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7.6 Reactivity Calculation by Perturbation Theory
The perturbation theory is used to estimate a small reactivity. Although the CITATION code is a
module code in the SRAC code system, the function installed in the original code 6) has not been
utilized since it requires the microscopic cross-sections which are not provided in the SRAC code
system.
A new routine is made to feed the macroscopic cross-sections into the first order perturbation
calculation. The forward and adjoint fluxes have to be prepared by the installed CITATION module. A
perturbed region can be specified by the following three modes;
(a) A whole volume specified by a zone number,
(b) A volume specified by mesh numbers of boundaries,
(c) A volume expressed by abscissa of boundaries, and several volumes can be simultaneously
accepted in a case. As shown in the input specification in Sect.2.8, a mixed mode of (b) and (c)
accepted.
By specifying a new mixture to replace the original mixture located at the perturbed region, the
change is automatically calculated from the difference of cross-sections of two mixtures.
The following results will be printed;
• The macroscopic cross-sections of the new mixture.
• The volume of the perturbed region and that of the zone including the region.
• The whole reactivity change, reactivity changes by reaction and by energy group, and their
fractions to the whole.
• The reactivity due to the change of leakage on each outer surface and by energy group.
• The summation over total perturbed regions
The following restrictions have to be noted.
• A perturbed region can not extend over two zones. If necessary, a region should be split
into two regions.
• When the geometry is 3D triangular or 3D hexagonal, the region specification by abscissa
is accepted only in Z-direction.
7.6.1 First Order Perturbation
The reactivity change ρ (Δk/kk’) by the first order perturbation theory is given by
2
ΔF
− ΔA
+ ΔS
− ΔL
− ΔDB
ρ =
(7.6-1)
F
where F is the total fission, ΔF the fission term, ΔA the absorption term, ΔS the scattering term, ΔL the
leakage term, ΔDB 2 the pseudo leakage term. These are given by
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