On the group approximation errors in description of neutron slowing-down at large distances from a source. Diffusion approach

The errors of multigroup calculating the neutron flux spatial and energy distribution in the fast reactor shield caused by using group and age approximations are considered. It is shown that at small distances from a source the age theory rather well describes the distribution of the slowing-down density. With the distance increase the age approximation leads to underestimating the neutron fluxes, and the error quickly increases at that. At small distances from the source (up to 15 lengths of free path in graphite) the multigroup diffusion approximation describes the distribution of slowing down density quite satisfactorily and at that the results almost do not depend on the number of groups. With the distance increase the multigroup diffusion calculations lead to considerable overestimating of the slowing-down density. The conclusion is drawn that the group approximation proper errors are opposite in sign to the error introduced by the age approximation and to some extent compensate each other