Neutron spectrum spatially dependent

IV. Spatially dependent velocity distributions. When the spectrum is independent of position, the central problem is the determination of the energy-transfer cross sections. The calculation of the spectrum once these cross sections are known is a straightforward procedure. The cross-section aspect of the problem is both more difficult from a physics point of view, and more time consuming from the point of view of machine computation. This situation is reversed when we come to consider the spatial dependence of the slow neutron spectrum. The cross sections needed are the same ones that already have been computed for the infinite medium spectrum problem. The transport equation must now be solved in at least two variables, and in a form for which the existing approximate techniques are not very well adapted. The focus of the problem therefore shifts to the development of appropriate techniques for solution of the transport equation when the energy and position variables are coupled in such a way that neutrons can both gain and lose energy in a collision. 

However, when calculating a thermal-spectrum core with large heterogeneities, the R-Z two-dimensional model is inadequate for design purposes. In a thermal-spectrum core, the spatial dependence of the thermal neutron flux is large. The fuel assemblies are loaded with a relatively complex pattern to flatten the neutron flux distributions. Hence, the calculation of such a core requires the modeling of each fuel assembly with a three-dimensional model as shown in Fig. 2.31. To conserve computational power, symmetric boundary conditions can be applied. 

This method can be considered, in the simplest case, merely as a measurement of the neutron flux present for a known quantity of fuel with a known cross section or for those experimentalists with a more advanced background, a more detailed consideration can be given to the energy spectrum of these neutrons, to the neutron-velocity dependence of the fissionable isotope, and to the spatial distribution of both the neutrons and the fissionable atoms. 

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