Dane Sabo
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19 lines
1.0 KiB
TeX
19 lines
1.0 KiB
TeX
\section*{Problem 4}
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The power trajectory would be exponentially positive as the reactor would become
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prompt critical. One would analyze the transient by using a robot to examine the
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reactor soup after the steam bomb goes off in the containment.
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But being serious, one may examine the power transient by evaluating \(\rho\)
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over time using the partial addition formula we used in the last problem.
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Because the reactor is prompt critical, we can essentially ignore the delayed
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neutrons. The point kinetic equations can also be used, but honestly a decent
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approximation will be a first order exponential growth with time constant
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derived from the prompt neutron lifetime.
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For a high enrichment fuel, the growth of the curve will be impeded by basically
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nothing. Fuel and moderator temperature effects will be minimal. For a low
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enrichment fuel, moderator temperature and fuel temperature effects will slow
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the exponential growth as temperature increases, but depending on reactor
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design, will not prevent catastrophic failure.
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