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Accounts of the "secret" of the hydrogen bomb describe Xrays from a primary fission explosion reflecting off of the bomb case (occasionally passing through polystyrene foam) and compressing and heating the fusion fuel. No mention is made of gamma rays doing the same thing. Is there a physical explanation for why X-rays are able to compress the secondary, but gamma rays are not? Does the primary fission reaction produce gamma rays as well as x-rays?

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The X-ray radiation is thermal i.e. it's generated by the very high temperatures as the primary goes off. The temperatures in an atomic bomb aren't high enough to generate thermal gamma rays. Presumably there must be some gamma radiation from nuclear reactions in the detonating primary, but this is small compared to the X-ray intensity.

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In addition to John Rennie's answer, which is correct, gamma rays have a wavelength smaller than an atomic radius, and generally go through matter a ways inside before scattering or getting absorbed. To get an implosion of the secondary, you want the material on the surface of the secondary fusion clump to ablate away. This means it has to shoot out atoms from the surface very fast. This process only works if the rays shining down on it are absorbed at the surface, not deep inside. As explained on Wikipedia, the ablation pressure is the major process for compressing the secondary.

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