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Protagoras comments on Harry Potter and the Methods of Rationality discussion thread, part 20, chapter 90 - Less Wrong Discussion
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Actually, most nuclear weapons get roughly comparable amounts of their force from fission and fusion, usually a little more from fission. Fission-only bombs are so much less powerful not because fission is but because they have very incomplete fission (around 1% for the Hiroshima bomb design, for example). The fusion reactions used in bombs produce a lot of excess neutrons, by design; all those neutrons flying around mean a lot more fission ends up happening. The only bombs that get most of their power from fusion are neutron bombs (which use a lot less fissionable material, and use the excess neutrons to increase the radiation damage) and clean bombs (which also use a lot less fissionable material, but replace it with lead to absorb the excess neutrons; clean is of course a relative term here).
The biggest difference as regards fission is that fusion bombs use U-238 as a power source, which is capable of releasing energy from fission, but which doesn't produce enough neutrons to sustain a chain reaction. But when fed excess neutrons from a fusion reaction, you get an immense energy release from a very cheap material that's used as the bomb casing.