It is shortly after detonation, I would like to know how it appeared few minutes later.

I remember I have seen some documentary movie about nuclear weapons and there was a test when some people stood on the ground and there was a high altitude blast directly above them. The blast as I remember looked VERY differently from those observed in lower altitudes. I think it was rather toroidal or something similar. And definitely there was not a mushroom cloud, probably due to much thinner atmosphere and so.