Asymptotic Diffusion Limits of the Multigroup Neutron Transport Equations

In this paper, the standard multigroup neutron diffusion equations are derived as an asymptotic approximation to the multigroup neutron transport equations. The asymptotic analysis employs a scaling that (1) is suggested by the multigroup neutron diffusion equations themselves and (2) generalizes the long-known asymptotic scaling for monoenergetic transport problems. Two other asymptotic scalings of the multigroup transport equations are also considered, both of which lead to a new “group-collapsed” (monoenergetic) “equilibrium” diffusion approximation. The standard multigroup and equilibrium diffusion approximations are shown to preserve certain nonasymptotic properties of the multigroup transport equations. Generalizations of the analyses in this paper, and possible practical applications, are discussed.