Perturbation Theory for Lattice Cell Calculations

Generalized perturbation theory (GPT) can be used as a means to evaluate sensitivity coefficients or to approximate variations in integrated lattice parameters resulting from small changes in local cell properties. Using a first-order perturbation approach, the changes in the integral parameters can be written as a sum of a direct term that takes directly into account the variations in the cell properties and an indirect term that approximates the neutron flux variations resulting from the perturbation. For a lattice cell code that relies on a collision probability technique to solve the transport equation, a problem related to the evaluation of the perturbed transport operator also arises because the collision probability matrix depends on the total cross section. A technique is presented to simulate these variations in the collision probability matrix using approximate source term variations. Comparison with exact calculations will show that the results obtained using GPT with these approximate source terms are reliable provided the perturbations remain small. Results for a parametric study of a two-dimensional pressurized water reactor 17 × 17 assembly and void reactivity calculations for a DUPIC-fueled CANDU cell are also presented.