Integral Transform Method for Solving Neutron Transport Problems with General Anisotropic Scattering in a Cylinder of Finite Height

Abstract

In this paper, we present the mathematical techniques that were developed for solving the integral transport equation for the criticality of a hoinogeneous cylinder of finite height with general anisotropic scattering. We write the integral transport equations for the Fourier transformed spherical harmonic moments of the angular flux. These moments are also represented by a series of products of spherical Bessel functions. The criticality problem is, then, posed by the matrix eigenvalue problem whose eigenvector is composed of the expansion coefficients mentioned above. An methodology of calculating the general matrix element is discussed by using the recursion relations derived in this paper. Finally, for the one-group criticality of finite cylinders, the benchmark results are generated when scattering is linearly anisotropic. Also, these benchmarks are solved and compared with the SN method of TWOTRAN.