Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2021 / Module NE1 / 4 / b / Solution

The first equation is a prescribed first-order removal law. For a constant absorption coefficient,

\frac{d N _{Th}}{N _{Th}} = - σ_{a Th} ϕ (t) d t .

Integrating from the initial condition gives

ln \frac{N _{Th} ( t )}{N _{Th0}} = - σ_{a Th} \int_{0}^{t} ϕ (t^{'}) d t^{'},

and hence

N_{Th} (t) = N_{Th0} e^{- σ_{a Th} Φ (t)} .

The neutron fluence

Φ

is the time integral of scalar neutron flux; it has inverse-area units, making

σ Φ

dimensionless. Constant flux is not needed for this integration, but a constant effective coefficient is.

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