Diffusion approximation to neutron transport equation in one dimensional spherical geometry with chebyshev polynomials

Since the second half of the 20th century, it has gained importance in reactor design seamlessly together with the use of active nuclear reactors for energy production. The determination of the diffusion coefficient and diffusion length has an important place in terms of providing preliminary results of the study of nuclear reactors. In this study, besides traditional and accepted methods a different solution method has been shown to use in the solution of the transport equation which is one of the important problems in the design and operation of the nuclear reactors. The transport equation is first investigate din general geometry and then the spherical transport equation without a source for one-speed neutrons is derived and reduced to the pseudo-slab transport equation to simplify the solution strategy. The neutron angular flux is first expanded in terms of the Legendre polynomials and then it is expanded in terms of the second kind of Chebyshev polynomials which constitutes the original part of this study. Then, the first orders approximations in both methods are done to calculate the diffusion coefficients and diffusion lengths for various values of the c (mean number of secondary neutron per collision). The numerical results obtained from these two methods are compared with the ones obtained from the methods stated in literature.