Depletion Perturbation Theory for the Constrained Equilibrium Cycle

Generalized perturbation theory for the coupled neutron/nuclide field is extended to the constrained equilibrium fuel cycle. A variational method is used to formulate the adjoint depletion equations for the two-point boundary value problem of the equilibrium cycle. The reactor operating constraints are treated using the methods of constrained sensitivity theory. A practical numerical algorithm is developed to solve the constrained equilibrium cycle adjoint equations and sensitivity coefficients are generated for several responses in a zero-dimensional, two-group example. In all cases, the sensitivities are in excellent agreement with the results of the direct subtraction of perturbed forward calculations.