Monte Carlo method for solving a B1 equation with complex-valued buckling in asymmetric geometries and generation of directional diffusion coefficients

Abstract

Direction-dependent diffusion coefficients generated using a Monte Carlo method that explicitly solves a heterogeneous B₁ equation are validated in this paper. The validation is conducted by comparing the direction-dependent neutron leakage using directional diffusion coefficients with the results of a neutron transport calculation. This paper develops a new method for critical buckling search calculation to solve a heterogeneous B₁ equation for an asymmetric unit cell in which the critical bucking has a complex value. A complex-valued critical buckling can be searched using the differential operator sampling method for estimating the sensitivity coefficients of keff with respect to the buckling. In an asymmetric unit cell, the neutron flux and the neutron current also have complex values. The real part of the neutron flux obtained by a critical buckling search calculation represents the neutron spectrum in the center portion of the finite geometry composed of the unit cells.