Eigenvalue Implicit Sensitivity to Self-Shielding Calculations in Heterogeneous Geometries

A method is proposed to evaluate implicit sensitivity coefficients for several types of reactor lattices, including pressurized water reactors and CANDU (CANada Deuterium Uranium) reactors, with different resonant and light isotope contents. The implicit sensitivity of the multiplication factor, resulting from a variation of an isotope density through the self-shielded cross sections, is computed for different cases. The precision of the method, the importance of the implicit coefficients with respect to the total sensitivity, and the contributions of all the isotopes are discussed and compared for the different systems. We also show how to compute the sensitivity coefficients in the unresolved energy groups, where the details of the resonances are not known. An equivalent dilution model is used for the self-shielding calculations. Complete transport calculations, using a collision probability method, are also used to compute reference values for the implicit sensitivities.