Application of the generalized collision probability to anisotropic diffusion coefficient calculation

Abstract

The effective diffusion coefficient in a cylindrical cell is calculated from the Benoist formula by applying the first-flight collision probability method in one-velocity. Following his formula, the diffusion coefficient is determined by a component of the tilted flux. The anisotropy and the space variation of the tilted flux is taken into account by using the Legendre expansion. The expansion coefficients are determined by the generalized first-flight collision probability. At the cell boundary, a new reflection condition is derived for the generalized collision probability instead of the usual isotropic reflection boundary condition. From numerical examples, it is seen that values of the radial diffusion coefficient calculated from the present method agree with those from the exact method in a square cell. Further, when the first term of the Legendre expansion is included, rapid convergence of the radial diffusion coefficient can be seen.