Perturbation theory based on the Variational Nodal Transport method in X-Y-Z geometry

A perturbation method based on the Variational Nodal Method (VNM) of solving the neutron transport equation is developed for three-dimensional Cartesian geometry. The method utilizes the solution of the corresponding adjoint transport equation to calculate changes in the critical eigenvalue due to changes in cross sections. Both first order and exact perturbation theory expressions are derived. The adjoint solution algorithm has been formulated and incorporated into the VNM option of the Argonne National Laboratory DEF3D production code. The perturbation method is currently implemented as a post-processor to the VNM option of the DIF3D code. To demonstrate the efficacy of the method, example perturbations are applied to the Takeda Benchmark Model 1. In the first perturbation example, the thermal capture cross section is increased within the core region. For the second perturbation example, the increase in the thermal capture cross section is applied in the control rod region. The resulting changes in the critical eigenvalue are obtained by direct calculation in the VNM and compared to the change approximated by the first order and exact theory expressions from the perturbation method. Exact perturbation theory results are inexcellent agreement with the actual eigenvalue differences calculated in the VNM. First order theory holds well for sufficiently small perturbations