linear relationship between reactivity and the reciprocal of uranium concentration in thermal spectrum molten salt reactors

Knowing the precise relationship between fuel loading and reactivity helps guide the smooth progress of reactor criticality extrapolation and online refueling in molten salt reactors (MSRs). This study aims to explore and explain the linear relationship between reactivity and the reciprocal of uranium concentration in thermal spectrum MSRs. By applying the neutron balance theory, we analyzed the absorption of neutrons by various nuclides under several single lattice models with varying fuel concentrations. Our findings reveal a simple linear correlation between reactivity and the reciprocal of uranium concentration, which is successfully explained from the perspective of nuclear reaction cross-sections that adhere to the 1/v law in a thermal neutron spectrum. Furthermore, we identified the single-group neutron absorption cross-sections of structural materials and carrier salts exhibit an approximate linear relationship with the single-group fission cross-section of 235U, and the reciprocal of the fission cross-section of 235U exhibits an approximate linear relationship with uranium concentration. This linear relationship will deviate as the volume fraction of molten salt continues to increase since more neutrons will be captured in the resonance energy spectrum. But it remains valid within a 25% volume fraction of molten salt, and still demonstrates its broad applicability in the physical design and operation of thermal molten salt reactors.