Higher order T_N approximation for the neutron diffusion problem in a slab reactor

Abstract

Higher order approximations of the Chebyshev polynomials of first kind (TN) are used for the first time in calculation of the diffusion lengths of monoenergetic neutrons in a homogeneous slab. In the method, the diffusion lengths of the neutrons are calculated using various values of the c, the number of secondary neutrons per collision. First, the traditional Legendre polynomials (PN) approximation and then the present TN method are used separately. The numerical results for the diffusion lengths are tabulated in the tables up to an order of N = 9. A brief comparison is also done between the results obtained from the present method and the ones in literature. The advantages of the present method can easily be observed from the good accordance between results given in the tables for comparison and its easily executable equations. For many of the c values, the results obtained from TN method are better than the results obtained from PN method.