A Perturbation Theory Based Analysis of Reactivity Feedbacks During Transients in Molten Salt Reactors

To assess the steady-state and dynamic behavior of molten salt reactors, multidimensional multiphysics tools are essential to capture the strong coupling between thermal-hydraulics and neutronics and to resolve the complex flow structures generated by the circulating liquid fuel. In homogeneous-fuel concepts, geometrical features such as abrupt changes in the flow passage and sharp edges promote the development of recirculation and stagnation zones, which induce the formation of non-uniform temperature distributions. These thermal-hydraulic fields influence the neutronic behavior through temperature-dependent neutronic parameters and the transport of the fuel. The reactor response therefore cannot be fully characterized on the basis of volume-averaged quantities alone, but requires the evaluation of the local neutronic effects driven by thermal-hydraulic redistributions. This work analyzes the local reactivity contributions associated with temperature-induced perturbations during transients in molten salt reactors by combining multidimensional multiphysics simulations with first-order perturbation theory. To this purpose, the solver developed at Politecnico di Milano coupling thermal-hydraulics and multigroup neutron diffusion, was extended with an adjoint multigroup diffusion module to evaluate the local contributions to the effective multiplication factor arising from temperature-induced perturbations. This approach sheds light on the relationship between multidimensional temperature fields and the resulting neutronic response. The same framework also enables a consistent comparison between stand-alone and coupled simulations, allowing the influence of the intermediate loop and Balance of Plant dynamics on the primary loop behavior to be analyzed. The methodology is applied to both an Unprotected Loss of Heat Sink (ULOHS) and operational load-following scenarios for a Molten Salt Fast Reactor case study. All these transients are exclusively driven by modifications of the heat-removal conditions at the primary heat exchanger, while the primary salt forced circulation is maintained at nominal operating conditions. The analyses demonstrate that variations in the heat-removal conditions lead to multidimensional temperature redistributions, giving rise to local perturbations of the neutronic parameters throughout the domain. Although the corresponding local contributions to the effective multiplication factor are significant, their integral contribution is largely compensated over the reactor volume. Accordingly, the system can stabilize toward new steady-state operating conditions characterized by different power and temperature levels despite the absence of externally imposed reactivity insertions. The comparison between stand-alone and coupled simulations highlights the importance of representing the dynamic response of the outer loops, which significantly influences the heat-removal conditions and the resulting equilibrium conditions. The load-following analyses demonstrate that the same physical mechanisms govern both accidental and operational transients, while the quantitative magnitude of the corresponding neutronic effects remains strongly dependent on the reactor geometry and the associated flow field. Overall, the proposed approach provides a consistent framework for characterizing the interplay between multidimensional thermal-hydraulic redistributions and the global neutronic response of circulating-fuel reactors.