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I happened to hear people saying that the nuclear fusion bomb tests could set the atmosphere on fire. I have some serious doubts about that - but I have no facts.
Nuclear fusion reaction requires $15*10^{6}$ kelvins to start. If we produce such temperature in "open air" would the atmosphere become a fuel for further fusion? Shouldn't the whole thing just be torn apart by its terrible pressure?

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    $\begingroup$ This questions was taken somewhat seriously while the first fusion explosives were being designed and built. I believe the fear was that the explosions would ignite nitrogen burning (i.e. chemistry) in the atmosphere and that this would prove to be self sustaining. Given that fusion bombs have been detonated in the atmosphere quite a few times the experimental answer seems to be "no". $\endgroup$ May 28, 2013 at 20:49
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    $\begingroup$ Regarding Nitrogen burning, does that release enough energy to be self-sustaining? If we could produce a bomb with enough energy to get it started would it actually chain reaction? It seems like if a fusion bomb can't start the process then there is no way enough energy could be released to sustain it. $\endgroup$ May 28, 2013 at 21:04
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    $\begingroup$ @BrandonEnright - As far as I remember, kinetics of nitrogen-oxygen reactions are very interesting - many species, dependence on high (around 2000-4000K) temperature. With the explosion (again, AFAIR) the main impediment to exothermic oxidation of nitrogen is the short time scale during which the necessary conditions hold. (Hope that someone from Chemistry SE would clear up the confusion.) $\endgroup$ May 28, 2013 at 21:26
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    $\begingroup$ AFAIK, the concerns early in the Manhattan Project all dealt with the initiation of a nitrogen nuclear fusion reaction, referred to figuratively as nitrogen burning. The OP seems to refer to this case; other comments seem to discuss chemical burning. $\endgroup$
    – DJohnM
    May 29, 2013 at 0:25
  • $\begingroup$ @dmckee I love that historical note. There are numerous texts from throughout the early and mid 20th century that hint at the concerns of runaway atmospheric burning (e.g. work by Akira Sakurai). I don't know if I feel relieved that there were scientists worried about that kind of thing; or concerned that it doesn't seem to have gotten that much attention... $\endgroup$ May 29, 2013 at 1:04

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From what I have read in "American Prometheus: The Triumph and Tragedy of J. Robert Oppenheimer" Teller was the first one to express this concern before the Trinity test. Also quoting from: http://www.sciencemusings.com/2005/10/what-didnt-happen.html

Physicist Edward Teller considered another possibility. The huge temperature of a fission explosion -- tens of millions of degrees -- could fuse together nuclei of light elements, such as hydrogen, a process that also releases energy (later, this insight would be the basis for hydrogen bombs). If the temperature of a detonation was high enough, nitrogen atoms in the atmosphere would fuse, releasing energy. Ignition of atmospheric nitrogen might cause hydrogen in the oceans to fuse. The Trinity experiment might inadvertently turn the entire planet into a chain-reaction fusion bomb.

Robert Oppenheimer, chief of the American atomic scientists, took Teller's suggestion seriously. He discussed it with Arthur Compton, another leading physicist. "This would be the ultimate catastrophe," wrote Compton. "Better to accept the slavery of the Nazis than run a chance of drawing the final curtain on mankind!"

Oppenheimer asked Hans Bethe and other physicists to check their calculations of the ignition temperature of nitrogen and the cooling effects expected in the fireball of a nuclear bomb. The new calculations indicated that an atmospheric conflagration was impossible." Bethe apparently then convincingly showed that the atmosphere would not be set on fire by a nuclear bomb.

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    $\begingroup$ But this reference, sciencemusings.com/2005/10/what-didnt-happen.html makes it clear that the concern was nitrogen fusion, not burning. $\endgroup$
    – DJohnM
    May 30, 2013 at 0:23
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    $\begingroup$ @physicsphile My concern was that throughout these comments, there is confusion about whether nuclear fusion of nitrogen, or chemical burning of $N_2$ and $O_2$, is the actual subject. The OP clearly is interested in fusion, as were Oppenheimer et al... $\endgroup$
    – DJohnM
    May 31, 2013 at 0:32
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    $\begingroup$ I don't think anyone is suggesting chemical burning, they are just using casual/descriptive language when they say "set the atmosphere on fire". $\endgroup$
    – Virgo
    May 31, 2013 at 11:32
  • $\begingroup$ Isn't the solar core, with it's low power density, another argument against an out of control fusion event? Any fusion heat would quickly dissipate without a thick jacket to keep it hot. $\endgroup$ Oct 19, 2014 at 11:08
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I'd simply like to add to physicsphile's answer.

The primary source for this question is

Konopinski, E. J; C. Marvin; Edward Telle, "Ignition of the Atmosphere with Nuclear Bombs", Los Alamos National Laboratory technical report #LA-602

It shows that the answer to the OP's question is "highly unlikely". It does not prove impossibility. It's an interesting read from the point of view that these were the calculations and reasonings that the whole future of life on Earth was decided with.

As a physicist, I would say the document is highly sound. Altogether acceptable for making decisions about money expenditure of any kind, even sound enough that one would OK an experiment that could risk even hundreds of lives with (although it is hard to think of a realistic example). But it's a little scary to think that the whole future of life on Earth was decided with it....

So let's look at the experimental data. We haven't ignited the atmosphere yet. I think this experimental fact is important for your question: as I understand it, the fine details of the explosion dynamics are to a large degree found by trial and error, and such experimental data are all classified anyway. But the following comments are probably relevant. The biggest bomb to date was the Soviet Tsar Bomba, which let slip $2.4\times10^{17}J$, or $2.6{\rm kg}$ (that's right, kilograms!) of energy (57MT TNT equivalent). The fireball from this monster was eight kilometres across. At this size of bomb, you have probably reached a scale where bigger bombs are going to mean a proportionally bigger volume of space at roughly the same temperatures (on the order of $10^8{\rm K}$). Moreover, Edward Teller calculated that at yields not much higher, the effect of increased yield (as far as the atmosphere is concerned) is negligible: a big chunk of the atmosphere around the blast is accelerated to Earth escape velocity and is lost into space, so adding yield simply means that the escaping gas is going to escape faster: it's not coming back once it reaches $11{\rm km\, s^{-1}}$, so what happens to it is irrelevant.

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  • $\begingroup$ Given the current political situation, I feel very uncomfortable reading about kilometres wide fireballs created by Russian bombs... $\endgroup$ Dec 19, 2014 at 10:54
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    $\begingroup$ Great find with that document -- I can only imagine how surreal it must have felt for the authors to write it. In any event, we also have been struck by plenty of far more energetic asteroids, so there was also direct experimental evidence even at the time that we wouldn't destroy the atmosphere. $\endgroup$
    – user10851
    Feb 16, 2016 at 1:57
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Summary: the main reactions in the air involve nitrogen, and in the sea, involve deuterium. Based on the knowledge Bethe had back in the 1940s and making very optimistic assumptions, runaway fusion in the air seemed to be impossible, but with a small safety factor less than 2 if you were to use a fusion bomb with a radius of 3 meters of liquid deuterium. That would be a superbomb vastly more powerful than any bomb we would conceivably make. Runaway fusion in the ocean never was plausible.

However by 1975 in a comment by Dr Gilbert on a paper on the topic, then it was clear that the atmosphere is nowhere near dense enough for a sustained fusion reaction even if the nitrogen reaction had the same energy yield as deuterium tritium fusion (the most reactive known fusion reaction) because of energy losses - and as for the sea, the energy losses for a fusion reaction would make it impossible even in a sea of pure D2O instead of H2O. The energy losses are too great for sustained fusion at the pressures we can attain in an Earth ocean.

This shouldn't be too surprising. After all in the early solar system especially in the first billion years or so the Earth was frequently hit by large impactors of one hundred kilometers in diameter or more. None of our nuclear bombs come close to producing those levels of heating of the atmosphere or ocean, and obviously they didn't cause sustained fusion reactions in the atmosphere or the ocean. After all there is lots of water in the ocean and it hasn't all been converted to helium, and the atmosphere hasn't been converted to magnesium - we'd surely see the signature of such an event even if it was later replenished somehow. Even the Chicxulub impactor was about 100 million megatons, in the energy it released, or two million times more powerful than the Tsar Bomba. See UT Austin scientist reports results from study of Yucatan crater linked to mass extinctions of dinosaurs

It is possible for brown dwarfs to have sporadic deuterium fusion but that is at much higher pressures in the cores of these objects. See THE DEUTERIUM-BURNING MASS LIMIT FOR BROWN DWARFS AND GIANT PLANETS

DETAILS

There's a good account here for the historical background and quotes and it summarizes the reactions they considered:

Dongwoo Chung, February 16, 2015, submitted as course work for Stanford university.

There are two competing accounts of how seriously they took it back then, both probably over dramatized in the telling.

Bob Serber:

Edward [Teller] brought up the notorious question of igniting the atmosphere. Bethe went off in his usual way, put in the numbers, and showed that it couldn't happen. It was a question that had to be answered, but it never was anything, it was a question only for a few hours. Oppy made the big mistake of mentioning it on the telephone in a conversation with Arthur Compton. Compton didn't have enough sense to shut up about it. It somehow got into a document that went to Washington. So every once in a while after that, someone happened to notice it, and then back down the ladder came the question, and the thing never was laid to rest.

Bucks interview with Compton

During the next three months scientists in secret conference discussed the dangers of fusion but without agreement. Again Compton took the lead in the final decision. If, after calculation, he said, it were proved that the chances were more than approximately three in one million that the earth would be vaporized by the atomic explosion, he would not proceed with the project. Calculations proved the figures slightly less - and the project continued.

As he says:

Both accounts certainly have an appealing dramatic flair in their respective ways, but when they paint such different pictures of the discussions involved, we must consider their exact details lost to posterity.

DETAILS OF BETHE'S CALCULATION

Dongwoo Chung seems to have made some minor numerical errors in his summaries of the paper, perhaps because the text is hard to read in places. So I'll go to the paper itself for the calculations.

Ignition of the atmosphere with nuclear bombs.

In short the main reactions in the air are

N14 + N14 → Mg24 + α + 17.7 MeV

Bethe calculates a safety factor of about 1.6 at about 10 MeV

However he works out a mean free path in air of 57 meters, so a region of at least 57 meters in radius needs to be heated for sustained fusion.

To heat up so much atmosphere to 10 MeV he works out needs 1,500 tons of fissile material to be burnt (he doesn't say if this is u235 or plutonium). But typically only 1% goes into heating up the air, so that would require 150,000 tons to be detonated at once to reach the 10 MeV temperature.

For a fusion reaction he calculates that to reach 10 MeV over a 57 meter radius would require 3 meters radius of liquid deuterium to be detonated all at once.

[Dongwoo Chung for some reason says it is 7 meters in radius - the text is a bit unclear in places, maybe he just misread it]

There is an additional reaction

N14 + N14 → O12 + C16 + 10.6 MeV

This requires "only" a 1 to 1.5 meter radius sphere of deuterium but the safety factor increases to 2.67

In the ocean the reactions are:

O16 + H1 → F17 + γ D2 + D2 → H3 + H1 D2 + D2 → He3 + n D2 + H1 → He3 + γ

But the safety factors here are far higher

UPDATED RESULTS GIVEN BY DR GILBERT IN 1975

These are comments by Dr Gilbert, Deputy Director of Military Application U. S. Energy R&D Administration Washington,

LLL Comments on the Ultimate Catastrophe

  • for the atmosphere, the atmosphere is far too low density for a sustained reaction

Simple calculations show that the atmosphere is of sufficiently low density that even with enormously high assumed cross-sections, burn proceeds much slower than the processes tending to clamp the matter into a low-temperature equilibrium with its radiation. The available energy per unit volume in air from even complete burnup of the atmospheric nitrogen is only sufficient to produce an equilibrium temperature of less than 1.5 kev, with over 99% of the energy in radiation.

Also explains earlier

The effects of anomalously large cross-sections for nitrogen burning have never been observed in stars, which have the required constituents, high temperatures, and billions of years of reaction time. The reaction, N14 + N14 -> + Mg24 was considered to be the dangerous by Konopinski, et. al, However, the strong electrostatic repulsion of the charged nitrogen ions requires a relative energy of approximately 8.6 MeV for them to approach close enough to fuse. ... We know of no way to produce temperatures even 10% of those required.

The cross-sections for the N14 (a,p) and O17 (a,n) reactions in the chain Dr. McNally considers "the most dangerous multiplying chain in air" have also been measured and show no resonance higher than 250 mb, more than an order of magnitude too low to sustain any fusion chain reaction, even if sufficient temperatures could be reached. ... Even if nitrogen were many times as reactive as DT, the most reactive known nuclear fuel, the thermonuclear energy generation rate at any plausible temperature would still not suffice to overcome the energy losses due to bremsstrahlung radiation and the inverse Compton effect.

  • For the sea, propagation fails even in a sea of pure D2O under high pressure.

the sea was modeled in the most simple yet conservative manner by assuming it was two percent D2O at high pressure--more than 100 times the actual deuterium concentration. Initial high temperatures near a 500 Mt massless energy source decreased by a factor ~100 in 2 x 10^-8 seconds. model sea produced an additional 0.006 percent of the source energy before the yield production stopped. The actual deuterium concentration in sea water would have decreased even this minute burn by a factor of approximately 20,000. In fact, propagation failed (by a large margin) in a model sea of pure D2O under high pressure!

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  • $\begingroup$ Sorry it is copy / paste from the pdf, still working on this I'll fix it. It's "~100 in 2 x 10^-8 seconds" Probably an issue in OCR of the image $\endgroup$ Jul 16, 2020 at 12:11
  • $\begingroup$ Should be okay now. $\endgroup$ Jul 16, 2020 at 12:24
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Around the 60s, a treaty was signed to ban development of nuclear fusion devices with yield greater than about 50 MT (don't remember exact number), in order to prevent fusion of atmospheric hydrogen, thus the uncontrolled multiplication of the device explosive yield. That was before the Threshold Test Ban Treaty was signed in 1974 and entered into force in 1990.

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  • $\begingroup$ Not an answer . $\endgroup$
    – Qmechanic
    Sep 30, 2017 at 15:23
  • $\begingroup$ There is very little hydrogen in atmosphere. $\endgroup$
    – Anixx
    Jul 16, 2020 at 12:28
  • $\begingroup$ I don't think there is any maximum yield treaty. The Tsar Bomba had a yield of 50 Mt and they could have made it 100 Mt but wanted a cleaner bomb so that they could detonate it over islands in the Arctic with a much cleaner mainly fusion bomb than the 100 Mt maximum design. But they weren't limited by any treaty. Bethe's superbomb that he originally thought might be close to able to detonate nitrogen in the atmosphere with a safety factor < 2 was far higher yield than anything practical for us to make so I can't see that leading to any treaty. en.wikipedia.org/wiki/Tsar_Bomba $\endgroup$ Jul 16, 2020 at 12:38
  • $\begingroup$ Plus as Annix says there is very little hydrogen in the atmosphere - mainly in the form of the hydrogen in water vapour. $\endgroup$ Jul 16, 2020 at 12:42

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