Algorithms for Calculating Effective Parameters of the Point Kinetics Equation Based on the Monte Carlo Method, Their Verification, and Validation

Transient modes and processes in nuclear reactors are modeled on the basis of the point kinetics equation using effective functionals: the fraction of delayed neutrons βeff and the generation time of prompt neutrons Λ. The parameter βeff also plays a key role in reactor measurements, is used in the inverted equations of point kinetics [1], and is the main unit of reactivity measurement (dollar). Accurate calculation of the functionals of the point kinetics equation in heterogeneous systems is a rather labor-intensive problem, since it is necessary to solve the adjoint transport equations to determine the neutron importance function. The calculations are especially difficult for cores with fuel containing a mixed nuclide composition of several main fissile elements or having a complex geometric structure that cannot be modeled by engineering calculation tools. In this case, programs based on the Monte Carlo method are used in practice. In this paper, three algorithms for calculating the effective parameters of the point kinetics equation on the basis of the Monte Carlo method that are implemented in the KIR code have been considered. The results of validation of the algorithm on a series of published benchmark experiments and results of verification on the basis of the results of the MCNP code, as well as in group test problems calculated using the discrete ordinates method, have been provided.