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Development of Depletion Perturbation Theory for Coupled Neutron/Nuclide Fields

M. L. Williams

Nuclear Science and Engineering

Volume 70 / Number 1 / April 1979 / Pages 20-36


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A perturbation formulation is developed for the space-energy-dependent burnup equations describing depletion and transmutation of nuclide densities in a coupled neutron-nuclide field, such as a reactor core. The formulation is developed in a form consistent with the computational methods used for depletion analysis. The analysis technique currently employed in most burnup calculations is first reviewed as a method for describing the nonlinear coupling between the flux and nuclide fields. It is shown that, based on the present formulation, three adjoint equations (for flux shape, flux normalization, and nuclide density) are required to account for the coupled variations arising from variations in initial conditions and nuclear data. The adjoint equations are derived in detail using a variational principle, and an algorithm is suggested for solving the coupled equations backward through time. Perturbation expressions are used to define sensitivity coefficients for responses that depend on the coupled interaction between the neutron and nuclide fields. The relation between coupled and noncoupled sensitivity theory is illustrated. Finally, two analytic example problems are solved that determine the sensitivity of some final nuclide concentration to changes in initial conditions. Results obtained from direct calculation and from the coupled perturbation theory are compared.

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