It is very time consuming to carry out full calculations of
neutron transport using the detailed PENDF cross sections that we
have discussed in the preceding pages, although it can be
done using continuous-energy Monte Carlo codes like MCNP, which
we will discuss later. Therefore, it is very common to reduce
the detail in the cross sections by averaging them over a set
of energy ranges called "groups." The GROUPR module of the NJOY
system carries out such averages for the pointwise cross sections,
and it also generates multigroup "matrices," which describe the
transfer of neutrons from one group to another.
The basis for GROUPR is the "multigroup Boltzmann transport equation," which can be written as
where slab geometry has been used for simplicity. The first term describes the spatial transport of neutrons in group g, the second accounts for reactions in group g, the third gives the source into group g from other groups, and the last includes any fixed sources and the source from fission. The flux and cross sections that appear here are defined as follows:
One of the reasons for doing a transport calculation is to obtain various "responses," such heating, production of a radionuclide, or production of helium. The responses can be computed using the multigroup flux together with a multigroup reaction cross section:
It is the mission of GROUPR to compute the cross sections with "g" subscripts, which are often called "multigroup constants." The Boltzmann equation itself is then solved in a separate neutron transport code, such as ANISN or DANT.
|23 January 2013||T-2 Nuclear Information Servicefirstname.lastname@example.org|