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We show that any lightning return-stroke model with specified longitudinal current distribution can be expressed, using the appropriate continuity equation, in terms of two current components, propagation current and corona current. For lumped-current-source (LCS)-type (transmission-line-type) models, the actual corona current is unipolar and directed radially out of the channel core, while for distributed-current-source (DCS)-type (traveling-current-source-type) models, it is also unipolar but directed into the channel core. The conversion between LCS and DCS return-stroke models alters the actual corona current (if any) of the model. A new formulation for LCS lightning return-stroke models is proposed using corona current and propagation current concepts. This formulation expresses the longitudinal current at height z' as the channel-base current minus the overall longitudinal current change from ground surface to z'. Dynamics of lightning-channel corona sheath surrounding the thin channel core are examined based on LCS and DCS models.