Eigenvalue sensitivity to system dimensions

Adjoint-based first-order sensitivity theory is applied to estimate the sensitivity of the keff eigenvalue to system geometric dimensions. Macroscopic cross sections in the neighborhood of a material interface are expressed in terms of a Heaviside step function. Differentiating the transport and fission operators of the transport equation with respect to the location of the interface results in a Dirac delta function. The final equation for the sensitivity has the forward-adjoint product integrals evaluated on the unperturbed interface; these are multiplied groupwise by the cross-section differences across the interface. The equation applies to the sensitivity of keff to the uniform expansion or contraction of a surface but not to a surface translation or rotation. The equation is related to an earlier one derived for internal interface perturbations in transport theory. The method is demonstrated and compared with direct perturbation calculations in spherical (r only) and cylindrical (r–z) geometries based on criticality benchmark experiments.