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I don't know what chain reaction exactly they were thinking of, but from modern fusion research, I believe we can confidently say that the atmosphere would need to be interior-of-a-large-star-level dense, and even then I'm not sure you'd get nitrogen fusing with anything without a lot of hydrogen or helium around. Nitrogen-nitrogen fusion seems extremely implausible for sure
Fusion of two nitrogen-14 nuclei and a hydrogen nucleus. That was the feared chain reaction, since both elements are abundant.
Source
Prolly the most relevant paragraph from the linked article for this discussion:
Basically the temperature of the atmosphere is over an order of magnitude too low to have any chance of ignition (need 10s of millions of K), and the reaction rate is thus several orders of magnitude lower than the threshold.
Thank you, the page you sourced references a 2024 paper inspired by the Oppenheimer movie that was super interesting to read
i think the idea is that the part that already fused creates a blast wave that could create the conditions, including preassure required for more fusion. i have no idea if it's possible though.