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Engineering return stroke models can be categorized either as current generation (traveling current source type) models or current propagation (transmission line type) models. The current generation models are described among other parameters by a corona current distributed along the channel. Recent studies show that there is equivalence between the models of current generation and current propagation types. Due to this equivalence, any engineering return stroke model of current propagation type can be described in terms of an equivalent corona current per unit channel length. The measurements conducted within 10-500 m from triggered lightning flashes show that the electric field of subsequent return strokes at these distances flattens within 15 mus or so. In this paper, the constraints imposed by this feature on the temporal and spatial variation of the equivalent corona current are investigated. The results show that in order for the close fields to flatten within 15 mus or so, the equivalent corona current, should be bipolar and the corona current wave shape at late times should be identical to that of the longitudinal current time derivative. This is in contrast to most of the engineering models of current generation type, in which the corona current is assumed to be unipolar.