Higher Order U_N Method for the Solution of the Neutron Diffusion Problem

Abstract

The first application of the U_N (Chebyshev polynomials of the second kind) method with higher order approximations is performed to solve the neutron diffusion problem in a slab reactor. The moments of equations are carried out by solving neutron transport equation using first the conventional spherical harmonics (P_N) and then the U_N method. These differential equations with constant coefficients are then solved together to obtain the diffusion equation corresponding to related approximation. The roots of the diffusion equation are estimated to calculate the diffusion lengths of the neutrons for various values of c, the number of secondary neutrons per collision. Numerical results obtained by the present method with its easily executable equations are tabulated with the ones already existing in literature. A good accordance is observed between them. Better results are also obtained than the conventional P_N method for certain values of c.

KEYWORDS:

• Neutron diffusion problem
• transport equation
• U_N method
• P_N method

Subject Classification Codes::

• 82D75
• 33C45