The spherical harmonics method for anisotropic scattering in neutron transport theory: the critical sphere problem

The transport of one-speed neutrons has been studied in a homogeneous spher e with Marshak boundary conditions. The scattering function is assumed to b e a combination of linearly anisotropic and strongly forward-back ward scat tering. Numerical results for the critical radius are obtained and tabulate d for different scattering parameters using the spherical harmonics method. We have also obtained the numerical values of the critical radius in the r ange of 1/c less than or equal to alpha, beta less than or equal to 1. The results indicate that the radius varies monotonically with increasing aniso tropy. The monotonic variation continues and limits to a non-zero value wit h an extreme forward bias and linear anisotropy. Finally, sonic results are discussed and compared with those already obtained by using various method s. It is shown that the spherical harmonics method gives generally accurate results and is easily applicable to this type of anisotropic scattering ke rnel. (C) 2001 Elsevier Science Ltd. All rights reserved.