Stability diagnosis of high-fidelity transport-depletion problems with Monte Carlo perturbation theory

© 2019 American Nuclear Society. All rights reserved. Obtaining a stable solution with coupled neutron transport and isotopic depletion has been cast as a non-linear root-finding problem by focusing on the corrector step of the standard predictor-corrector algorithm. This allows a Jacobian matrix to be defined, relating the isotopic field at one iteration to the isotopic field at the previous iteration. The spectral radius of the Jacobian defines the stability of the coupled system. Using perturbation theory, the Jacobian has been calculated for a PWR pin undergoing burn-up – with and without xenon equilibriation – and its numerical stability is examined. The results suggest that PWR pins with uniform coolant density are in fact numerically stable – observed instabilities result purely from statistical effects in the Monte Carlo solver.