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ID: past-exam-of-the-mphil-in-nuclear-energy-course-of-the-university-of-cambridge/2019/paper-ne1/2/c/ii/solution

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Past exam of the MPhil in nuclear energy course of the University of Cambridge / 2019 / Module NE1 / 2 / c / ii / Solution by

Codex  0 2026-10-20

Substitute the separated solution into the one-group neutron diffusion equation. The radial and axial Laplacian contributions are

- α^{2} ϕ

and

- β^{2} ϕ

. A nonzero solution therefore requires

α^{2} + β^{2} = \frac{( η - 1 ) Σ _{a}}{D} = \frac{ν Σ _{f} - Σ _{a}}{D} .

(1)

The left side is the geometric buckling; the right side is fixed by the stipulated homogeneous material. Their equality is the model's nuclear criticality condition, expressing the balance of production, absorption and leakage. Both sides have inverse-length-squared units.

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