JAEA-Conf 2011-002 - 日本原子力研究開発機構
JAEA-Conf 2011-002 - 日本原子力研究開発機構
JAEA-Conf 2011-002 - 日本原子力研究開発機構
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2. Foundation of sensitivity analyses<br />
In the present study, only criticality k is treated as an integral parameter. Sensitivity<br />
coefficients of k to the nuclear data ,<br />
k<br />
S , can be easily calculated by the first order<br />
perturbation theory with forward and adjoint neutron fluxes. Usually<br />
k<br />
S is interpreted as a<br />
relative change in k due to a relative change in , and is defined as dk k<br />
d S k . This<br />
definition is however inappropriate to describe sensitivities to higher order Legendre coefficients<br />
of scattering matrices l a since a l can take both positive and negative values, and a value close<br />
to zero. Thus the definition of sensitivity coefficients is modified as dk k<br />
d<br />
<br />
S k in the<br />
present study.<br />
The so-called library effect is calculated as follows. Let us consider two multi-group libraries,<br />
LIB1 and LIB2. Here criticalities calculated with these two libraries are written as<br />
LIB2<br />
k . A difference in these criticalities<br />
coefficients of elastic scattering matrices are calculated as<br />
<br />
k,<br />
LIB1<br />
k <br />
S<br />
l , g<br />
g '<br />
n l1 g g'<br />
<br />
LIB1<br />
k and<br />
LIB 2 LIB1<br />
k k k due to differences in Legendre<br />
LIB2<br />
LIB1<br />
a a <br />
l,<br />
gg<br />
' <br />
l,<br />
gg<br />
'<br />
<br />
LIB1<br />
0,<br />
gg<br />
'<br />
, (1)<br />
where n denotes nuclides, l denotes the Legendre order, g and g ' denote energy groups,<br />
respectively. This k corresponds to the library effect of higher order Legendre coefficients.<br />
Usually, higher order Legendre components of scattering matrices l, g<br />
g ' are stored in<br />
multi-group cross section libraries. Thus Legendre coefficients of scattering matrices a '<br />
l,<br />
g g<br />
are derived from scattering matrices stored in multi-group libraries as al , g<br />
g ' l,<br />
g<br />
g ' 0,<br />
g<br />
g '<br />
<br />
.<br />
Note that infinite dilution cross sections are used for the present library effect calculations as<br />
usual.<br />
If we focus on a difference in Legendre components (cross sections), not in Legendre coefficients,<br />
of scattering matrices, a library effect is calculated with the following equation:<br />
<br />
k , LIB1<br />
k <br />
S<br />
l , g g<br />
'<br />
n l1 g g'<br />
<strong>JAEA</strong>-<strong>Conf</strong> <strong>2011</strong>-<strong>002</strong><br />
LIB2<br />
LIB2<br />
LIB1<br />
LIB1<br />
a a <br />
l,<br />
g<br />
g '<br />
0,<br />
g<br />
g '<br />
l,<br />
g<br />
g '<br />
0,<br />
g<br />
g '<br />
3. Numerical procedure<br />
The following are fast neutron systems for which sensitivity analyses are carried out in the<br />
present study. The specifications of these systems are derived from the ICSBEP handbook [1]:<br />
- HEU-MET-FAST-001 (Godiva): a bare sphere of highly enriched uranium.<br />
<br />
.
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