Application of theBnTheory to Unit Cell Calculations

Abstract

The integral transport equation is solved in square unit cells by assuming the existence of a fundamental mode. The equations governing the B{sub n} method are given without making the small buckling approximation. First, the angular flux is factorized into two parts: a periodic microscopic fine-structure flux and a macroscopic form with no angular dependence. The macroscopic form only depends on a buckling vector with a given orientation. The critical buckling norm, along with the corresponding fine-structure flux, is obtained using collision probability calculations that are repeated until criticality is achieved. The procedure allows the periodic or reflective boundary conditions of the unit cell to be taken into account using closed-form contributions obtained from the cyclic tracking technique. Numerical results are presented for one-group heterogeneous cell problems with isotropic and linearly anisotropic scattering kernels, some of which include void regions.