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That's a popular misconception, IIRC. Actually, in thermonuclear weapon the bulk of energy comes from fission. [1] Fusion is technically only used to get the high energy neutrons to get the bulk of fissionable material to undergo fission. So, ironically, calling it a "fusion bomb" is very much like calling your car an electric hybrid.

1. http://en.wikipedia.org/wiki/Thermonuclear_weapon

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Where those weapons get the most energy from depends heavily on the design. It's true that multi-stage thermonuclear devices often have a final fission stage where huge amounts of energy are released, however if one were to purposefully maximize energy release while minimizing fallout there are some relatively clean fusion/fission ratios achievable.

For instance, the test version of the Tsar bomb had its last fission stage removed, reportedly resulting in a 97% fusion detonation. Of course, those still cause a huge lethal neutron flux, but at least the amount of fission material released is pretty small in relation to the overall power of the device.

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