Purely hypothetical since any kind of testing in atmosphere/space is banned by international legislation/agreement.
The humans have already bombed Luna so ... what could be expected to happen on Saturn if a hydrogen bomb were to explode in it's atmosphere? Would the explosion set the planet's atmosphere ablaze?
Nothing devastating would happen. When the comet Shoemaker Levy hit Jupiter, with considerably more energy than an H-bomb, it made a big bang but Jupiter is still there.
Saturn's atmosphere can't burn because there is no free oxygen present. In fact there is regular lightning on Saturn, so if the atmosphere was going to catch fire it would have done so by now.
I wonder if you were thinking the H-bomb would start a hydrogen fusion reaction in Saturn's atmosphere. If so, no runaway fusion reaction would occur as the density and temperature is far too low.
The density is not high enough in Jupiter or Saturn to achieve a sustainable environment for the fusion of hydrogen and helium.
