Point kinetic model of the early phase of a spherically symmetric nuclear explosion

Abstract

A concise point kinetic model of the explosion of a prompt supercritical sphere driven by a nuclear fission chain reaction is presented. The findings are in good agreement with the data available for Trinity, the first detonation of a nuclear weapon conducted by the United States Army as part of the Manhattan project. Results are presented for an implosion device containing pure plutonium-239, although the model can be easily applied to, e.g., uranium-235. The fizzle probability and corresponding yield of a fission bomb containing plutonium recovered from reactor fuel and therefore containing significant amounts of spontaneously fissioning plutonium-240 which can induce a predetonation of the device is illustrated by adding a corresponding source term in the presented model. Related questions whether a bomb could be made by developing countries or terrorist organizations can be tackled this way. Although the information needed to answer such questions is in the public domain, it is difficult to extract a consistent picture of the subject for members of organizations who are concerned about the proliferation of nuclear explosives.