Effect of Higher-Order Harmonics on the Steady-State Neutron Flux in Accelerator-Driven Subcritical Reactors

Higher-order neutron fluxes (i.e., higher-order harmonics) are widely applied in perturbation theory and modal kinetics, and they are important for research on the physical characteristics of accelerator-driven subcritical reactors (ADSRs). This paper presents a computational scheme for reconstructing the neutron flux in the steady state according to the biorthogonal properties of the forward and adjoint neutron fluxes, which can be used to analyze how higher-order harmonics affect the steady-state neutron flux under λ- and prompt α-modes. Simulation results indicated that a modal synthesis method based on λ- and prompt α-modes can effectively reconstruct the steady-state neutron flux and core power in an ADSR with a power reconstruction accuracy of within 5%. The higher-order harmonics can be classified into three types according to their physical characteristics: the first type contributes significantly to the steady-state neutron flux, the second type contributes almost nothing to the steady-state neutron flux, and the third type contributes nothing to the steady-state neutron flux. The external neutron source contributes only to specific harmonic expansion orders, which are characterized by significant axial and radial symmetry for both the λ- and prompt α-modes.