Any smoke is certainly NOT normal - and a very real concern!
It indicates (1) far too much current flow, or (2) a poor connection that is generating too much resistence, or both.
Personally, I would NOT ride that bike until I was absolutely certain I had found the problem and corrected with it - sounds like you may be dealing with the possibility of fire!
There should be a lock washer on each battery post, just under the nut. It should not loosen after a start or two - it should not loosen until you turn it with a wrench.