Two-Step Monte Carlo Calculation Method for Sensitivity Coefficients of Reactor Period with Respect to Kinetics Parameters

The calculation of the inverse reactor period α, which is a fundamental mode eigenvalue of the α-mode nonlinear Boltzmann eigenvalue equation, depends on the kinetics parameters (delayed neutron fractions, precursor decay constants, and delayed neutron spectra) used in the calculation. Recently, we developed a Monte Carlo method to calculate the derivatives of the k-eigenvalue with respect to α. Here, the k-eigenvalue is not a critical eigenvalue; rather, it is a fictitious eigenvalue introduced to determine the α value that satisfies the α-mode nonlinear equation. The sensitivity coefficients of α with respect to the kinetics parameters are expressed as the ratio of the two derivatives: the derivative of the k-eigenvalue with respect to the kinetics parameters and that with respect to α.

This study introduces a new step for calculating the derivatives of the k-eigenvalue with respect to kinetics parameters using the differential operator sampling method. The sensitivity coefficients obtained using the Monte Carlo method have been validated based on their close agreement with the reference solutions obtained using a deterministic method.