A new concept of Monte Carlo kinetics parameter calculation using complex-valued perturbation

Abstract

A new Monte Carlo method to calculate two types of kinetics parameters, the effective delayed neutron fraction (βeff) and the prompt neutron generation time (Λ), is proposed in this paper. The new method uses perturbation techniques in which extra delayed neutrons or a fictitious 1/v-absorber is added to the unperturbed system to calculate the βeff or Λ, respectively. In the new method, the perturbation is added as a complex-valued perturbation. This paper conjectures that the change in the eigenvalue due to the perturbation is accurately approximated by the imaginary part of the eigenvalue of the complex-valued perturbed equation. The conjecture is corroborated by certain numerical tests presented in this paper. A Monte Carlo calculation algorithm is established to solve the complex-valued perturbed eigenvalue equation. One single Monte Carlo calculation to solve the complex-valued eigenvalue equation yields highly accurate approximations of the exact kinetics parameters with much less computational costs compared with the previously proposed method that uses multiple Monte Carlo runs.