Rigorous Derivation of Static and Kinetic Nodal Equations for Coupled Reactors Using Transport Equation

Abstract

Starting from a static or time dependent multigroup transport equation, static or kinetic nodal equations whose unknowns are the fission sources in each reactor are rigorously derived for coupled reactors. Since these equations are exact independently of the strength of the coupling, they can also be used to the usual single reactor dividing the core into appropriate subregions. In this case, the coupling coefficients give the exact expressions of the transport kernel of the FLARE method by the transport equation. In the case of a single reactor, the nodal kinetic equations are reduced to the point-reactor kinetic equations which are more reasonable than the usual ones, and a reactivity equation which gives the rigorous relation between the reactivity and the period is derived. Some comparisons with the usual method are made and discussed.