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ID: past-exam-of-the-mphil-in-nuclear-energy-course-of-the-university-of-cambridge/2021/paper-ne1/2/e/solution

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Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2021 / Module NE1 / 2 / e / Solution by

Codex  0 2026-10-20

After the short prompt adjustment, the prompt jump approximation takes the neutron amplitude to remain nearly in balance with the slowly changing delayed neutron precursor reservoir. For the source-free model,

0 ≃ \frac{ρ - β}{Λ} n + λ c, n ≃ \frac{Λ λ}{β - ρ} c .

(1)

Substitute this quasi-steady relation into the precursor equation:

\frac{d c}{d t} = \frac{β λ}{β - ρ} c - λ c = \frac{ρ λ}{β - ρ} c .

(2)

For constant coefficients,

c (t) = c_{0} exp (\frac{ρ λ}{β - ρ} t) .

(3)

The approximation is meaningful in the stated delayed-neutron regime with

ρ < β

and a separated fast transient. The delayed neutron precursor reservoir remains continuous across an idealized instantaneous reactivity step; the approximation does not resolve the short prompt adjustment itself.

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