Extension of the formula between reactivity and concentrations of fissile and non-fissile nuclide in the fuel salt for thermal neutron spectrum molten salt reactors

Due to the unique properties of liquid fuel in molten salt reactors (MSRs), reactor reactivity is directly correlated with the fuel salt composition. Previous studies have established and verified a linear relationship between reactivity and the inverse of fissile nuclide concentration in thermal spectrum MSRs. This paper aims to expand the relationship to non-fissile nuclides. Non-fissile nuclides, including carrier salts, and fission products, are widely distributed within MSRs. Unlike fissile nuclides, increasing the concentration of these non-fissile isotopes reduces reactivity. By applying the "1/v law" for neutron absorption cross-sections in the thermal neutron energy range, we demonstrate that reactivity is linearly related to the concentration of these non-fissile isotopes, in contrast to fissile ones. Furthermore, a generalized relationship expressing reactivity as a function of both fissile and non-fissile nuclide concentrations is developed and validated. This formula enables the calculation of reactor reactivity for any fuel salt composition without requiring repeated neutron transport calculations, offering significant potential for criticality and burnup calculations in MSRs. • A formula establishing the relationship between the reactivity and concentrations of fissile and non-fissile nuclide in a molten salt reactor is derived. • This relationship is applicable if the absorption or fission cross-section of the nuclide follows the 1/v law. • This relationship yields reasonably accurate results with a need of only a few data points.