MATHEMATICAL DESCRIPTIONS OF A NEUTRON POPULATION
Transport theory [58] offers the most accurate description of a reactor’s neutron population in terms of a vector flux, but it has stringent computational demands. However, other than very close to strong absorbers or emitters,[30] neutronic velocity vectors are approximately isotropic and neutron migration can be readily computed when treated like the diffusion of gas molecules. Accordingly, with appropriate boundary conditions neutron conservation is characterized by a scalar neutron flux f as [58]
(2.21)
where
f — Scalar neutron flux = Number of neutrons per square centimeter per second D — Diffusion coefficient ^2a — Macroscopic absorption coefficient S — Expected neutron production rate per unit volume V — Neutron speed in each chosen energy band of a simulation
Two — or threedimensional multigroup[31] diffusion calculations of proposed core geometries have been validated by experimental zeroenergy assemblies, and they have been proven successful in the United Kingdom for designing AGRs, SGHWR, PFR, and naval PWRs.
The fixed compact core geometries associated with fast reactors and PWRs have normalized neutron flux profiles that are largely governed by the escape of neutrons from the fissile core region, and so are substantially independent of output power. In addition fuel enrichment is deliberately increased toward the core periphery to “flatten” the radial flux profile and thereby enhance economics. These considerations intuitively suggest that the dynamics of these reactor types can be
Table 2.1 Delayed Neutron Data for BWRs and PWRs with Uranium Fuel

closely approximated by onedimensional distributed models [117], and experiments confirm this conjecture. Moreover the point kinetics model in Section 2.3 can also be derived [117] more rigorously by applying the analytical technique of adjoint (conjugate) linear mappings to these distributed model equations. This further simplification to a point model has proved sufficient for many control and overall plant simulations. However, because steam is a far weaker absorber than its liquid phase, the neutron flux profile in direct cycle systems (e. g., BWRs) changes materially with output power, so these reactor dynamics necessarily require the simultaneous solution of the distributed neutron diffusion and thermalhydraulic equations [145]. Most neutrons (socalled prompt) are released at fission but a very small minority appear somewhat later as various fission products undergo radioactive decay. Table 2.1 lists the pertinent parameters for these delayed neutrons and their precursors. Later in Section 2.5 they are shown to influence reactor dynamics seemingly out of all proportion to their relative concentrations.