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For some reason EZNEC+ does show both currents coming down to zero. Although the curve is more sudden here than on the CST model. I think that's due to the absence of the opposing current inside the basket but not sure. In any event, EZNEC+ does show the ends currents down to zero and your 4NEC2 is showing maximum current in the center of a 1/4 wave element. It does not appear that you need to add a phase shift between the sources since the phase shift between the two currents is a result of their sources being at different ends.