Two-point and two-energy group kinetics model of the ANS reactor

The production of extremely high thermal neutron fluxes ({approximately}10{sup 20}/m{sup 2}{center dot}s) with reasonable power levels ({approximately}300 MW) requires the combination of a very undermoderated core and a low-absorbing moderator/reflector (like D{sub 2}O). Candidate designs for the reactor of the advanced neutron source (ANS) project have in common the strong coupling between two neutron fields with very different spectra: predominance of epithermal neutrons in the core and thermal neutrons in the reflector. Because there are large variations of the neutron spectra within a few centimetres in a small core, concerns might arise regarding the validity of the conditions under which the point kinetic approach is valid, i.e., the factorization of the flux as the product of two functions: one depending on phase space {mu}(r,v) and the other depending only on the time t. In this paper, the authors present a two-point (c and r are the core and reflector, respectively) and two-energy group (1 and 2 are the fast and thermal groups, respectively) model used to calculate power transients in order to detect conditions under which one-point kinetics is not a valid approximation.