PN solutions of the time-dependent neutron transport equation with anisotropic scattering in a homogeneous sphere

Abstract

In an earlier paper, the spherical harmonics method for the solution of the time-dependent transport equation with the Marshak boundary conditions was presented in order to investigate the effect of a strongly anisotropic scattering law on the slab thickness. Here, the previous work is extended to the study of the time-dependent problems in a homogeneous sphere with the same scattering function as used in the previous work. The time-dependent neutron transport equation is solved in the manner used for a critical sphere and all radii for a given time-dependent system are determined by finding the critical radii for the corresponding critical system. The PN calculations of the critical radii were carried out for various combinations of the anisotropy parameters and the fundamental time eigenvalues. Some indications of the accuracy of the method were given for the problem of interest and the variation of the radius with anisotropic scattering was studied. We also obtained numerical values of the critical radii in the range of (1-),1. Finally, some results were discussed and compared with those already obtained by various methods.