Higher harmonic analyses of the Rossi-α method and application of dynamic mode decomposition for time decay constant determination in a 1D subcritical system

Abstract

An exact formula for the joint probability of pair neutron detection for the Rossi-α method, which is composed of the sum of a large number of higher harmonics, is verified in this study by comparing it with a Monte Carlo simulation. A simple conventional formula for the Rossi-α method cannot yield an accurate fundamental mode time-decay constant α owing to the effect of higher harmonics. Dynamic mode decomposition (DMD) is applied to the eigendecomposition of autocorrelation functions in a subcritical system. Through DMD, the autocorrelations obtained from the deterministic exact formula, which is free from stochastic noise, are accurately decomposed into major higher harmonic components. The DMD results obtained from a Monte Carlo simulation are inferior to the deterministic results due to stochastic noise. These findings suggest that if detection positions are properly allocated within a subcritical system, DMD can yield a satisfactorily accurate fundamental mode α-eigenvalue.