Nonmonotonic behavior of the ‘C’ eigenvalue of the one-speed neutron transport problem in two-dimensional cylindrical (R,Z) geometry

Abstract

Nonmonotonic variation of the ‘C’ eigenvalue (average number of secondaries per collision) with increasing α, the strength of forward scattering, has been observed earlier for one-dimensional infinite homogeneous slabs and infinitely long homogeneous cylinders. We have developed the Integral Transform (IT) method, an accurate semi-analytical method to obtain the C eigenvalue for a homogeneous cylinder (two-dimensional system). We are thus able to detect any nonmonotonic variation of C (with α) using the Sahni and Sjöstrand criterion. Along with the IT method, we also present the results obtained by the well-known numerical techniques like the discrete ordinates method using a high quadrature order and the Monte Carlo method for the same problem. The S_N results show disagreement with the other two methods when one of the dimensions is very small (< 0.05λ_t). We believe that even the 16^th order quadrature set cannot integrate the angular flux accurately in these extreme situations.