An iterative fission matrix scheme for calculating steady-state power and critical control rod position in a TRIGA reactor

Although Monte Carlo simulations are the most accurate representation of nuclear reactor cores, they can be computationally expensive. This computational expense can prohibit the use of Monte Carlo in situations that require sequences of neutronics calculations, such as accounting for temperature feedback. In the present work, we demonstrate a fission matrix methodology to calculate the fission source in the Penn State Breazeale Reactor while accounting for control rod movement and fuel temperature feedback. A fission matrix A, represents the rate of fission neutron production in a reactor core, where the a_ij entry of the matrix is equal to the neutrons produced in cell i per neutron born from cell j. The fission source distribution and multiplication factor k_eff are the principle eigenvector and principle eigenvalue, respectively, of the fission matrix. Given a varied core temperature distribution, a new fission matrix can be obtained by interpolating from a database of pre-calculated fission matrices. This approach shows promise in accurately and quickly calculating the reactivity and fission source distributions for a system with an arbitrary temperature distribution. In the present work, the largest resulting relative error of the calculated power distribution per pin was 1.52% compared to a Serpent criticality simulation, and all calculated eigenvalues were within 50 pcm, which corresponds to 0.1–0.4 cm of rod insertion depending on whether rods are inserted in the center or edge of the core. In contrast, the critical rod position varies by 13.49 cm for the cases considered (0–650 kW). The present database is composed of data from 78 Monte Carlo calculations, but enables subsequent neutronics calculations to be done in a fraction of a second. Future work would be to implement correction factors for neighboring temperature differences in three-dimensional models, incorporate xenon feedback, and investigate ways to decrease database size.