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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?

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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.

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You are talking about the upper atmosphere. You need to know whether there is a dense deuterium layer segregated deep in the interior, and whether an uncontrolled explosion in an all deuterium environment can produce fusion. –  Ron Maimon Jul 30 '12 at 15:27
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An elevated fraction of deuterium is required to propagate a thermonuclear detonation wave, but even relatively low atomic fractions, such as 1:300, should allow ignition. See "Necessary Conditions For The Initiation And Propagation Of Nuclear Detonation Waves In Plane Atmospheres" (section VIII) by Weaver & Wood for more details. –  mmc Jul 30 '12 at 16:25
    
@RonMaimon & mmc: Didn't occur to me there might be a segregated layer ... good call. Thank you (+: –  Everyone Jul 30 '12 at 17:59
    
@mmc: thanks for the link, that's a fascinating article. –  John Rennie Jul 30 '12 at 19:11

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