Sensitivity analysis for delayed neutron data

In this paper a framework is derived based on first order perturbation theory to calculate the sensitivity of a transient in a nuclear reactor to delayed neutron parameters. The approach is based on the Adjoint Sensitivity Analysis Procedure as outlined in Cacuci Cacuci, D., 2003. Sensitivity and Uncertainty Analysis. Theory, vol. I. CRC Press]. In this paper, the required adjoint system is defined and discussed, and an analytical solution is provided for a simplified case. Application of the ASAP requires that the time-dependent adjoint for neutrons and precursors is solved, and the implementation of such a solver is discussed. Proof-of-concept calculations have been performed for a 0D and a 3D case. It is found that sensitivities for the delayed neutron data are generally low. For increasing transients, the sensitivities increase with reactivity, with the highest sensitivities occuring for the delay groups with largest delayed neutron fraction _βk${\beta }_k$, and for the largest ratio _λk/_βk${\lambda }_k/{\beta }_k$. For decreasing transients, the trends are less clearly defined, with some sensitivities increasing, and others decreasing, for increasingly negative reactivity. The proof-of-concept calculations have shown that the ASAP method yields good accuracy, but especially for 2D or 3D problems the method requires the use of advanced ordinary differential equation (ODE) solvers with built-in sensitivity capabilities, to keep the memory requirements and computational overhead in manageable bounds.