Starting from the neutron transport balance integrated over solid angle (a continuity…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Nuclear Physics · Partial differential equations and boundary-value problems

The Nucleus Resolved, Ch The reactor as a field equation: diffusion, criticality, feedback and burn-up

Problem

Starting from the neutron transport balance integrated over solid angle (a continuity equation for the scalar flux

\phi(\vec r,t)

and the current

\vec J(\vec r,t)

), derive the one-group time-dependent diffusion equation

D_{\rm diff}\nabla^2\phi - \Sigma_a\phi + S = \frac{1}{v}\frac{\partial\phi}{\partial t}.

State the closure relation you use to eliminate

\vec J

in favour of

\phi

, and give

D_{\rm diff}

in terms of the transport cross section

\Sigma_{tr}

. Then name two distinct locations inside an operating reactor core where this equation is known to fail, and for each say in one sentence which assumption behind the closure breaks down there.

Related theory

Nuclear Physics

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