities of the current derivative at the place of the return-stroke wave front. Obtained results show good matching with the measured data for far distances (bipolar structure of the field derivative) as well as for very close distances from the strike point (monopolar structure of the field derivative). The presence of the upward connecting leaders from the elevated object and their influence on the line charge distribution along the bottom portion of the channel is considered. Given results provide better understanding of the channel corona sheath dynamics based on the remote measurements of the radiated LEMP as well as on the measured electric an- - d magnetic field waveforms in the immediate vicinity of the lightning channel.